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1 Optimization and Allocation

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

September 5, 2007

Lecture 1

Overview: Themes, Types of Markets, Economic

Measurement, Economic Analysis

Microeconomics is a branch of economics that studies how individuals and firms make decisions to allocate limited resources, typically in markets where goods or services are being bought and sold.

Outline 1. Chap 1: Optimization and Allocation 2. Chap 1: Definition and Various Type of Markets 3. Chap 1: Economic Measurement 4. Chap 1: Economic Analysis

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Optimization and Allocation

Consumer theory. Maximize preference (with limited income or time) Producer theory. Maximize profit (with limited capital)

2

Definition and Various Type of Markets

Market. A place where buyers and sellers come together to exchange some product or good.

Product and Factor Markets Market Product Market Factor Market

Buyers individuals firms

Sellers firms individuals

Table 1: Product and Factor Markets.

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3 Economic Measurement

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In a factor market, buyers are firms who need to hire workers and borrow money for capital expenditure, and sellers are individuals who provide labor and save money in banks.

Types of Markets Based on Influence on Price Market Type

Competitive

Monopolistic

Oligopoly

Monopoly

Monopsony Oligopsony

Products homogeneous heterogeneous

Sellers many many a few one many many

Buyers many many many many one

a few

Table 2: Types of Markets Based on Influence on Price.

Table 2 shows different markets based on product differentiation and influ­ ence on price. Influence on price increases in moving from Competitive markets to Monopoly.

3

Economic Measurement

Flow and Stock Variables Stock variables. Not measured with respect to time. e.g. price, wealth, in­ ventories. Flow variables. Measured per some unit of time. e.g. production, consump­ tion, income. Two additional flow variables: Expenditure. EXPENDITURE = PRICE × CONSUMPTION. Revenue. REVENUE = PRICE × PRODUCTION.

Prices Nominal price. The absolute or current dollar price of a good or service when it is sold. Real price. The price relative to an aggregate measure of prices or constant dollar price. It also measures prices relative to others. Price after adjust­ ment for inflation. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


4 Economic Analysis

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CPI(Consumer Price Index). Total spending on a market basket of goods. Formula of inflation rate: (Gross) Inflation rate =

CPI (current year) . CPI (base year)

Formula of real price: Real price =

Nominal price (current year) , Inflation rate (base year to current year)

or Real price =

Nominal price (current year) . CPI(current)/CPI(base)

Example. For instance, the average tuition of college: Year 1970 1990 2002

Nominal Price 2,530 12,018 18,273

CPI 38.8 130.7 181.0

Real Price (base year 1970) 2,530 3,569 3,917

Table 3: Average Tuition of College 1970 to 2002. Notice that from 1970 to 2002 nominal price increases by 7 times but real price increases by 1.5 times.

4

Economic Analysis

Positive analysis. Study the relationship of cause and effect (Questions that deal with explanation and prediction). Normative analysis. Analysis examining questions of what ought to be (Of­ ten supplemented by value judgments).

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1 Demand and Supply Curves

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

September 7, 2007

Lecture 2

The Basics of Supply and Demand

MARKET

⎧ ⎫ ⎪ ⎪ BUYERS =⇒ DEMAND ⎪ ⎪ ⎨ ⎬ ⎪ ⎪ ⎩

SELLERS =⇒ SUPPLY

EQUILIBRIUM

⎪ ⎪ ⎭

Outline 1. Chap 2: Demand and Supply Curves 2. Chap 2: Equilibrium in the Market 3. Chap 2: Government Interventions

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Demand and Supply Curves

Quantity Demanded and Quantity Supplied QD (Quantity demanded). Depends on price. QD = D(P ).

(1.1)

QS (Quantity supplied). Depends on price. QS = D(P ). Notes:

(1.2)

1. Market demand/supply is the sum of individual demands/supplies. 2. Assume individuals are price takers who cannot affect price.

Demand and Supply Curves From Equations (1.1) and (1.2), draw demand curves and supply curves as follows: Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


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Figure 1: Supply curve. Price higher, Figure 2: Demand curve. Price quantity supplied more. higher, quantity demanded less.

Figure 3: Shift in supply curve.

Figure 4: Shift in demand curve.

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2 Equilibrium in the Market

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Supply curve See Figure 1 and Figure 3: 1. Change in price causes change in quantity supplied, on the graph, there is movement along the curve accordingly. 2. Change in something other than price causes change in supply, on the graph, the supply curve shifts. Example. Production cost falls → supply curve S shifts to S’ (See Fig­ ure 3). Demand curve See Figure 2 and Figure 4: 1. Change in price causes change in quantity demanded, on the graph, there is movement along the curve accordingly. 2. Change in something other than price causes change in demand, on the graph, the demand curve shifts. Example. People’s income increases → demand curve D shifts to D’ (Fig­ ure 4).

Substitutes and Complements Substitutes. Increase in the price leads to an increase in the demand of the other. Example (Italian and French bread). Price of Italian bread increases, de­ mand of French bread increases. Complements. Increase in the price leads to a decrease in the demand of the other. Example (Pasta and pasta sauce). Price of pasta increases, demand of pasta sauce decreases.

2

Equilibrium in the Market

Equilibrium state: • No shortage • No surplus • Equilibrium price clears the market. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


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Figure 5: Demand and Supply curves. Equilibrium state. Refer to Figure 5. (P0 , Q0 ) is the equilibrium state, which is the intersection point of the demand and supply curves.

Price

Supply =⇒ Change in equilibrium

Change in Demand

Quantity

Surplus and Shortage Surplus. Price P1 is higher than P0 and will fall down. Shortage. Price P2 is lower than P0 and will raise up.

Comparative Static Analysis and Comparative Dynamics Comparative static analysis. Compares the new and old equilibrium and not the actual path through time of the change. Comparative dynamic analysis. Traces out the path over time. This course will cover primarily Comparative Static analysis. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


3 Government Interventions

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Figure 6: Decrease in raw material prices. Examples Example (Decrease in raw material prices). Raw material prices �→ Supply �→ Price � and Quantity � (Figure 6). Example (Increase in income). Income �→ Demand�→ Price � and Quantity � (Figure 7). Dual shifts in supply and demand When supply and demand change simultaneously, the impact on the equilibrium price and quantity is determined by the size and direction of the changes and the slope of two curves.

3

Government Interventions

How can government help sellers? Discuss two methods.

Problem Description Assume that QD = 10 − P, QS = −2 + P. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


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Figure 7: Increse in income. The original equilibrium point is P0 = 6, QD0 = QS0 = 4, and the revenue before government intervention is: REV EN U E = P0 × QD0 = 6 × 4 = 24. The government’s goal: increase sellers’ revenue.

Price Floor The first method: set a price floor. Assume the lowest price is set to be 8, thus: QD = 2, QS = 6. The revenue after using method 1 is: REVENUE = P × QD = 8 × 2 = 16 < 24. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


3 Government Interventions

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Subsidy The second method: provide subsidy. Customers get a 2 unit price refund per unit quantity bought, thus the quantity demanded changes: QD = 10 − (P − 2) = 12 − P. The new intersection point is P = 7, QD = QS = 5. The revenue after using method 2 is: REVENUE = P × QD = 7 × 5 = 35 > 24. For this example, providing subsidies achieves the government’s goal to increase seller’s revenue, but setting price floor does not and even makes the revenue less.

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1 Price Elasticity of Demand

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

September 10, 2007

Lecture 3

Elasticities of Demand Elasticity. Elasticity measures how one variable responds to a change in an­ other variable, namely the percentage change in one variable resulting a one percentage change in another variable. (The percentage change is independent of units.)

Outline 1. Chap 2: Price Elasticity of Demand 2. Chap 2: Income Elasticity of Demand 3. Chap 2: Cross Price Elasticity of Demand 4. Chap 2: Comparison of Elasticity Over Short Run and Long Run

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Price Elasticity of Demand

Price elasticity of demand. Price elasticity of demand measures the per­ centage change in quantity demanded resulting from one percentage change in price. D EE

%△QP = = %△P

△Q Q △P P

.

Example Calculation Figure 1 shows a demand curve: Q(P ) = 8 − 2P. When the price changes from 2 to 1, the price elasticity of demand is: EPD |p=2→1 =

ΔQ Q ΔP P

=

2 4 −1 2

= −1.

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1 Price Elasticity of Demand

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Figure 1: Price Elasticity of Demand.

If the direction of change is opposite, from 1 to 2, then the price elasticity of demand is: ΔQ −2 1 Q D EP |P =1→2 = ΔP = 61 = − . 3 1 P The two quantities are different. To solve this conflict, consider small changes in P and Q, and define: dQ P dQ Q EPD = dP = . Q dP P Thus, at the point P = 2, the price elasticity of demand is: EPD |P =2 =

P dQ 2 = × (−2) = −1. Q dP 4

Properties of Price Elasticity of Demand 1. Price elasticity of demand is usually a negative number. 2. |EP | > 1 indicates that the good is price elastic, perhaps because the good has many substitutes; |EP | < 1 indicates that the good is price inelastic, perhaps because the good has few substitutes. 3. Given a linear demand curve, EP is not a constant along the curve. For example, for curve in Figure 1, EP = −∞ at top portion, but zero at bottom portion. 4. Discuss two extreme situations: |EP | = 0, quantity independent of price Figure 2 and |EP | = ∞, quantity very sensitive to price. See Figure 3. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Income Elasticity of Demand

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Figure 2: Extreme demand elas- Figure 3: Extreme demand elas­ ticity. |EP | = 0, quantity inde- ticity. |EP | = −∞, quantity very pendent of price. sensitive to price. 5. The constant elasticity demand function is Q = aP b , since EP =

dQ P P aP b = abP b−1 = b = b. dP Q Q Q

Refer to Figure 4. 6. How do total consumer expenditure change when the price of a good changes? dExp d(P QD (P )) dQ = =Q+P = Q(1 + EP ) = Q(1 − |EP |). dP dP dP • If |EP | > 1, total expenditure decreases when price increases; • If |EP | < 1, total expenditure increases when price increases. Example (Cell phone). People need to do business in the morning, so EP is low, so cell phone companies increase the rate while customers will expend more; but EP is high in the evening since people do not have to talk, so cell phone companies lower the rate to encourage customer expenditure.

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Income Elasticity of Demand

Income elasticity of demand. Income elasticity of demand measures the per­ centage change in quantity demanded resulting from one percentage change in income. Similarly, dQ I dQ Q EI = dI = . Q dI I The income elasticity of demand is usually positive. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


3 Cross Price Elasticity of Demand

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Figure 4: Constant Demand Elasticity.

3 Cross Price Elasticity of Demand Cross price elasticity of demand. Cross price elasticity of demand measures the percentage change in quantity demanded of a good (x) resulting from one percentage change in price of another good (y). EQxP y =

dQx Qx dPy Py

=

Py dQx . Qx dPy

â&#x20AC;˘ If y is a substitute of x, the cross price elasticity of demand is positive. â&#x20AC;˘ If y is a complement of x, the cross price elasticity of demand is negative.

4 Comparison Between Elasticity Over Short Run and Long Run Is demand more elastic in the long run or short run? Consumption goods. For consumption goods, the demand is more elastic in the long run. Because people need goods for daily life and buy them constantly, the short run demand is inelastic. Faced with high prices in the long run, they may change habits or ďŹ nd more substitutes.

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4 Comparison Between Elasticity Over Short Run and Long Run

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Durable goods. For durable goods, the demand is more elastic in the short run. Consider cars. If price of of cars increase, in the short run people might use their current cars longer. In the long run, though, people have to replace their cars.

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1 Price Elasticity of Supply

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

September 12, 2007

Lecture 4

Price Elasticity of Supply; Consumer

Preferences

Outline 1. Chap 2: Elasticity - Price Elasticity of Supply 2. Chap 3: Consumer Behavior - Consumer Preferences

1

Price Elasticity of Supply

Price elasticity of supply. The percentage change in quantity supplied re­ sulting from one percentage change in price.

EPS =

dQS QS dP P

=

P dQS . QS dP

In the short run, if price increases, firms will want to produce more but cannot hire workers and buy machines immediately, thus the supply is less elastic. In contrast, supply is more elastic in the long run. Example (Example in Elasticities of Demand). Assume the quantity demanded is QD = 14 − 3P + I + 2PS − PC . • P - Price • I - Income • PS - Price of substitute • PC - Price of complement Calculate EPD , EI , EQPS and EQPC when P = 1, I = 10, PS = 2 and PC = 1. Solution: Given the values of variables, the quantity demanded is: QD = 14 − 3 × 1 + 10 + 2 × 2 − 1 = 24.

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2 Consumer Preferences

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The elasticities are EPD =

P dQD 1 1 = × (−3) = − , QD dP 24 8

EI =

I dQ 10 5

= ×1= , Q dI 24 12

EQPS = EQPC =

2

PS dQ 2 1 = ×2= , Q dPS 24 6

PC dQ 1 1 = × (−1) = − . Q dPC 24 24

Consumer Preferences Consumer behavior

Consumer preferences Budget constraints

=⇒

• What amount and types of goods will be purchased. • Origin of demand, how to decide demand.

Topics 1. Preference 2. Indifference Curve, Marginal Rate of Substitution (MRS) 3. Utility Functions

Preference Notation • A ≻ B: A is preferred to B. • A∼ B: A is indifferent to B. Basic assumptions for preferences • Completeness - can rank any basket of goods.

(always possible to decide preference or indifference)

• Transtivity - A≻B and B≻C implies A≻ C. This assumption seems obvious, but can have contradiction (see example below).

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2 Consumer Preferences

Good A Good B Good C

Property I 3 2 1

3

Property II 1 3 2

Property III 2 1 3

Table 1: Example of contradiction of transitivity. Example (A contradiction of transtivity). Chart below lists 3 goods and 3 properties, assume that people will prefer one to another if 2 properties are better. Table 1. Actually A ≻ B, B ≻ C and C ≻ A - this loop contradicts the assumption. • Non-satiation - more is better. (Monotonicity) Assume we discuss goods, since in general, more is not always better. • Convexity - given two indifferent bundles, always prefer the average to each of them. In Figure 1, the average point C is more preferred to A or B.

Figure 1: Convexity of indifference curve.

Indifference Curve, Marginal Rate of Substitution (MRS) Properties of indifference curves • Downward sloping: if not, non-satiation violated. Refer to Figure 1. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Consumer Preferences

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Figure 2: Compare the Shapes of Indifference Curve.

• Cannot cross: if not, non-satiation and transitivity cannot be satisfied simultaneously. In Figure 1, assume there is another indifference curve through A and D. A ∼ B, A ∼ D =⇒ B ∼ D. However, B≻D in this figure. Contradiction exists. • Shape: describes how willing one is to substitute one good for another. See Figure 2. Marginal rate of substitution (MRS) Marginal rate of substitution (MRS). How many units of Y one is willing to give up in order to get one more unit of X. −Δy −dy = Δx dx

People prefer a balanced basket of goods.

• MRS decreasing. • Preferred set is convex. • The left one in Figure 2 makes more sense in the real world. Perfect substitution. MRS is constant.

Perfect complements. Indifference curves are shaped as right angles.

Example (Perfect complements). Buying shoes. People need both the left one and the right one.

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2 Consumer Preferences

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Figure 3: Perfect Substitution and Perfect Complements.

Figure 4: IndiďŹ&#x20AC;erence Curve with Utility Function u(x, y) = xy.

Utility Functions Utility function. Assigns a level of utility to each basket of consumption. Example (A sample utility function). u(x, y) = xy. For example, (5,5) is indiďŹ&#x20AC;erent to (25,1) and (1,25). Ordinal utility function. Ranks the preferences, but does not indicate how much one is preferred to another. Cardinal utility function. Describes the extent to which one of the bundles is preferred to another. Only the ordinal utility function is required in this course.

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1 Utility Function, Deriving MRS

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

September 14, 2007

Lecture 5

Deriving MRS from Utility Function, Budget

Constraints, and Interior Solution of

Optimization

Outline 1. Chap 3: Utility Function, Deriving MRS 2. Chap 3: Budget Constraint 3. Chap 3: Optimization: Interior Solution

1

Utility Function, Deriving MRS

Examples of utility: Example (Perfect substitutes). U (x, y) = ax + by.

Example (Perfect complements). U (x, y) = min{ax, by}.

Example (Cobb-Douglas Function). U (x, y) = Axb y c .

Example (One good is bad). U (x, y) = −ax + by. An important thing is to derive MRS. M RS = −

dy = |Slope of Indifference Curve|. dx

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1 Utility Function, Deriving MRS

2

10 9 8 7 U(x,y)=ax+by=Const

y

6 5 4 3 2 1 0

0

2

4

6

8

10

x

Figure 1: Utility Function of Perfect Substitutes

10 9 8 7

y

6 5 U(x,y)=min{ax,by}=Const 4 3 2 1 0

0

2

4

6

8

10

x

Figure 2: Utility Function of Perfect Complements

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1 Utility Function, Deriving MRS

3

10

8

y

6 a b

U(x,y)=Ax y =Const 4

2

0

0

2

4

6

8

10

x

Figure 3: Cobb-Douglas Utility Function

10

9

8

7

y

6

5

U(x,y)=â&#x2C6;&#x2019;ax+by=Const

4

3

2

1

0

0

2

4

6

8

10

x

Figure 4: Utility Function of the Situation That One Good Is Bad

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2 Budget Constraint

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Because utility is constant along the indifference curve, u = (x, y(x)) = C, =⇒ ∂u ∂u dy + = 0, =⇒ ∂x ∂y dx dy = dx

∂u ∂x ∂u ∂y

.

M RS =

∂u ∂x ∂u ∂y

.

− Thus,

Example (Sample utility function). u(x, y) = xy 2 . Two ways to derive MRS: • Along the indifference curve

xy 2 = C. r c y= . x

Thus,

√ dy c y M RSd = − = 3/2 = . dx 2x 2x • Using the conclusion above M RS =

2

∂u ∂x ∂u ∂y

=

y2 y = . 2xy 2x

Budget Constraint

The problem is about how much goods a person can buy with limited income. Assume: no saving, with income I, only spend money on goods x and y with the price Px and Py . Thus the budget constraint is Px · x + Py · y � I. Suppose Px = 2, Py = 1, I = 8, then 2x + y � 8. The slope of budget line is

dy Px = . dx Py Bundles below the line are affordable. Budget line can shift: −

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2 Budget Constraint

5

10

8

y

6

4

2x+y≤8

2

0

0

2

4

6

8

10

x

Figure 5: Budget Constraint

10

9

8 7 2x+y≤8

y

6 5 4

2x+y≤6

3 2 1 0

0

2

4

6

8

10

x

Figure 6: Budget Line Shifts Because of Change in Income

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3 Optimization: Interior Solution

6

10 9 8 7 2x+y≤8

y

6 5 4

x+y≤4

3 2 1 0

0

2

4

6

8

10

x

Figure 7: Budget Line Rotates Because of Change in Price • Change in Income Assume I ′ = 6, then 2x + y = 6. The budget line shifts right which means more income makes the affordable region larger. • Change in Price Assume Px′ = 2, then 2x + 2y = 8. The budget line changes which means lower price makes the affordable region larger.

3

Optimization: Interior Solution

Now the consumer’s problem is: how to be as happy as possible with limited income. We can simplify the problem into language of mathematics:    xPx + yPy � I  x�0 max U (x, y) subject to . x,y   y�0

Since the preference has non-satiation property, only (x, y) on the budget line can be the solution. Therefore, we can simplify the inequality to an equality: xPx + yPy = I. First, consider the case where the solution is interior, that is, x > 0 and y > 0. Example solutions: • Method 1

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3 Optimization: Interior Solution

7

10 9 8 7

y

6 5 U(x,y)=Const

4 3 2

P x+P y=I x

y

1 0

2

4

6

8

10

x

Figure 8: Interior Solution to Consumer’s Problem From Figure 8, the utility function reaches its maximum when the indif­ ferent curve and constraint line are tangent, namely: Px ∂u/∂x ux = M RS = = . Py ∂u/∂y uy – If

Px ux > , Py uy

then one should consume more y, less x. – If

Px ux < , Py uy

then one should consume more x, less y. Intuition behind

Px Py

= M RS:

Px Py

is the market price of x in terms of y, and MRS is the price of x in terms of y valued by the individual. If Px /Py > M RS, x is relatively expensive for the individual, and hence he should consume more y. On the other hand, if Px /Py < M RS, x is relatively cheap for the individual, and hence he should consume more x. • Method 2: Use Lagrange Multipliers L(x, y, λ) = u(x, y) − λ(xPx + yPy − I).

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3 Optimization: Interior Solution

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In order to maximize u, the following first order conditions must be satis­ fied: ∂L = 0 =⇒ ∂x ∂L = 0 =⇒ ∂y

ux = λ, Px uy = λ, Py

∂L = 0 =⇒ xPx + yPy − I = 0. ∂λ Thus we have

Px ux = . Py uy

• Method 3 Since xPx + yPy + I = 0,

y=

I − xPx

. Py

Then the problem can be written as max u(x, y) = u(x, x,y

I − xPx ). Py

At the maximum, the following first order condition must be satisfied: ux + uy (

∂y Px ) = ux + uy (− ) = 0. ∂x Py =⇒ Px ux = . Py uy

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1 Corner Solution of Optimization

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

September 17, 2007

Lecture 6

Optimization, Revealed Preference, and

Deriving Individual Demand

Outline

1. Chap 3: Corner Solution of Optimization 2. Chap 3: Revealed Preference 3. Chap 4: Deriving Individual Demand, Engle Curve

1

Corner Solution of Optimization

When we have an interior solution, Px Ux = Py Uy must be satisfied. However, sometimes a consumer gets highest utility level when x = 0 or y = 0. If that’s the case, we have corner solutions, and Px Ux �= , Py Uy as shown in Figure 1. In Figure 1, because people cannot consume negative amounts of goods (bundle A), their best choice is to consume bundle B, so the quantity of y consumed is zero. Conditions for corner solutions: • •

M RS =

Ux Px > when y = 0. Uy Py

M RS =

Ux Px < when x = 0. Uy Py

Example (An example of consumer’s problem). The parameters are Px = 1, Py = 1, Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


1 Corner Solution of Optimization

Figure 1: Corner Solution to Consumerâ&#x20AC;&#x2122;s Problem.

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2


2 Revealed Preference

3

I = 2. The utility function is

√ U (x, y) = x + 2 y.

The budget constraint is x + y = 2. According to the condition for an interior solution: Px Ux = . Py Uy =⇒

1 1 = 1 . √ 1 y

=⇒

y = 1 =⇒ x = 1.

If the price y changes to 1: Py = 1, then the solution is y = 4 =⇒ x = −3 < 0, which is impossible. Then we have the corner solution: x = 0, y = 2. x = 0 since consumer wants to consume as little as possible.

2

Revealed Preference

In the former chapters, we discussed how to decide optimal consumption from utility function and budget constraint: Utility

Function =⇒ Optimal Consumption

Budget Constraint And now we discuss how to know consumer’s preference from budget constraint and consumption: Budget Constraint =⇒ Preference Consumption

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3 Deriving Individual Demand, Engle Curve

4

10

9

8

7

6

y

X: 1.929 Y: 5.142

D

5 X: 1.478 Y: 3.761

4

C A

3

X: 4.751 Y: 2.124

2 X: 3.949 Y: 1.101

1

0

B

0

1

2

3

4

5 x

6

7

8

9

10

Figure 2: A Contradiction of Preference. A and B are the Choices. Example (Revealed preference). In Figure 2, two budget constraint lines inter­ sect. Assume one person’s choices are A and B respectively. Then we have A � C,

B � D.

And Figure 2 obviously shows that C ≻ B,

D ≻ A.

Thus, A � C ≻ B � D ≻ A, which is a contradiction, which means utility does not optimized and the choice is not rational.

3

Deriving Individual Demand, Engle Curve

Use the following utility function again: √ U (x, y) = x + 2 y, with a budget constraint: Px x + Py y = I.

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3 Deriving Individual Demand, Engle Curve

When I�

5

Px2 , Py

we have an interior solution. M RS = Px /Py . Thus, x=

I Px − , Px Py

y=

When I�

Px Py

�2

.

Px2 , Py

we have a corner solution. x = 0, y=

I . Py

• Figure 3 shows a demand function of y and Py as an example. (Assume that I, x and Px are held constant.) • Engle Curve describes the relation between quantity and income. Figure 4 shows the relation between x and income, and Figure 5 shows that between y and income. Normal good. Quantity demanded of good increases with income. Inferior good. Quantity demanded of good decreases with income. Substitutes. Increase in price of one leads to an increase in quantity demanded of the other. Complements. Increase in price of one leads to an decrease in quantity demanded of the other. For this problem, P2

• if I < Pxy , x and y are neither substitutes nor complements, and x is a normal good. • if I �

Px2 Py ,

x and y are substitutes, and y is a normal good.

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3 Deriving Individual Demand, Engle Curve

Figure 3: Demand Function for Goods â&#x20AC;&#x2DC;yâ&#x20AC;&#x2122;.

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6


3 Deriving Individual Demand, Engle Curve

7

10

9

8

7

x

6

5

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2

1

P2/P x

0

0

1

2

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y

5 I

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8

9

10

Figure 4: The Relation between Income and Quantity Demanded of ‘x’. Engle curve of x.

10

9

8

7

y

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5

4

3

2

1 P2/P x

0

0

1

2

3

4

5

I

y

6

7

8

9

10

Figure 5: The Relation between Income and Quantity Demanded of ‘y’. Engle curve of y.

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1 Substitution Effect, Income Effect, Giffen Goods

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

September 19, 2007

Lecture 7

Substitution and Income Effect, Individual and

Market Demand, Consumer Surplus

Outline 1. Chap 4: Substitution Effect, Income Effect, Giffen Goods 2. Chap 4: From Individual Demand to Market Demand 3. Chap 4: Consumer Surplus

1

Substitution Effect, Income Effect, Giffen Goods

Substitution and Income Effects The impact of price change on quantity demanded are divided into two effects: Substitution effect. Substitution effect is the change in an item’s consump­ tion associated with a change in the item’s price with the utility level held constant. Income effect. Income effect is a change in an item’s consumption associated with a change in purchasing power with the price held constant. Figure 1 shows the two effects: L is the old budget line. Px decreases, and hence the new budget line is L′ . A is the optimal consumption before price change, and C is the optimal consumption after price change. L′′ is a line that has the same slope as L′ and is tangent with the green indifference curve that passes through A, and B is the tangent point. • The change from A to B is because of the substitution effect; • The change from B to C is because of the income effect. So the total effect is point A moving to C.

Inferior Good and Giffen Good Now consider different positions of C (Figure 1): • The income effect is B changing to C. In this case, an increase in income causes an increase in the demand of x. x is a normal good. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


1 Substitution Effect, Income Effect, Giffen Goods

Figure 1: Substitution Effect and Income Effect.

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2


1 Substitution Effect, Income Effect, Giffen Goods

3

• The income effect is B changing to C ′ or C ′′ . In these cases, an increase in income causes a decrease in the demand of x. x is an inferior good; • If the total effect is A changing to C ′′ , such that a decrease in price causes a decrease in the demand, we call x is a Giffen good.

Normal good Inferior good

Price increases substitution effect income effect substitution effect income effect

quantity increases quantity increases quantity increases quantity decreases

Table 1: Normal Good and Inferior Good In Table 1, if x is a normal good, both substitution and income effects increase its quantity; if x is an inferior good, discuss as follows: 1. substitution effect > income effect

→ quantity increases

2. substitution effect < income effect → quantity decreases. This unusual good is called a Giffen good. A Giffen good must be an inferior good, but an inferior good is not necessarily a Giffen good. Giffen good. Good with an upward demand curve. (Figure 2) Example (Giffen Good Example: Irish Potato Famine). People consumed lots of potato but little meat (and other food) since meat was more expensive. Price of potato rose. People had less money to consume meat, so they ate more potatoes instead of meat.

An Example of Substitution Effects and Income Effects Utility function Figure 3:

√ U (x, y) = x + 2 y.

Parameters: Px = 1, Py = 1, I = 5. The optimal solution is: x = 4, y = 1.

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1 Substitution Effect, Income Effect, Giffen Goods

4

6

5.5

5

4.5

P

4

3.5

3

2.5

2

1.5

1

0

0.5

1

1.5

2 Q

2.5

3

3.5

4

D

Figure 2: Demand Curve of Giffen Good. i.e. the solution is at point A: (4, 1).

If price of x changes to 2, Px′ = 2, then the new optimal solution is:

x=

1 , 2

y = 4. ( 12 ,4).

i.e. the solution is at point C: Try to find out the substitution effect, i.e. the change from A to B.

At B, the slope of the indifference curve equals the slope of the new budget

constraint.

Thus,

1 P′ 2 M RS = 1 = x′ = . √ P 1 y y =⇒ y = 4. On the other hand, U (x, y) = x + 2 ×

√ √ 4 = 4 + 2 × 1.

=⇒ x = 2. Thus, point B is at (2,4). Decomposition of the two effects: Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 From Individual Demand to Market Demand

5

5

4.5

4

C (1/2,4)

B (2,4)

3.5

y

3

2.5

2

1.5

A(4,1)

1

0.5

0

0

0.5

1

1.5

2

2.5 x

3

3.5

4

4.5

5

Figure 3: Showing the Substitution effect and Income Effect. • Substitution effect (A to B) (4,1) =⇒ (2,4). • Income effect (B to C) (2,4) =⇒ ( 12 ,4).

2

From Individual Demand to Market Demand

Assume in a market there are two individuals A and B. And their demand functions are: QA = 1 − P, 1 QB = 1 − P. 2 When P < 1, both individuals consume, and the market demand is the sum of the individual demands: 2 Q = QA + QB = 2 − P. 3 However, if P is larger than 1, only B consumes, so the market demand equals the demand of B. Thus, the market demand function is � 2 − 32 P if P � 1 Q= . 1 − 12 P if P > 1 Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


3 Consumer Surplus

6

This is shown in Figure 4.

3

Consumer Surplus

Willingness to Pay. The sum of the ‘values’ of each of the units that con­ sumers consume. Consumer Surplus. The difference between Willingness to Pay and the actual Expenditure. Example. Figure 5 shows the demand curve of a good. Assume now the price is 15, then only the highest 6 individuals consume: W ILLIN GN ESS T O P AY = 20 + 19 + 18 + 17 + 16 + 15 = 105. On the other hand, the expenditure is EXP EN DIT U RE = 6 × 15 = 90. Therefore, CON SU M ER SU RP LU S = 105 − 90 = 15.

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3 Consumer Surplus

Figure 4: Derived Market Demand from Individual Demands.

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3 Consumer Surplus

8

25

P

20

15

10

5

0

2

4

6

8

10 Q

12

14

16

18

20

Figure 5: Demand Curve for a Good. Used in consumer surplus calculation.

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1 Irish Potato Famine

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

September 21, 2007

Lecture 8

Irish Potato Famine, Network Externalities and

Uncertainty

Outline 1. Chap 4: Irish Potato Famine 2. Chap 4: Network Externalities 3. Chap 5: Uncertainty

1

Irish Potato Famine

Typical Giffen good. In Year 1845-1849, people consumed more potatoes when the price increased. (Figure 1)

2

Network Externalities

Network externality. One person’s demand depends on the demands of other people. • [Bandwagon effect (Figure 2)] Positive network externality. When more people buy, you will buy more.

Example. iPod: buy to be in style.

– Market demand more elastic than real demand curve. – Seller sets lower price. Example. Operating system: more software available. Example. Internet telephone. • [Snob effect (Figure 3)] Negative network externality. When others buy, you will not buy. – Market demand more inelastic than real demand curve. – Seller sets Higher price. Example. Designer clothes: want to be special.

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3 Uncertainty

2

10

9 Original Budget Constraint 8 A−>B: Substitution Effect B−>C: Income Effect

7

Potato

6

5

4

C

3

A 2

B New Budget Constraint

1

0

0

0.5

1

1.5

2

2.5 Other Food

3

3.5

4

4.5

5

Figure 1: Irish Potato Famine: Price Higher, Consume More

3

Uncertainty

An Outline in Uncertainty • Preference, Decision • Expected Value / Variability, Risk Standard Deviation • Expected Utility To measure risk we must know: • All of the possible outcomes. • The probability that each outcome will occur, the sum of the proba­ bilities that each outcome will occur = 1. Example. Probability of Weather • Sunny 70%. • Rainy 5%. • Cloudy 25%. The sum of all the probabilities is 100%. Objective probability. Based on observed frequency of past events.

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3 Uncertainty

3

Figure 2: Bandwagon EďŹ&#x20AC;ect: Positive Network Externalities

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3 Uncertainty

4

Figure 3: Snob EďŹ&#x20AC;ect: Negative Network Externalities

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3 Uncertainty

5

Subjective probability. Based on perception, theory and understanding of outcomes. Measures to characterize payoffs and degree of risk.

Job 1 Job 2

Example (Job). Outcome 1 Outcome 2 $2000 with probability 50% $1000 with probability 50% $1510 with probability 99% $510 with probability 1% Table 1: Compare Two Jobs, Each has Two Outcomes

Expected value. E(x) = p1 x1 + p2 x2 + ... + pn xn , where x is a random variable, which has realizations x1 , x2 , ..., xn with probability p1 , p2 , ..., pn respectively. Discuss the example. Expected val­ ues of salary from job 1 and 2 are: E(job1) = 0.50 × 2000 + 0.50 × 1000 = 1500. E(job2) = 0.99 × 1510 + 0.01 × 510 = 1500. Since E(job1) = E(job2), we do not know which job is better. Standard deviation. � σ(x) = p1 [x1 − E(x)]2 + p2 [x2 − E(x)]2 + ... + pn [xn − E(x)]2 . We can consider the risks of those jobs from standard deviation: � σ1 = 0.50 × (2000 − 1500)2 + 0.50 × (1000 − 1500)2 = 500, � σ2 = 0.99 × (1510 − 1500)2 + 0.01 × (510 − 1500)2 = 99.5. Since σ1 > σ2 , for less risk, we will choose job 2. Expected utility. E[u(x)] = p1 u(x1 ) + p2 u(x2 ) + ... + pn u(xn ).

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1 Preference Toward Risk

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

September 26, 2007

Lecture 9

Preference Toward Risk, Risk Premium,

Indifference Curves, and Reducing Risk

Outline 1. Chap 5: Preference Toward Risk 2. Chap 5: Risk Premium 3. Chap 5: Indifference Curve 4. Chap 5: Reducing Risk: Diversification

1

Preference Toward Risk - Risk Averse / Neu­ tral / Seeking (Loving)

Three different kinds of behaviors:

Risk Averse (Figure 1) • Facing two payoffs with the same expected value, prefer the less risky one. • Diminishing marginal utility of income. • Relation between the utility of expected value and expected utility u(E(x)) > E(u(x)). Example. u(x) = ln x.

Risk Neutral (Figure 2) • Facing two payoffs with the same expected value, feel indifferent. • Linear marginal utility of income. • Relation between the utility of expected value and expected utility u(E(x)) = E(u(x)). Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Risk Premium

2

3

2.5

u(x)

2

1.5

1

0.5

0

0

1

2

3

4

5 x

6

7

8

9

10

Figure 1: The Utility Function of Risk Averse. Example. u(x) = x.

Risk Seeking (Figure 3) • Facing two payoffs with the same expected value, prefer the riskier one. • Increasing marginal utility of income. • Relation between the utility of expected value and expected utility u(E(x)) < E(u(x)). Example. u(x) = x2 .

2

Risk Premium

Risk premium. The maximum amount of money that a risk-averse person would pay to avoid taking a risk. Example (Job Choice). Assume that a risk-averse person whose utility function corresponds with the curve in Figure 4 has two possible incomes.

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2 Risk Premium

3

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u(x)

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Figure 2: The Utility Function of Risk Neutral.

70

60

50

u(x)

40

30

20

10

0

0

1

2

3

4

5 x

6

7

8

9

10

Figure 3: The Utility Function of Risk Seeking.

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3 Indifference Curve between Expected Value and Standard Deviation

4

20

18

16

14

u(x)

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5

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15

20

25

30

x

Figure 4: Risk Premium: A Utility Function. • His income I might be 10 with probability 0.5 and 30 with probability 0.5. Then the expected value of income I is: E(1) = 10 × 0.5 + 30 × 0.5 = 20, with an expected utility: E(u(I)) = u(10) × 0.5 + u(30) × 0.5 = 10 × 0.5 + 18 × 0.5 = 14. • If we offer him a fixed income I ′ , I ′ = 16, then his expected utility is: E(u(I ′ )) = u(16) × 1 = 14 × 1 = 14. One can see that E(u(I)) = E(u(I ′ )). However, E(I) − E(I ′ ) = 4. This means the person is willing to give up a value of 4 in exchange for a riskless income. Thus, the risk premium is Risk P remium = E(I) − E(I ′ ) = 20 − 16 = 4.

3

Indifference Curve between Expected Value and Standard Deviation

The indifference curve we discussed before is about the quantities of two different goods, now we consider the indifference curve about expected value and standard deviation (Figure 5).

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3 Indifference Curve between Expected Value and Standard Deviation

5

1330

1320

1310

1300

Ex

1290

1280

1270

1260

1250

1240 400

500

600

700 σ

800

900

1000

Figure 5: Indifference Curve between Expected Value and Standard Deviation. Job 1 Job 2

Probability 0.5 900 625

Probability 0.5 1600 2025

Table 1: The Income and Probability of Two Jobs.

Example (Job choice). Suppose one has the following utility function √ u(x) = x and two job choices (see Table 1). Calculate expected utilities: √ √ E(u(x1 )) = 0.5 × 900 + 0.5 × 1600 = 35, √ √ E(u(x2 )) = 0.5 × 625 + 0.5 × 2025 = 35.

Thus, these two jobs give the person the same utility level, i.e. they are on a same indifference curve. In order to plot the indifference curve, we should calculate their expected values and standard deviations. E(x1 ) = 1250 σ(x1 ) = 494 E(x2 ) = 1325 σ(x2 ) = 990 Job 2 has higher expected value of income but it is riskier. (Figure 5) Compare Figure 6 and Figure 7. The former is more risk averse since one must compensate more for more risk. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


3 Indifference Curve between Expected Value and Standard Deviation

6

90

80

70

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Ex

50

40

30

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10

Figure 6: Indifference Curve between Expected Value and Standard Deviation, Larger Slope.

20

18

16

14

Ex

12

10

8

6

4

2

0

0

1

2

3

4

5 σ

6

7

8

9

10

Figure 7: Indifference Curve between Expected Value and Standard Deviation, Smaller Slope.

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4 Reducing Risk: Diversification

4

7

Reducing Risk: Diversification

Diversification. Reducing risk by allocating resources to different activities whose outcomes are not closely related. Example (Selling air conditioner and heater). Suppose that the weather has a probability 0.5 to be hot and 0.5 to be cold. Table 2 shows the company’s profit if all its efforts in selling air conditioners (heaters) and the weather turns out to be hot (cold). Weather Air Conditioner Heater

Hot 30,000 12,000

Cold

12,000

30,000

Table 2: Diversification: Selling Air Conditioners and Heaters.

• If one only sells air conditioners or heaters, E(prof it) = 21, 000, σ(prof it) = 9, 000. • If the company puts half of its efforts in selling air conditioners and half of its efforts in selling heaters, then the profit is always 21,000 no matter the weather is cold or hot. E(prof it) = 21, 000, σ(prof it) = 0. Thus we should choose to sell both to reduce risk.

Example (Example: Stock versus mutual fund). Mutual fund may have

the same return as stock but much less risk.

Example. ”Don’t put all your eggs in one basket.”

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1 Reducing Risk: Insurance

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

September 28, 2007

Lecture 10

Insurance and Production Function Outline 1. Chap 5: Reducing Risk: Insurance 2. Chap 6: Outline of Producer Theory 3. Chap 6: Production Function: Short Run and Long Run

1

Reducing Risk: Insurance

Reducing Risk: • Diversification • Insurance Example (House insurance). Assume that one house has the proba­ bility p to catch fire, with loss l each time, i.e. the owner’s wealth will reduce from y1 to y2 = y1 −l. If the owner pay premium k to buy an insurance which covers the loss l when there is a fire, her wealth will be y3 = y1 − k, for the situations listed (see Table 1).

No Fire Fire

No Insurance y1 y2 = y1 − l

Insurance y3 = y1 − k y3 = y1 − k

Table 1: Wealth of House Owner in Different Situations. Assuming the owner is a risk-averse, the utility function is concave. u′′ (y) < 0

If the expected wealth at both situations is equal, y3 = (1 − p) × y1 + p × y2 . We have

k = p × l.

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1 Reducing Risk: Insurance

Figure 1: The Utility Function of Risk Averse Person.

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2


1 Reducing Risk: Insurance

3

The insurance premium is equal to the expected payout by the in­ surance company, and we say the insurance is actuarially fair. Since the person is risk-averse, u(y3 ) > (1 − p) × u(y1 ) + p × u(y2 ). she will choose to buy insurance. If the insurance is actuarially unfair, k > p × l. Then y3 < (1 − p) × y1 + p × y2 . We do not know if the person wants to buy or not until we get her specific utility function, but it is easy to imagine she may buy insurance if k is close to pl. Now we consider what is the maximum insurance premium that the companies can charge and the costumer is still willing to buy the insurance. In this case, let y3′ be the house owner’s wealth after being charged the maximum premium. Then, (Figure 1) u(y3′ ) = pu(y2 ) + (1 − p)u(y1 ). Thus the maximum insurance premium charged is k ′ = y1 − y3′ = y1 − E(y) + Risk P remium = p × l + Risk P remium So are insurance companies more willing to take risk? If not, why are they willing to sell insurance? The Law of Large Numbers can explain this. Let L be the total loss from n customers, It is a random variable. L The average loss shared by each customer is L n , and E( n ) = n × p. The expected payout for L by the insurance company will be E(L) = n × p × l When n→∞ The probability that the loss shared by each customer is equal to a fixed number pl is almost 1. (Figure 2) L = p × l) →n→∞ 1. n Note that this argument only applies to the situation when customers’

fire accident events are independent.

Example (Illegal parking). Government has two reasonable methods

to punish illegal parking.

– Hire more police, get caught almost for sure but fine is low. – Hire less police, get caught sometimes but the fine is high. The latter might be more effective since people are risk averse abd are afraid to take risk of being fined to park illegally. P robability(

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1 Reducing Risk: Insurance

Figure 2: Distribution of

4

L n

with DiďŹ&#x20AC;erent Customer Numbers.

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2 Outline of Producer Theory

5

2 Outline of Producer Theory • Production Function: Inputs to Outputs • Given Quantity Produced, Choose Inputs to Minimize the Cost • Choose Quantity to Maximize Firm’s Profit The Production Function is q = F (k, L). The two inputs: k: Capital L: Labor It is easier to change labor level but not to change capital in a short time. Short run. Period of time in which quantity of one or more inputs cannot be changed. For example, capital is fixed and labor is variable in the short run. Long run. Period of time need to make all production inputs variable. In the long run, both capital and labor are variable.

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1 Short Run Production Function

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

October 1, 2007

Lecture 11

Production Functions Outline 1. Chap 6: Short Run Production Function 2. Chap 6: Long Run Production Function 3. Chap 6: Returns to Scale

1

Short Run Production Function

In the short run, the capital input is fixed, so we only need to consider the change of labor. Therefore, the production function q = F (K, L) has only one variable L (see Figure 1). Average Product of Labor. APL =

Output q = . Labor Input L

Slope from the origin to (L,q). Marginal Product of Labor. M PL =

∂Output ∂q = . ∂Labor Input ∂L

Additional output produced by an additional unit of labor. Some properties about AP and M P (see Figure 2). • When M P = 0, Output is maximized. • When M P > AP, AP is increasing. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


1 Short Run Production Function

2

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Q

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Figure 1: Short Run Production Function.

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5

AP

4

3

2

1

0

MP

0

1

2

3

4

5 L

6

7

8

9

10

Figure 2: Average Product of Labor and Marginal Product of Labor.

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2 Long Run Production Function

3

• When M P < AP,

AP is decreasing.

• When

M P = AP,

AP is maximized. To prove this, maximize AP by first order condition: ∂ q(L) =0 ∂L L =⇒

∂q 1 q − 2 =0 ∂L L L

=⇒

∂q q = ∂L L

=⇒

M P = AP. Example (Chair Production.). Note that here APL and M PL are not con­ tinuous, so the condition for maximizing APL we derived above does not apply. Number of Workers 0 1 2 3

Number of Chairs Produced 0 2 8 9

APL N/A 2 4 3

M PL N/A 2 6 1

Table 1: Relation between Chair Production and Labor.

2

Long Run Production Function

Two variable inputs in long run (see Figure 3). Isoquants. Curves showing all possible combinations of inputs that yield the same output (see Figure 4). Marginal Rate of Technical Substitution (M RT S). Slope of Isoquants. dK dL How many units of K can be reduced to keep Q constant when we increase L by one unit. Like M RS, we also have M RT S = −

M RT S =

M PL . M Pk

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2 Long Run Production Function

4

10

9

8

7

k=3

Q

6

5

k=2

4

k=1

3

2

1

0

0

1

2

3

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5 L

6

7

8

9

10

4.5

5

Figure 3: Long Run Production Function.

5

4.5

4

3.5

k

3

2.5

2

1.5

1

0.5

0

0

0.5

1

1.5

2

2.5 L

3

3.5

4

Figure 4: K vs L, Isoquant Curve.

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3 Returns to Scale

5

Proof. Since K is a function of L on the isoquant curve, q(K(L), L) = 0 =⇒

∂q dK ∂q + =0 ∂L dL ∂L

=⇒ −

dK M PL = . dL M PK

Perfect Substitutes (Inputs). (see Figure 5)

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k

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5 L

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10

Figure 5: Isoquant Curve, Perfect Substitutes. Perfect Complements (Inputs). (see Figure 6)

3

Returns to Scale

Marginal Product of Capital. M PK =

∂q(K, L) ∂K

Marginal Product of Labor

K constant , L ↑ → q?

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3 Returns to Scale

6

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k

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Figure 6: Isoquant Curve, Perfect Complements. Marginal Product of Capital L constant , K ↑ → q? What happens to q when both inputs are increased? K ↑ , L ↑ → q? Increasing Returns to Scale. • A production function is said to have increasing returns to scale if Q(2K, 2L) > 2Q(K, L), or Q(aK, aL) = 2Q(K, L), a < 2. • One big firm is more efficient than many small firms. • Isoquants get closer as we move away from the origin (see Figure 7).

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3 Returns to Scale

7

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9

8

Q=3

7

k

6

5

Q=2

4

3

2

Q=1

1

0

0

2

4

6

8

10

12

14

L

Figure 7: Isoquant Curves, Increasing Returns to Scale.

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1 Returns to Scale

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

October 3, 2007

Lecture 12

Production Functions and Cost of Production Outline 1. Chap 6: Returns to Scale 2. Chap 6: Production Function Derivation 3. Chap 7: Cost of Production

1

Returns to Scale

Increasing Returns to Scale (Lecture 11)

Constant Returns to Scale • Doubling the inputs leads to double the output: Q(2K, 2L) = 2Q(K, L). • One big firm is as good as many small firms. • Isoquants are equally distant apart (see Figure 1).

Decreasing Returns to Scale • Doubling the inputs leads to an output less than twice the original output: Q(2K, 2L) < 2Q(K, L). • Small firms are more efficient. • Isoquants become further apart (see Figure 2).

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1 Returns to Scale

2

12

10

k

8

6 Q=3

4 Q=2

2 Q=1

0

0

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9

L

Figure 1: Isoquant Curves, Constant Returns to Scale.

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k

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5

Q=3

4

3

2

Q=2

1

0

Q=1

0

1

2

3

4

5 L

6

7

8

9

10

Figure 2: Isoquant Curves, Decreasing Returns to Scale.

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2 Production Function Derivation

3

Example (Cobb-Douglas Production Function.). Q(K, L) = ALα K β . We double both inputs to see what type of returns to scale the production function has. Q(2K, 2L) = A(2L)α (2K )β = 2α+β ALα K β = 2α+β Q(K, L). 1. If

α + β > 1,

returns to scale is increasing. 2. If α + β = 1, returns to scale is constant. 3. If

α + β < 1,

returns to scale is decreasing.

2

Production Function Derivation

Assume that the firm has two technologies A and B , and the corresponding outputs are x y qA = min{ , }, 2 1 x y qB = min{ , }, 1 2 where the inputs x and y are perfect complements (see Figure 3). To derive production function, we must know which technology the firm chooses. If the firm choose either A or B, but not both, the isoquant curve for the production function is the black line (see Figure 3). This isoquant curve is not convex. However, the firm can adopt technologies at the same time, and this makes the isoquants convex (see Figure 4). Thus the production function is: ⎧ y ⎨ min{ x2 , 1 }, when x > 2y. x+y q(x, y) = , when 1 y � x � 2y. ⎩ 3 x y 2 min{ 1 , 2 }, when x < 12 y.

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2 Production Function Derivation

Figure 3: Deriving Production Function, Using Technology A or B.

Figure 4: Deriving Production Function, Using Technology A and B.

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4


3 Cost of Production

3

5

Cost of Production

Cost comes from factor price and how many units are used. Accounting Cost. Actual expenses plus depreciation. Economic Cost. Cost to a firm of using resources in production. Also called opportunity cost, the most valuable forgone alternative. Job 1 Job 2

Wage 150 200

Transportation Cost 0 20

Accounting Cost 0 20

Opportunity Cost 180 150

Table 1: Accounting Cost and Opportunity Cost. Example (Two job opportunities (see Table 1)). If the person accepts Job

2, the most valuable forgone opportunity is Job 1.

Opportunity cost does not really happen but must be considered.

Sunk Cost. Expenditure that has been made and cannot be recovered. Example (Two building choices). A firm has two building choices. For Building 1, they have paid 500,000, and will pay 5,000,000 in the future; for Building 2, they have not paid anything, and will pay 5,300,000 in the future. Although Building 2 is cheaper than Building 1, the firm will choose Building 1 because the 500,000 is sunk. Total Cost. Total Cost = Variable Cost + Fixed Cost. Fixed Cost. A cost that is actually incurred, but independent of the level of output. Variable Cost. A cost that is actually incurred, and dependent of the level of output.

Example (Short Run). Capital K is fixed, and Labor L is variable; hence,

the cost of K is a fixed cost, and the cost of L is a variable cost.

Here is another definition of sunk cost.

Sunk Cost. A fixed cost which is also independent of output, but whose cost is not incurred, because of no cash outlay and no opportunity cost. Usually fixed costs are considered sunk costs because they happen before production begins.

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1 Short-Run Cost Function

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

October 15, 2007

Lecture 13

Cost Functions Outline 1. Chap 7: Short-Run Cost Function 2. Chap 7: Long-Run Cost Function

Cost Function Let w be the cost per unit of labor and r be the cost per unit of capital. With the input Labor (L) and Capital (K), the production cost is w × L + r × K. A cost function C(q) is a function of q, which tells us what the minimum cost is for producing q units of output. We can also split total cost into fixed cost and variable cost as follows: C(q) = F C + V C(q). Fixed cost is independent of quantity, while variable cost is dependent on quan­ tity.

1

Short-Run Cost Function

In the short-run, firms cannot change capital, that is to say, r × K = const. Recall the production function given fixed capital level K in the short run (refer to Lecture 11) (see Figure 1). Suppose w = 1, the variable cost curve can be derived from Figure 1. Adding r × K to the variable cost, we obtain the total cost curve (see Figure 2). Average total cost is AT C =

TC FC + V C rK wL(q; K) = = + . q q q q

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1 Short-Run Cost Function

2

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Q

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Figure 1: Short Run Production Function.

50

45

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TC

35

C

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25

20

15

10

VC

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0

0

1

2

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5 q

6

7

8

Figure 2: Short Run Cost Function.

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1 Short-Run Cost Function

3

we can rewrite AT C as AT C =

rK w + , q APL

in which the average variable cost is VC wL(q; K) w = = . q q APL Likewise, we rewrite the marginal cost: MC =

dT C dV C dL(q) w w = =w = ∂q = . dq dq dq M PL ∂L

In Lecture 11, we discussed the relation between average product of labor and marginal product of labor (see Figure 3). We draw the curves for AV C and

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AP

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0

MP

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5 L

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9

10

Figure 3: Average Product of Labor and Marginal Product of Labor. M C in the same way (see Figure 4). The relation between M C and AV C is: • If

M C < AV C,

AV C decreases;

• if

M C > AV C,

AV C increases;

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2 Long-Run Cost Function

4

30

25

C

20

MC

ATC

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0

AVC

0

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Figure 4: Average Cost, Average Variable Cost, and Marginal Cost. • if

M C = AV C,

AV C is minimized. Now consider the total cost. Note that the difference between AT C and AV C decreases with q as the average fixed cost term dies out (see Figure 4). The relation between M C and AT C is: • If

M C < AT C,

AT C decreases;

• if

M C > AT C,

AT C increases;

• if

M C = AT C,

AT C is minimized.

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2 Long-Run Cost Function

5

5

4.5

4

3.5

k

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4.5

5

Figure 5: Isoquant Curve.

2

Long-Run Cost Function

In the long-run, both K and L are variable. The isoquant curve describes the same output level with different combination of K and L (see Figure 5). The slope of an isoquant curve is −M RT S = −

M PL . M PK

Similarly, the isocost curve is constructed by different (K, L) with the same cost (see Figure 6). The isocost curve equation is: rK + wL = const, therefore, it is linear, with a slope − wr . Now we want to minimize the cost rK +wL subject to an output level Q(K, L) = q. This minimum cost can be obtained when the isocost curve is tangent to the isoquant curve (see Figure 7). Thus the slopes of these two curves are equal: M RT S =

M PL w = . M PK r

Now consider an increase in wage (w). The slope of the isocost curve increases (see Figure 8), and the firm use more capital and less labor. The firm’s choice of input moves from A to B in the figure. The expansion path shows the minimum cost combinations of labor and capital at each level of output (see Figure 9). Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Long-Run Cost Function

6

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Figure 6: Isocost Curve.

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Figure 7: Minimize the Cost Subject to a Output Level.

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2 Long-Run Cost Function

7

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B

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A

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Figure 8: The Change of Cost Minimized Situation.

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K

8

Expansion Path

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3

2

2

3

4

5

6

7 L

8

9

10

11

12

Figure 9: Expansion Path.

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2 Long-Run Cost Function

8

Example (Calculating the Cost.). Given the production function 2

2

q = L3 K 3 . In the short run, 3

CSR (q; K) = rK + w

q2 , K

where K is fixed.

In the long run, according to the equation

M PL w = , M PK r we have

K w = . L r

Then the expansion path is

w L. r Substituting this result into the production function, we obtain K=

3 r 1 L = q 4 ( )2 , w 3 w 1 K = q 4 ( )2 . r Hence, the long-run cost function is: 3

CLR (q) = wL + rK = 2q 4

√ wr.

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1 Relation Between Long Run Cost Short Short Run Cost

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

October 17, 2007

Lecture 14

The Cost of Production and Profit

Maximization

Outline 1. Chap 7: Relation Between Long Run Cost and Short Run Cost 2. Chap 7: Economies of Scale 3. Chap 7: Economies of Scope, Learning

1

Relation Between Long Run Cost Short Short Run Cost

Since firms can change capital in the long run, the long run cost is always no more than the short run cost: CL R(q) � CSR,K (q). Figure 1 shows three short-run total cost given different capital level. In the long run, firms will choose the capital level which minimizes the total cost. Thus, the long-run total cost is equal to the minimum of all possible short-run total cost, and so long run total cost is the envelope of all short run total costs. Likewise, long-run average cost is the envelope of all short run average cost. From Figure 1, we know for a given product q, long run marginal cost is equal to the corresponding short run marginal cost. Long run total cost and marginal cost also have the following relation: (see Figure 2) • If LM C < LAC,

LAC is decreasing;

• if LM C = LAC,

LAC is minimized;

• if LM C > LAC,

LAC is increasing.

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1 Relation Between Long Run Cost Short Short Run Cost

2

10

9

8 TCSR3

7

C

6

5 TCSR2 4 TCLR

3 TCSR1

2

1

0

0

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2

3

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5 q

6

7

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10

Figure 1: Deriving Long Run Total Cost from Short Run Total Cost.

15 SMC3

SMC2

10

LMC

C

SMC1 SAC1

SAC2 SAC3

5 LAC

0

0

5

10

15

q

Figure 2: Deriving Long Run Average Cost and Marginal Cost from Short Run Average Cost and Marginal Cost.

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2 Economies of Scale

2

3

Economies of Scale • Constant economies of scale: C(aq) = aC(q), a > 1,

and in this case, AC is constant;

• Economies of scale:

C(aq) < aC(q), a > 1,

and in this case, AC is decreasing; • Diseconomies of scale: C(aq) > aC(q), a > 1,

and in this case, AC is increasing.

10 9 8 7

AC

C

6 5 4

economies of scale

3

diseconomies of scale

2 1 0

0

1

2

3

4

5

q

6

7

8

9

10

Figure 3: Production Dependence of Average Cost, Different Economies of Scale.

3

Economies of Scope, Learning

Economies of Scope. When producing more than one type of product that are closely linked, the cost is lower than when producing them separately. Product Transformation Curve. Shows various combinations of outputs that can be produced with a given set of inputs.

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3 Economies of Scope, Learning

4

Example (Product Transformation Curve with Economies of Scope). To produce 1 car and 1 truck, if we produce them separately, we need 2 units of K and 2 units of L; but if we produce them together, we only need 1.5 units of K and 1.5 units of L (see Figure 4). In this case, it is cheaper to produce them together; thus the firm has economies of scope.

2

1.8

1.6

1.4

Trucks

1.2

1

K=1.5 L=1.5 (1,1)

0.8 K=1 L=1 (0.7,0,7)

0.6

0.4

0.2

0

0

0.2

0.4

0.6

0.8

1 Cars

1.2

1.4

1.6

1.8

2

Figure 4: Product Transformation Curve with Economies of Scope. In the case of economies of scope, the product transformation curve is neg­ atively sloped and concave. The degree of economies of scope is defined as follows: SC =

C(q1 ) + C(q2 ) − C(q1 , q2 ) . C(q1 , q2 )

• If SC > 0,

it is economies of scope;

• if SC < 0,

it is diseconomies of scope.

The learning curve for a firm is shown in Figure 5, with the firm’s cumulative output as the vertical coordinate, and amount of inputs needed to produce a unit of output as the horizontal coordinate. Learning causes a difference in cost between the new firm and the old firm (see Figure 6). Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


3 Economies of Scope, Learning

5

10

9

Hours of Labor Per Unit of Output

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1

0

0

1

2

3 4 5 6 7 Cumulative Number of Outputs Produced

8

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9

10

Figure 5: Learning Curve of a Firm.

10

9

8

AC

7

C

6

5

4

3

AC*

2

1

0

0

1

2

3

4

5 q

6

7

8

Figure 6: Shift of Cost Curve from Learning.

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3 Economies of Scope, Learning

Figure 7: Structure of Production Theory.

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6


1 Profit Maximization

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

October 19, 2007

Lecture 15

Short Run and Long Run Supply Outline 1. Chap 8: Profit Maximization 2. Chap 8: Short Run Supply 3. Chap 8: Producer Surplus 4. Chap 8: Long Run Competitive Equilibrium

1

Profit Maximization

For perfect competition in a product market, we make some assumptions: • Price taking: either individual firms or consumers cannot affect the price. • Product homogeneity: product of all firms are perfect substitutes. • Free entry and exit: no special cost to enter or exit the market. Firms choose the level of output to maximize their profits. Profit equals total revenue minus total cost, namely π(q) = R(q) − C(q) = P (q)q − C(q). To maximize the profit, the following condition must hold: dπ(q) dR dC = − = M R(q) − M C(q) = 0, dq dq dq and thus M R(q) = M C(q). Since R(q) = P q, we have M R(q) =

dR(q) = P, dq

and M R = AR, Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Short Run Supply

2

thus M C(q) = P = M R = AR is the maximization condition. Note that the condition is not sufficient. In Figure 1), if the price is P2 , q2 and q3 both satisfy the condition, but only q3 maximizes the profit. 10 9 8

P1

7

C

6

MC

5 4 3

P 2

2 1 0

q

q

2

0

1

q1

3

2

3

4

5

6

7

8

9

10

q

Figure 1: Profit Maximization.

2

Short Run Supply

Assume the firm has production costs shown in Figure 2, let us discuss its behavior under different prices. • When P = P1 , the firm is making profits, so it will continue to produce; • When P = P2 , the firm has losses but still continues to produce, because if it shuts down, the profit is −F C, and if continuing to produce, the profit is R − T V C − F C > −F C. • Since R < SV C, when P = P3 , the profit if the firm shuts down, −F C, is more than the profit if it continues, R − T V C − F C, so it will shut down. When the firm produces, it chooses the output level where M C(q) = P . There­ fore, the firm’s supply curve when it produces is just the part of M C above T V C. When P < AV C, the firm shuts down and q = 0. We can derive market supply from an individual firm’s supply (see Figure 3). Define elasticity of market supply as follows: ES =

dQ/Q . dP/P

Figure 4 and 5 stand for inelastic and elastic supply curves, respectively. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Short Run Supply

3

10

9

8

MC P1

7

C

6

ATC

5

4 P2

3

2

AVC P3

1

0

0

1

2

3

4

5 q

6

7

8

9

10

Figure 2: Individual Firmâ&#x20AC;&#x2122;s Supply in Short Run.

10

9

8

7 MC1

P

6

Market Supply

MC2

5

4

3

2

1

0

0

1

2

3

4

5 q

6

7

8

9

10

Figure 3: Market Supply in Short Run.

Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Short Run Supply

4

10

9

8

7

P

6

MC

5

4

3

2

1

0

0

1

2

3

4

5 q

6

7

8

9

10

9

10

Figure 4: Inelastic Market Supply Curve.

10

9

8

7

P

6

MC

5

4

3

2

1

0

0

1

2

3

4

5 q

6

7

8

Figure 5: Elastic Market Supply Curve.

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2 Short Run Supply

5

10 9 8 7

P

6 5 4 3 2 1 0

0

1

2

3

4

5

6

7

8

9

10

q

Figure 6: Perfectly Inelastic Market Supply Curve.

10 9 8 7

P

6 5 4 3 2 1 0

0

1

2

3

4

5

6

7

8

9

10

q

Figure 7: Perfectly Elastic Market Supply Curve.

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3 Producer Surplus

6

Similarly, we have perfectly inelastic market supply (see Figure 6) and perfectly elastic market supply (see Figure 7). Perfectly elastic market supply happens when M C = const.

3

Producer Surplus

Producer Surplus is the difference between the firm’s revenue and the sum of the total variable cost of producing q (see Figure 8): P S = R − T V C = R − T V C − F C + F C = P rof it + F C. Thus, producer surplus is the sum of profit and fixed cost.

8

7

6

MC

P

5

4

3

AVC

2

1

0

0

1

2

3

4 q

5

6

7

8

Figure 8: Producer Surplus.

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1 Long Run Competitive Equilibrium

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

October 19, 2007

Lecture 16

Long Run Supply and the Analysis of

Competitive Markets

Outline 1. Chap 8: Long Run Equilibrium 2. Chap 8: Long Run Market Supply 3. Chap 9: Gains and Losses from Government Policies

1

Long Run Competitive Equilibrium

In Figure1, an existing firm’s marginal cost and average total cost are SM C and SAC. The short-run market price is 7, so existing firms are making profits. In the long run, capital can be changed; old firms expand, new firms enter the market, thus the supply increases, which leads to price decreasing. The price will decrease until P = LM C = LAC, so that firms have no economic profit. In the long run, firms earn zero profit, and in the short run, firms can have positive profit. However, the short run profit is not always higher because firms can also have negative profit (when P < AT C). 10 9

LMC

8

SMC

P7 6

SAC

5

LAC

4 3 2 1 0

0

1

2

3

4

5 x

6

7

8

9

10

Figure 1: Long Run Equilibrium Price.

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2 Long Run Market Supply

2

At long run competitive equilibrium: • All firms are maximizing profit, or M R = M C. • No firm has incentive to enter or exit earning zero economic profit (this is the difference between short run and long run). • QD = QS . In Figure 2, suppose the original price is 4. Existing firms make profit, so new firms enter the market and the market supply curve shifts from S1 to S2 . Now the market price is 3, existing firms make no profit, and new firms stop entering. Thus, the equilibrium is reached. In Figure 3, the original price 2 is lower than AC. Firms have a loss and start leaving the market, and the market supply shifts from S1 to S2 . 5

5

4.5

4.5

S2

4

4

LAC

3.5

S1

3.5 3

3

2.5

2.5

2

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LMC

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1.5

1

1

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2.5

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4.5

5

D

0

0.5

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1.5

2

2.5

3

3.5

4

4.5

5

4.5

5

Q

Q

(a) Long Run Cost.

(b) Shift of Equilibrium.

Figure 2: Long Run Equilibrium, High Price.

5

5

4.5

4.5

4

S1

3.5

3

3

2.5

2.5

2

2

LMC

1.5

1.5

1

1

0.5

0.5

0

S2

4

LAC

3.5

0

0.5

1

1.5

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2.5

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3.5

4

4.5

5

0

D

0

0.5

Q

(a) Long Run Cost.

1

1.5

2

2.5

3

3.5

4

Q

(b) Shift of Equilibrium.

Figure 3: Long Run Equilibrium, Low Price.

2

Long Run Market Supply

Assume that: • All firms have the same technology; • Initially firms produce at minimum long run average cost. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Long Run Market Supply

3

Constant-Cost Industry In constant-cost industry, price of inputs does not change. If the price is higher than minimum LAC. new firms will keep entering, so the supply is perfectly elastic at P = minimumLAC. Long run supply is a horizontal line at the price equal to the minimum LAC (see Figure 4(b)). 5

4

4.5

3.8

4

3.6

LAC

3.5

2

3

2.8

LMC

1.5

2.6

1

2.4

0.5

0

SL

P*

3.2

2.5

P

P

3.4

P*

3

2.2

Q* 0

0.5

1

1.5

2

2.5 Q

3

3.5

4

4.5

2

5

0

0.5

1

1.5

2

2.5 Q

3

3.5

4

4.5

5

(a) Long Run Cost in Constant-Cost In- (b) Supply Curve in Constant-Cost In­ dustry. dustry.

Figure 4: Long Run Market Equilibrium in Constant-Cost Industry.

Increasing-Cost Industry Price of some or all inputs rises as production is expanded and demand of inputs increases. When the price increase from P ∗ to P ′ , firms are making profit. Old 5

4.5

4

LAC

3.5

P*

3

5

P

4.5 2.5

P’

4 3.5

2

P

SL

P*

3

LMC

1.5

2.5 2

1

1.5 0.5

0

1

Q* 0

0.5

1

1.5

2

2.5 Q

0.5 3

3.5

4

4.5

5

0

0

0.5

1

1.5

2

2.5

Q

3

3.5

4

4.5

5

(a) Long Run Cost in Increasing-Cost (b) Supply Curve in Increasing-Cost InIndustry. dustry.

Figure 5: Long Run Market Equilibrium in Increasing-Cost Industry. firms expand and new firms enter, so the demand of inputs increase, and so do the prices of inputs. Firm’s cost curves increase to LM C ′ and LAC ′ / Since now firms have zero profit, new firms stop entering. The quantity supplied increases but is still finite. Thus the supply curve is upward sloping.

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3 Gains and Losses from Government Policies

3

4

Gains and Losses from Government Policies

Consumer Surplus and Producer Surplus Consumer Surplus. Area between demand curve and market price (see Fig­ ure 6). Producer Surplus. Area between supply curve and market price (see Fig­ ure 6).

5

4.5

S

4

3.5

Consumer Surplus 3

P

Producer Surplus 2.5

2

D

1.5

1

0.5

0

0

0.5

1

1.5

2

2.5 Q

3

3.5

4

4.5

5

Figure 6: Consumer Surplus and Producer Surplus. CS (Consumer Surplus) plus P S (Producer Surplus) is maximized at the quan­ tity when demand equals supply.

Price Ceiling When there is no intervention, the equilibrium price and quantity are P ∗ and Q∗ , respectively. Now government sets a price ceiling, namely, a maximum price P¯ (see Figure 7). The changes in consumer surplus and producer surplus are as follows: ΔCS = A − B, ΔP S = −A − C, ΔCS + ΔP S = −B − C. Deadweight loss, or net loss of CS + P S, is −(B + C) in this case. Government should maximize economic efficiency: maximize CS + P S. If policies cause deadweight loss, they impose an economy cost on the economy. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


3 Gains and Losses from Government Policies

5

5 4.5

4

P

P¯3.5

P *3

P

2.5

B C

A

2

1.5

1

0

Q∗

Q′

0.5 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Q

Figure 7: Price Ceiling.

Price Floor Government sets a price floor (price support), namely, a minimum price P (see Figure 8). The changes in consumer surplus and producer surplus from the competitive equilibrium (P ∗ , Q∗ ) to the new equilibrium (P , Q′ ) are as follows: ΔCS = −A − B;

ΔP S = A − C;

ΔCS + ΔP S = −B − C.

Thus there is still a deadweight loss.

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3 Gains and Losses from Government Policies

6

5

4.5

S

4

3.5

B C

P

3

A

2.5

D

2

1.5

1

0.5

0

0

0.5

1

1.5

2

2.5 Q

3

3.5

4

4.5

5

Figure 8: Price Floor.

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1 Agricultural Price Support

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

October 24, 2007

Lecture 17

Supply Restrictions, Tax, and Subsidy Outline 1. Chap 9: Agricultural Price Support 2. Chap 9: Supply Restrictions 3. Chap 9: Tax and Subsidy

1

Agricultural Price Support

In this case, government sets prices higher than the free market level, and buys excess supply (see Figure 1). The buyer’s price is shown on the y-axis in the following graphs. The original consumer surplus equals the area between the 10 9 8 S

7 P

2

P

6

A

P

B

D

1

5 4

E

3

D

2 1 0

Q

Q

2

0

1

2

3

Q

1

4

3

5 Q

6

7

8

9

10

Figure 1: Agricultural Price Support. demand curve and the line of price P1 ; after the price support, it equals the area between the demand curve and the line of price P2 , thus ΔCS = −(A + B). The original producer surplus equals the area between the supply curve and the line of price P1 ; after the price support, it equals the area between the supply Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Supply Restrictions

2

curve and the line of price P2 , thus ΔP S = A + B + D. Government buys quantity Q3 − Q2 at price P2 ; the cost equals the area of the rectangular ΔG = −(B + D + E). The deadweight loss to the society is DW L = −(B + E).

2

Supply Restrictions

Government restricts quantity supplied to be less than Q1 (see Figure 2). The 10

9

8

S

P

7 6

P1

5

P0

4

P2

A

B C

D

3 2 1 0

Q

Q0

1

0

2

4

6

8

10

Q

Figure 2: Supply Restriction. original consumer surplus equals the area between the demand curve and the line of price P0 ; after the supply restriction, it equals the area between the demand curve and the line of price P1 , thus ΔCS = −(A + B). The original producer surplus equals the area between the supply curve and the line of price P0 ; after the supply restriction, it equals the area of the trapezoid, with the supply curve, the line of price P1 , the line of quantity Q1 , and the price axis as its sides, thus ΔP S = A − C. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2.1

Zero Quota

3

Thus, the deadweight loss is DW L = −(B + C). Example government measures include import quota and tariff, which benefit domestic producers but hurt consumers.

2.1

Zero Quota

SD is the domestic supply, and DD is the domestic demand. If no import is allowed, the domestic price is P0 . Without restriction on import, the domestic price would be the same as the world price PW , which is lower than PD (see Figure 3). Without import quota restriction, consumer surplus equals the area 10 9 8 S

7

D

P

6 5

P0

4

PW

A

B

C

3

DD

2 1 0

Q

Q

S

0

1

2

3

Q

0

4

D

5 Q

6

7

8

9

10

Figure 3: Zero Quota. between the domestic demand curve and the line of price PW ; if the quota is zero, it equals the area between the domestic demand curve and the line of price P0 , thus ΔCS = −(A + B + C). Without quota restriction, producer surplus equals the area between the domes­ tic supply curve and the line of price PW ; if the quota is zero, it equals the area between the domestic supply curve and the line of price P0 , thus ΔP S = A. The deadweight loss is DW L = B + C.

2.2

Non-Zero Quota

Given the same SD , DD , and PW , now suppose the government sets non-zero quota k. The domestic price P1 is where the difference between domestic demand Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2.3

Import Tariff

4

10 9 8 7

SD

P

6 5 4

P1

3

PW

A

B

C

D D

D

2 1 0

QS 0

2

QS1

QD1 4

QD 6

8

10

Q

Figure 4: Non-Zero Quota. (QD1 ) and domestic supply (QS1 ) is k (see Figure 4). Likewise, the change of consumer surplus ΔCS = −(A + B + C + D); and the change of domestic producer surplus ΔP SD = A. The net domestic loss equals −(ΔCS + ΔP S) = B + C + D. The foreign producer surplus increases by excess profits, which equal the area of rectangular C ΔP SF = C. The total deadweight loss is DW L = B + D. The domestic loss is Domestic Loss = B + C + D.

2.3

Import Tariff

Government imposes a tariff P1 − PW on each unit imported (see Figure 5). The change of consumer surplus and domestic producer surplus are Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


3 Tax and Subsidy

5

10

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8

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SD

P

6 5

P

1

4

PW

3

A

B

C

D DD

2 1

0

QS 0

QS1

2

QD1 4

Q D 6

8

10

Q

Figure 5: Import Tariff. ΔCS = −(A + B + C + D) and ΔP SD = A, respectively. Foreign producers gain nothing, that is to say ΔP SF = 0, because C becomes the revenue of government ΔG = C. The deadweight loss is DW L = B + D, which equals to the domestic loss.

3

Tax and Subsidy

Assume that government imposes a $1 tax on each cigarette unit. Given the market price P , if the tax is paid by • producers, then buyers pay P and producers get P − 1; • consumers, then buyers pay P + 1 and producers get P . Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


3 Tax and Subsidy

6

Therefore, the price paid by buyers and the price received by producers always have a difference of 1 (see Figure 6). Let PB be the buyer’s price and PS be the seller’s price. PD − PS = 1. In figure 6, we put buyer’s price on the y axis. Therefore, with the tax, the supply curve moves from S to S ′ . The equilibrium buyer’s price is PD , and the equilibrium seller’s price is PS . Thus, the consumer surplus and producer 5 4.5 S’

4 buyer’s price 3.5 3

S

P

A

P

D

2.5

P0

2

B D

C

P

D

S

1.5 1 0.5 0

Q1

Q

0

0

1

2

3

4

5 Q

6

7

8

9

10

Figure 6: Tax. surplus both decrease: ΔCS = −(A + B), ΔP S = −(C + D). Government revenue ΔG = A + C. So, the deadweight loss is DW L = B + D.

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1 Tax

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

October 26, 2007

Lecture 18

Tax, Subsidy, and General Equilibrium Outline 1. Chap 9: Tax 2. Chap 9: Subsidy 3. Chap 16: General Equilibrium 4. Chap 16: Exchange Economy

1

Tax

Government imposes a $1 tax on every unit sold (see Figure 1), as discussed in Lecture 17. The buyer’s price is shown on the y-axis. The consumer surplus 5 4.5 S’

4 buyer’s price 3.5

3

S

P

A

P

D

2.5

2

P0

B D

C

P

D

S

1.5

1

0.5 0

Q

Q

1

0

0

1

2

3

4

5 Q

6

7

8

9

10

Figure 1: Tax. and producer surplus both decrease: ΔCS = −(A + B), ΔP S = −(C + D). Government revenue ΔG = A + C. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Subsidy

2

So the deadweight loss is DW L = B + D. The burden of a tax is shared by consumers and producers; the relative amount borne by consumers and producers depends on relative elasticities of demand and supply. • If the demand is inelastic (see Figure 2), 10

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PD

S

P

6

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P0 P

S

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B

C

D

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D

2

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8

9

10

Figure 2: Tax Burden on Buyers, Relative Inelastic Demand Curve. ΔCS = −(A + B),

ΔP S = −(C + D),

buyers bear most of the burden of the tax.

• If the supply is inelastic (see Figure 3),

ΔCS = −(A + B),

ΔP S = −(C + D),

producers bear most of the burden of the tax. Pass-through fraction is the percentage of a tax borne by consumers. It tells the fraction of tax ”passed through” to consumers through higher price. If ED = 0, say the demand is perfectly inelastic (see Figure 4), buyers bear all of the tax burden: ES = 1. ES − ED

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2 Subsidy

3

10 9 8 S

7

P

6

P D P0

5

A

B D

C

4 PS

3

D

2 1 0

0

2

4

6

8

10

Q

Figure 3: Tax Burden on Producers, Relative Inelastic Supply Curve.

Figure 4: Tax Burden on Buyers, Perfectly Inelastic Demand Curve.

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2 Subsidy

4

5 4.5

4

S

3.5

P

3

2.5

2

PS P

C

D

P

A

B

0

E

B

1.5

D

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Q

0

Q

1

0

0

1

2

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5 Q

6

7

8

9

10

Figure 5: Subsidy.

2

Subsidy

Government subsidizes $1 for each unit sold (see Figure 5). In this case, sellers’ price is higher than buyers’ price: PB = PS + 1. The consumer surplus increases by ΔCS = A + B; and the producer surplus increases by ΔP S = C + D. Government expenditure equals the whole area between PB and PS under the quantity Q1 ΔG = −(A + B + C + D + E). The deadweight loss is DW L = E. Likewise we can discuss the benefit of subsidy: D • if E ES is small, namely, the demand is more inelastic, the benefit of subsidy goes mostly to buyers; D • if E ES is large, namely, the supply is more inelastic, the benefit of subsidy goes mostly to sellers.

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3 General Equilibrium

3

5

General Equilibrium

Partial equilibrium. Ignores effects form other markets. General equilibrium. Simultaneous determination of the prices and quanti­ ties in all relevant markets, taking into account feedback effects. Feedback effect. The price or quantity adjustment in one market caused by price and quantity adjustments in related markets. Example (DVD and Movie Tickets Markets). The price of a DVD is $3, and the price of a movie ticket is $6 at equilibrium. Now tax $1 on the movie ticket (see Figure 6). The specific process of price change is listed as follows: MOVIE TICKET : ′ SM → SM ,

Price change:6 → 6.35; DVD : The price change of movie tickets shifts the demand curve of DVD. DV → DV′ , Price change:3 → 3.5; MOVIE TICKET : The price change of DVD shifts the demand curve of movie tickets. ′ DM → DM ,

Price change:6.35 → 6.75; and so on. The final equilibrium prices are P (M OV IET ICKET ) = 6.85; P (DV D) = 3.58. If we ignore the feedback effects, we might underestimate the price change bought by the tax.

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3 General Equilibrium

6

10 9

SM*

8

SM

7

P

6 5 4

DM

3 2 1 0

0

2

4

6

8

10

Q

(a) Price Change of Movie Ticket. 10 9 8 7

SV

P

6 5 4 3

DV*

2 1 0

QV*

Q

V

0

1

2

3

4

5 Q

D

V

6

7

8

9

10

(b) Price Change of DVD.

Figure 6: General Equilibrium of DVD and Movie Ticket Markets.

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4 Exchange Economy

4

7

Exchange Economy

Assume that: • there are two consumers A and B; • there are two goods, food and clothing; • the quantities of food and clothing are 10 and 6, and A has 7 food and 1 clothing, while B has 3 food and 5 clothing; • they know each others’ preferences; • transaction cost is zero. The edgeworth box is shown in Figure 7. 6

O

B

5

Clothing

4

3

2

1

A(7F,1C)=B(3F,5C) OA

0

0

1

2

3

4

5 Food

6

7

8

9

10

Figure 7: Edgeworth Box.

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1 Exchange Economy

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

October 29, 2007

Lecture 19

Efficiency in Exchange, Equity and Efficiency, and Efficiency in Production Outline 1. Chap 16: Exchange Economy 2. Chap 16: Contract Curve 3. Chap 16: General Equilibrium in a Competitive Market 4. Chap 16: Utility Possibilities Frontier 5. Chap 16: Production in Edgeworth Box

1

Exchange Economy

In the Edgeworth box (see Figure 1) given endowment E, the area between A’s and B’s utility curves contains all beneficial trades, but not all are efficient; that is to say, both A and B are better off in this area, but they will keep trading until they cannot make both of them better. Then the possible efficient allocation given the endowment E should satisfy that: • there is no more room for trade, • thus M RSA = M RSB .

2

Contract Curve

Contract curve shows all possible efficient allocations; it contains all points of tangency between A’s and B’s indifference curves (see Figure 2).

3

General Equilibrium in a Competitive Market

Assume that consumers are price-takers. There are two consumers, A and B, and two goods, X and Y, in the market. The total endowment of X is x units,

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3 General Equilibrium in a Competitive Market

2

10

OB

9

8

UB

7

6

Clothing

5

D

4

UA

3

C

2

E

1

0

OA 0

Food 1

2

3

4

5

6

7

8

9

10

Figure 1: Finding the EďŹ&#x192;cient Allocation in Edgeworth Box.

10

OB

9

8

7

6

5

4

3

2

1

0

OA 0

1

2

3

4

5

6

7

8

9

10

Figure 2: Contract Curve.

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4 Utility Possibilities Frontier

3

and the total endowment of Y is y units. Obviously, demand equals supply at equilibrium. We denote the equilibrium state by ∗ ∗ (Px∗ , Py∗ , (x∗A , yA ), (x∗B , yB )).

If we suppose A has one unit of X and two units of Y initially, the budget constraint is xA Px + yA Py = Px + 2Py , and divide it by Py , xA

Px Px + yA = + 2; Py Py

so we only care about the price ratio PPxy . For convenience, we usually set Py∗ to 1 so that the expression above has five unknowns. To find the equilibrium, several conditions should be satisfied: ∗ ∗ • (xA , yA ) maximize A’s utility subject to the budget constraint, then we obtain two equations; ∗ • (x∗B , yB ) maximize B’s utility subject to the budget constraint, likewise we can obtain another two equations; ∗ ∗ • the quantity is conserved, or x∗A + yA = x and x∗B + yB = y (actually one of these equations is redundant because it is automatically satisfied given the preceding four and another from these two equations).

Finally, we obtain five equations. Therefore, the problem can be solved (see Figure 3). Assume that yA + yB > Y and xA + xB < X; it is not at equilibrium, because Px > Px∗ , so price of X will decrease. At equilibrium, we must have the right price ratio. For example, if the price for X is Px , Px > Px∗ , then yA + yB > y and xA + xB < x. Y has excess demand, and X has excess supply.

4

Utility Possibilities Frontier

Utility possibilities frontier shows the utility levels when the two individuals have reached the contract curve (see Figure 4). Choosing a point below the frontier, for example, A, the allocation is inefficient; choosing a point above the frontier, for example, B, the allocation is unobtainable.

5

Production in Edgeworth Box

Now we discuss the producer’s problem. There are two industries. One produces food and the other produces clothing. The isoquant curves are shown in the Edgeworth box (see Figure 5). E is their initial endowment of inputs. An

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5 Production in Edgeworth Box

4

10

x*

O

B

9

B

8

y*B

7 6

UB

5 4 3

1 0

A

A

2

Budget

Constraint

O

x*A

A

0

E: Initial Endowment

U

y*

1

2

3

4

5

6

7

8

9

10

Figure 3: Contract Curve.

10

. Point B

0

−10

Utility of B Point A

.

−20

−30

Utility of A

−40

−50

0

1

2

3

4

5

6

7

8

9

10

Figure 4: Utility Possibilities Frontier.

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5 Production in Edgeworth Box

5

allocation of inputs is technically efficient if the output of one good cannot be increased without decreasing the output of another, so M RT SF = M RT SC . At competitive equilibrium in the input market, • wage and rent are equal for all industries; • total L and K in all industries are equal to aggregate available supplies. Similar to the consumers’ problem, the general equilibrium can be characterized by (w, r, (LF , KF ), (LC , KC )). Production possibilities frontier shows various combinations of two goods that can be produced with fixed quantity of input demanded from production con­ tract curve. 10

OClothing

9 8 7

QF

6

Capital

5 4

Q

C

3 2 1 0

E

OFood 0

1

Labor 2

3

4

5

6

7

8

9

10

Figure 5: Production in a Edgeworth Box.

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1 Production Possibilities Frontier

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

October 31, 2007

Lecture 20

Production Possibilities Frontier and Output

Market Efficiency

Outline 1. Chap 16: Production Possibilities Frontier 2. Chap 16: Output Market Efficiency

1

Production Possibilities Frontier

Marginal rate of transformation (M RT ): • How much clothing must be given up to produce one additional unit of food. • The absolute value of the slope of the production possibilities frontier. • If M RT increases in food, then the production possibilities frontier is concave. • M RT =

M CF . M CC

Proof. Reducing $1 input from clothing, C decreases by 1 input to food, F increases by MC . Thus, F M RT =

2

ΔC = ΔF

1 MCC 1 MCF

=

1 MCC

; adding $1

M CF . M CC

Output Market Efficiency

Suppose we have two industries, clothing and food, in the market. Consumers have demand for the two goods. They have a representative utility U (C, F ). A Pareto efficient result occurs when the production possibilities frontier is tangent to the indifference curve (see Figure 3). That is to say, M RT = M RS. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Output Market EďŹ&#x192;ciency

2

10

9

OC

8

7

6

5

4

3

2

OF

1

0

0

1

2

3

4

5

6

7

8

9

10

9

10

Figure 1: Production Contract Curve.

10

9

Clothing 8

7

C

6

5

Production Possibilities Frontier

4

3

2

Food

1

0

0

1

2

3

4

5 F

6

7

8

Figure 2: Production Possibilities Frontier.

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2 Output Market EďŹ&#x192;ciency

3

10

9

8

7

C

6

Indifference Curve

5

Production Possibilities Frontier

4

3

2

1

0

0

1

2

3

4

5 F

6

7

8

9

10

Figure 3: Production Possibilities Frontier and IndiďŹ&#x20AC;erence Curve.

10

9 8 7

C

6

Indifference Curve

5

Production Possibilities Frontier

4 3 2 1 0

0

1

2

3

4

5 F

6

7

8

9

10

Figure 4: Equilibrium in the Output Market.

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2.1

General equilibrium in the output market

4

The prices are PF for food, and PC for clothing. When the market reaches its equilibrium, industries are maximizing their profits, so M CF (q) = PF ; M CC (q) = PC . Thus, M RT =

M CF PF = . M CC PC

Consumers maximize their utility, so M RS =

PF . PC

Combining the equations together, we obtain (see Figure 4) M RT =

PF = M RS. PC

Consider non-equilibrium prices PF′ and PC′ , PF′ PF < . ′ PC PC Given the prices, food has a shortage and clothing has an excess (see Figure 5). The prices will change to adjust to the equilibrium state, namely, PF′ increases and PC′ decreases.

2.1

General equilibrium in the output market

Example (Gains from Free Trade). Assume that Holland and Italy both produce cheese and wine, unit of labor required is provided in Table 2.1). If these Holland Italy

Cheese 1 6

Wine 2 3

Table 1: Unit of Labor Required in Cheese and Wine Production. two countries cannot trade cheese or wine, we consider the domestic markets separately. The price ratio is not the same: H I PW PW < . I PCH PC

Consumer utility levels are UH and UI , respectively. However, if they can trade,

Holland exports cheese and imports wine, and Italy exports wine and imports

cheese. The prices ratio will adjust to agree, and people in both countries are

better off because both indifference curves move upwards (see Figure 6). The

′ new utility levels are UH and UI′ .

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2.1

General equilibrium in the output market

5

10

9

8

7

C

6

Supply

5

Demand

4

3

2

1

0

0

1

2

3

4

5 F

6

7

8

9

10

Figure 5: Non-equilibrium Consumption and Production.

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2.1

General equilibrium in the output market

6

14

Holland

12

10

8

UHâ&#x20AC;&#x2122;

6

4

UH

2

0

0

1

2

3

4

5

6

7

8

9

10

8

9

10

(a) Trade in Holland. 10

Italy

9 8 7

C

6

Uâ&#x20AC;&#x2122;

5

I

4 3

U

I

2 1 0

0

1

2

3

4

5 W

6

7

(b) Trade in Italy.

Figure 6: Gains from Free Trade.

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1 Why Markets Fail

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

November 2, 2007

Lecture 21

Why Markets Fail Outline 1. Chap 16: Why Markets Fail

1 1.1

Why Markets Fail Market Power

Inefficiency arises when a producer or supplier of a factor input has market power, for example, monopoly power, that can profitably charge a price greater than marginal cost.

1.2

Incomplete Information

For example, in the second-hand car market, sellers know more about the cars than buyers. Final allocation might be inefficient when there is incomplete information.

1.3

Externalities

Consumption or production has indirect effect on other consumption or pro­ duction, which is not reflected in market prices. An example is air and water pollution by a factory.

1.4

Public Goods

For one firm’s new technology, others may copy it if there is no patent law; all firms are thus waiting for others to invent.

Examination 2 Review Examination: Chapter 6, 7, 8, 9, and 16. (Review Lectures 10–20.)

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1 Monopoly

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

November 7, 2007

Lecture 22

Monopoly Outline 1. Chap 10: Monopoly 2. Chap 10: Shift in Demand and Effect of Tax

1

Monopoly

The monopolist is the single supply-side of the market and has complete control over the amount offered for sale; the monopolist controls price but must operate along consumer demand.

1.1

Revenue in Monopoly

Review the revenue in perfect competition: R = PQ AR = M R = P.

(1.1) (1.2)

Revenue of monopolist is also R = P (Q)Q, but P changes with Q because the monopolist faces the whole market demand and his quantity supplied affects the market price. Then the average revenue is AR =

R = P (Q); Q

and the marginal revenue is MR =

dR d(P Q) dP = = P (Q) + Q . dQ dQ dQ

The relation between P and Q is determined by the demand curve (see Figure 1). Since dP < 0, dQ M R < P (Q). Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


1.2

Output Decision in Monopoly

2

Example (A Demand Function). Suppose the price is P = 10 − QD , where QD is the quantity demanded. Calculate the average revenue and the marginal revenue: AR = P = 10 − Q; dP MR = p + Q = 10 − 2Q. dQ

15

10

Demand Curve P1

5

P2

0

0

Q1

5

Q2

10

15

Figure 1: Demand and Supply of Monopolist.

1.2

Output Decision in Monopoly

The monopolist will maximize its profit π(Q) = R(Q) − C(Q), which is the difference of revenue and cost. When maximized, dπ dR dC = − = 0, dQ dQ dQ namely, M R = M C, so the monopolist would choose this point to produce; because P > M R, Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


1.3

Lerner’s Index

3

P > M C. The profit equals to (AR − AC)Q = (P − AC)Q (see Figure 2).

15

MC Demand Curve

10

P

AR AC

P* 5

0

0

MR

Q*

5

10

15

Q

Figure 2: Output Decision of Monopolist.

1.3

Lerner’s Index

Rewrite the marginal revenue: MR = P + Q

dP Q dP 1 = P + P( )=P +P . dQ P dQ ED

The monopolist chooses to produce the quantity where MC = MR = P + P Thus,

1 . ED

1 P − MC = , |ED | P

(1.3)

which is the makeup over M C as a percentage of price; this fraction is less than 1. L = P −PMC measures the monopoly power of a firm and is called Lerner’s index.

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2 Shift in Demand and Effect of Tax

4

• In a competitive market,

M C = P,

and the makeup is zero. • In a monopolistic market, M C < P, and the makeup is larger than zero. Comments: 1. The makeup increases with the inverse of demand elasticity. 2. The larger the demand elasticity, the less profitable it is to be a monopolist (see Figure 3 and 4). 3. A monopolist never produces a quantity at the inelastic portion of demand curve, since the makeup right hand side of Equation 1.3 is less than one.

10

9

D

8

P*

7

MR

6

5

4

MC

3

2

1

0

Q* 0

1

2

3

4

5

6

7

8

9

10

Figure 3: Inelastic Demand.

2

Shift in Demand and Effect of Tax

Compare the competitive market and the monopolistic markets.

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2.1 Supply Curve of Competitive Market and Monopolistic Markets

5

10

9

8

P*

7

MR D

P

6

5

4

MC

3

2

1

0

Q* 0

1

2

3

4

5 Q

6

7

8

9

10

Figure 4: Elastic Demand.

2.1

Supply Curve of Competitive Market and Monopolis­ tic Markets

The supply curve in competitive markets is determined by M C, and there is no supply curve for monopolistic markets.

2.2

Shift in Demand

In competitive markets, when demand shifts, the changes in price and quantity has a positive relation, namely, if the price raises, the quantity increases. In monopolistic markets, when the demand shifts, it may be the case that only price changes (see Figure 5), only quantity changes (see Figure 6), or both change.

2.3

EďŹ&#x20AC;ect of Tax

In competitive marketes, buyerâ&#x20AC;&#x2122;s prices raise less than the tax, and the burden is shared by Producers and Consumers; in monopolistic markets, the price might raise more than tax (see Figure 7).

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2.3

EďŹ&#x20AC;ect of Tax

6

15

AR2 MR2

10

MC

P

P2 P1

5

0

MR1

AR1

Q1=Q2 0

5

10

15

Q

Figure 5: Only Price Change in Monopoly.

15

AR2 10

MC

P

MR2

5

P1=P2 MR1

0

AR1

Q1 0

Q2 5

10

15

Q

Figure 6: Only Quantity Change in Monopoly.

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2.3

EďŹ&#x20AC;ect of Tax

7

10

9

8

D

7

MR P

6

5

P2

MC2=MC1+T

4

3

P1

MC1

2

1

0

0

1

2

3

4

5 Q

6

7

8

9

10

Figure 7: Price Might Raise More than Tax.

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1 Multi-Plant Firm

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

November 9, 2007

Lecture 23

Monopoly and Monopsony Outline 1. Chap 10: Multi-Plant Firm 2. Chap 10: Social Cost of Monopoly Power 3. Chap 10: Price Regulation 4. Chap 10: Monopsony

1

Multi-Plant Firm

How does a monopolist allocate production between plants? Suppose the firm produces quantity Q1 with cost C1 (Q1 ) for plant 1, and quan­ tity Q2 with cost C2 (Q2 ) for plant 2. The total quantity is QT = Q1 + Q2 . And the profit is π = QT P (QT ) − C1 (Q1 ) − C2 (Q2 ) = (Q1 + Q2 )P (Q1 + Q2 ) − C1 (Q1 ) − C2 (Q2 ). To solve, use the first order constraint: dπ dP (Q1 + Q2 ) dC1 = P (Q1 + Q2 ) + (Q1 + Q2 ) − = 0, dQ1 dQ1 dQ1 Since P (QT ) + QT

dP (QT ) dP (QT ) = P (QT ) + QT = M R(QT ), dQ1 dQT M R(QT ) = M C1 (Q1 ).

Similarly, M R(QT ) = M C2 (Q2 ). Thus, M R(QT ) = M C1 (Q1 ) = M C2 (Q2 ).

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2 Social Cost of Monopoly Power

2

2

Social Cost of Monopoly Power

Firstly, compare the producer and consumer surplus in a competitive market and a monopolistic market. In the competitive market, the quantity is determined by M C = AR, while in the monopolistic market, the quantity is determined by MC = MR (see Figure 1). Therefore, in going from a perfectly competitive market to a

10

9

8

7

P

6

PM

5

4

A

PC MR

3

D=AR

MR

2

1

0

MC

B C

0

1

2

QM Q C 3

4

5 Q

6

7

8

9

10

Figure 1: Consumer and Producer Surplus in Monopolist Market. monopolistic market, the change of consumer surplus and producer surplus are, respectively, ΔCS = −(A + B), and ΔP S = A − C. The deadweight loss is DW L = B + C. In fact, social cost should not only include the deadweight loss but also rent seek­ ing. The firm might spend to gain monopoly power by lobbying the government and building excess capacity to threaten opponents.

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3 Price Regulation

3

3

Price Regulation

In perfectly competitive markets, price regulation causes deadweight loss, but in monopoly, price regulation might improve efficiently. Now we discuss four possible price regulations in monopolistic markets. P1 , P2 , P3 , P4 are: • P1 ∈ (PC , PM ); • P2 = PC ; • P3 ∈ (P0 , PC ); • P4 < P0 .

10

9

8

7

MC

P

6

5

4

3

PM

AC

PC P0

MR

2

D=AR

1

0

0

1

2

QM Q C 3

4

5 Q

6

7

8

9

10

Figure 2: Comparing Competitive and Monopolist Market. Price between the competitive market price and monopolist market price. Suppose the price ceiling is P1 . The new corresponding AR and M R curves are shown in Figure 3. Given the new M R curve, the equilibrium quantity will be Q1 . Q1 ∈ (QM , QC ).

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3 Price Regulation

4

10 9 8 7

MC

P

6 5 4

P MP P 1 C

MR

3 2 1 0

0

1

2

Q Q1Q M C 3

4

AR 5 Q

6

7

8

9

10

Figure 3: Price between the Competitive Market Price and Monopolist Market Price. Price equal to the competitive market price. The new corresponding M R and AR curves are shown in Figure 4. In this case the equlibrium price and quantity are as same as those of the competitive market. Price between the competitive market price and the lowest average cost. Suppose the price ceiling is P3 . The new corresponding M R and AR curves are shown in Figure 5. The equilibrium quantity will be Q3 . Q3 ∈ (QC , Q0 ). The new bold line describes the relation between price and quantity. Price lower than the lowest average cost. The firm’s revenue is not enough for the cost, thus it will quit the market. There is no production. The analysis shows that if the government sets the price ceiling equal to P2 , the outcome is the same as in a competitive market, and there is no deadweight loss. Natural monopoly. In a natural monopoly, a firm can produce the entire output of the industry and the cost is lower than what it would be if there were other firms. Natural monopoly arises when there are large economies of scale (see Figure 6). If the market is unregulated, the price will be PM and the quantity will be QM . To improve efficiency, the government can regulate the price. If the price is regulated to be PC , the firm cannot cover the average cost and will go out of business. PR is the lowest price that the government can set so that the monopolist will stay in the market.

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3 Price Regulation

5

10 9 8 7

MC

P

6 5

PC

4

MR

3 2

AR

1 0

0

1

2

3

QC 4

5 Q

6

7

8

9

10

Figure 4: Price Equal to the Competitive Market Price.

10

9

8

7

MC

P

6 5 4 3

AC

PCP P0 3 MR

2 1 0

0

1

2

3

Q AR QC 3 4

5 Q

6

7

8

9

10

Figure 5: Price between the Competitive Market Price and the lowest Average Cost.

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4 Monopsony

6

10

9

8

7

P

6

5

4

PM P

AC

R

3

2

MC

P

C

1

0

0

1

2

Q MRQR M 3

4

Q AR C 5 Q

6

7

8

9

10

Figure 6: Regulating the Price of a Natural Monopoly.

4

Monopsony

Monopsony refers to a market with only one buyer. In this market, the buyer will maximize its profit, which is the difference of value and expenditure: max Π(Q) = V (Q) − E(Q). When the profit is maximized, d (V (Q) − E(Q) = 0. dQ Thus M V = M E, namely, the marginal value (additional benefit form buying one more unit of goods) is equal to the marginal expenditure (addtional cost of buying one more unit of goods).

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1 Monopsony

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

November 14, 2007

Lecture 24

Monopoly and Monopsony Outline 1. Chap 10: Monopsony 2. Chap 10: Monopoly Power 3. Chap 11: Price Discrimination

1

Monopsony

A monopsony is a market in which there is a single buyer. Typically, a monop­ sonist chooses to maximize the total value derived from buying the goods minus the total expenditure on the goods: V (Q) − E(Q). Marginal value is the additional benefit derived from purchasing one more unit of a good; since the demand curve shows the buyer’s additional willingness to pay for an additional unit, marginal value and the demand curve coincide. Marginal expenditure is the additional cost of buying one more unit of a good. Average expenditure is the market price paid for each unit, which is determined by the market supply (see Figure 1). Now compare the competitive and monopsony market. • Competitive buying firms are price takers: The price P ∗ is fixed; therefore, E = P ∗ × Q. And then

AE = M E = P ∗

(see Figure 2). • Monopsonist:

E = PS∗ (Q) × Q.

By definition, AE = and ME =

E = PS (Q); Q

dE dPS (Q) = PS (Q) + Q∗ × . dQ dQ

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2 Monopoly Power

2

10

9

8

ME

7

S=AE

Price

6

5

PC

4

PM

B A

C

3

D=MV 2

1

0

0

QM 1

2

QC 3

4

5 Quantity

6

7

8

9

10

Figure 1: Monopsony Market. Since the supply curve is upward sloping, M E > PS (Q) = AE. To maximize V (Q) − E(Q), we have M V (Q) = M E(Q). Buyers gain A−B from monopsony power, while sellers lose A+C (see Figure 1); the deadweight loss is B + C.

2

Monopoly Power

There usually is more than one firm in the market, and they have similar but different goods. The Lerner’s index is L=

P − MC 1 = , P |Ed |

in which |Ed | is the elasticity of demand for a firm, as oppose to market demand

elasticity.

There are several factors that affect monopoly power.

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3 Price Discrimination

3

10

9

8

7

S Price

6

PC

5

4

D

3

2

1

0

QC 0

1

2

3

4

5 Quantity

6

7

8

9

10

Figure 2: Competitive Buying Market. • Elasticity of Market Demand: If the market demand is more elastic, the firm’s demand is also more elastic. In a competitive market, elasticity of demand for a firm is infinite. With more than one firm, a single firm’s demand is more elastic than market demand. • Number of Firms in Market: With more firms, the firm’s demand elasticity is higher, namely, the market power is less. • Interaction among Firms: If competitors are more aggressive, firms have less market power; if firms collude, they thus have more market power.

3

Price Discrimination

Without market power, the producer would focus on managing production; with market power, the producer not only manages production, but also sets price to capture consumer surplus.

First Degree Price Discrimination Knowing each consumer’s identity and willingness to pay, the producer charges a separate price to each customer. • M R(Q) = PD (Q).

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3 Price Discrimination

4

10

9

MC

8

7

6

5

4

D=AR 3

2

MR

1

0

0

1

2

3

4

5

6

7

8

9

10

Figure 3: First Degree Price Discrimination. • Choose Q∗ such that

M R(Q∗ ) = M C(Q∗ )

Q∗ is efficient. • When the consumer surplus is zero, the producer surplus is maximized. This kind of price discrimination is not usually encountered in real world.

Second Degree Price Discrimination The producer charges different unit prices for different quantity purchased. It applies to the situation when consumers are heterogeneous and the seller cannot tell their identity, and consumers have multiple unit demand.

Third Degree Price Discrimination Refer to next lecture.

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1 Third Degree Price Discrimination

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

November 16, 2007

Lecture 25

Pricing with Market Power Outline 1. Chap 11: Third Degree Price Discrimination 2. Chap 11: Peak-Load Pricing 3. Chap 11: Two-Part Tariff

1

Third Degree Price Discrimination

Third degree price discrimination is the practice of dividing consumers into two or more groups with separate demand curves and charging different prices to each group (see Figure 1). Now maximize the profit: 10

10

9

9

9

8

8

7

7

7

6

6

6

P1

5

4

4

3

3

2

2

Q1 MR1

1

0

D1

0

1

2

3

4

8

Price

5

Price

Price

10

4

P2

5 Quantity

6

7

8

(a) Group 1.

9

10

3

2

1

0

MC

5

0

1

D2

MR2

Q2 2

3

4

5 Quantity

6

7

1

8

9

10

(b) Group 2.

0

MR(QT)

QT 0

1

2

3

4

5 Quantity

6

7

8

9

10

(c) Total Market.

Figure 1: Third Degree Price Discrimination. π(Q1 , Q2 ) = P1 (Q1 )Q1 + P2 (Q2 )Q2 − C(Q1 + Q2 ); first order conditions

and

∂π =0 ∂Q1 ∂π =0 ∂Q2

give M R1 (Q1 ) = M C(Q1 + Q2 ),

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2 Peak-Load Pricing

2

and M R2 (Q2 ) = M C(Q1 + Q2 ); finally, M R1 (Q1 ) = M R2 (Q2 ) = M C(Q1 + Q2 ). Because M R1 = P1 (1 −

1 ), |E1 |

M R2 = P2 (1 −

1 ), |E2 |

and

we have

P1 1 − 1/|E1 | = ; P2 1 − 1/|E2 |

since |E1 | < |E2 |, P1 > P2 .

10

10

10

9

9

9

8

8

7

7

7

6

6

6

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5

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4

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3

2

2

1

0

MR1

0

1

D1 2

8

P2

3

4

5 Quantity

6

7

8

9

10

(a) Group 1.

MC(QT)

5

4

3

2

D2

Q2 MR2

1

0

Price

Price

Price

Sometimes a small group might not be served (see Figure 2). The producer only

0

1

2

3

4

1

5 Quantity

6

7

(b) Group 2.

8

9

10

0

MR(QT)

QT 0

1

2

3

4

5 Quantity

6

7

8

9

10

(c) Total Market.

Figure 2: Third Degree Price Discrimination with a Small Group. serves the second group, because the willingness to pay of the first group is too low.

2

Peak-Load Pricing

Producers charge higher prices during peak periods when capacity constraints cause higher M C. Example (Movie Ticket). Movie ticket is more expensive in the evenings. Example (Electricity). Price is higher during summer afternoons. For each time period, MC = MR (see Figure 3).

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3 Two-Part Tariff

3

10

10

9

9

8

MC

7

7

6

6 Price

Price

8

5

4

3

5

PM

4

3

PL

MR1

1

0

1

D1

QL 2

3

4

D2

MR2

2

2

0

MC

1

5 Quantity

6

7

8

9

0

10

QM 0

1

2

(a) Period 1.

3

4

5 Quantity

6

7

8

9

10

(b) Period 2.

Figure 3: Peak-Load Pricing.

3

Two-Part Tariff

The consumers are charged both an entry (T ) and usage (P ) fee, that is to say, a fee is charged upfront for right to use/buy the product, and an additional fee is charged for each unit that the consumer wishes to consume. Assume that the firm knows consumer’s demand and sets same price for each unit purchased. Example (Telephone Service, Amusement Park.). When there is only one consumer. If the firm sets usage fee P = M C, consumer consumes Q∗ units (see Figure 4), and the firm can set entry fee T = A, and extract all the consumer surplus. • If setting P1 > M C, total revenue is

R1 = A1 + P1 × Q1 ,

and cost is

C1 = M C × Q1 ,

then the profit is

π1 = A − B1 .

• If setting P2 < M C, total revenue is

R2 = A2 + P2 × Q2 ,

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3 Two-Part Tariff

4

10

9

8

7

CS

Price

6

A

5

MC

4

3

D

2

1

Q* 0

0

1

2

3

4

5 Quantity

6

7

8

9

10

Figure 4: Entry Fee of One Consumer.

10

10

9

9

8

8

CS 7

4

B2

5

3

D

2

1

1

2

3

P2

2

D

1

Q1 0

MC

A2

4

P1

3

0

CS

6

MC

B1

5

Price

6 Price

7

A1

Q* 4

5 Quantity

Q2

Q* 6

7

8

9

10

(a) Price Higher than Marginal Cost.

0

0

1

2

3

4

5 Quantity

6

7

8

9

10

(b) Price Lower than Marginal Cost.

Figure 5: Two-Part Tariff.

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3 Two-Part Tariff

5

and cost is

C2 = M C × Q2 ,

then the profit is

π2 = A − B2 .

Either B1 or B2 is positive, so the best unit price that maximized the producer surplus is exactly M C.

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1 Two-Part Tariff

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

November 19, 2007

Lecture 26

Pricing and Monopolistic Competition Outline 1. Chap 11: Two-Part Tariff 2. Chap 11: Bundling 3. Chap 12: Monopolistic Competition

1

Two-Part Tariff

When there are two consumers. Consumer 1 has higher demand than consumer 2. If setting P = M C, consumer 1 consumes Q1 units and consumer 2 consumer Q2 units. A1 is consumer 1’s consumer surplus, and A2 is consumer 2’s consumer surplus. Assume that 2A2 > A1 . Then the maximum entry fee the firm can charge is A2 . If more than A2 is charged, consumer 2 would not consume. 10

9

8

A1

7

Price

6

A2

5

MC

4

3

D1

2

Q2

1

0

0

1

2

3

D2

Q1 4

5 Quantity

6

7

8

9

10

Figure 1: Entry Fee of Two Consumers.

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1 Two-Part Tariff

2

Now consider the case that price is higher or lower than the marginal cost. • If setting

P > M C, T = A′2 ,

we have

π1 = A′2 + Q′1 × (P − M C) = A2 + C,

and

π2 = A′2 + Q′2 × (P − M C) = A2 − B,

thus

π = π1 + π2 = 2A2 + C − B.

Because C>B (see Figure 2),

π > 2A2 .

• If setting P < M C, T = A′′2 we have

π1 = A′′2 − Q′′1 × (M C − P ) = A2 − D,

and

π2 = A′′2 − Q′′2 × (M C − P ) = A2 − E,

thus

π = π1 + π2 = 2A2 − D − E.

Always

π < 2A2 .

Summary: the firm should set • usage fee P > M C, namely, larger than the marginal cost; • entry fee

T = A2 ,

namely, equal to the remaining consumer surplus of the consumer with the smaller demand. Summary: If the demands of two consumers are more similar, the firm should set usage fee close to M C and higher entry fee; if the demands of two consumers are less similar, the firm should set higher usage fee and lower entry fee.

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1 Two-Part Tariff

3

10

9

8

7

Price

6

A’1

5

A’2

4

3

P

C

B

2

MC

1

0

Q’2 0

1

2

Q’1 3

4

5 Quantity

6

7

8

9

10

Figure 2: Two-Part Tariff: Price Higher than Marginal Cost

10

9

8

7

Price

6

5

4

A’’1

A’’2

3

MC

2

D

1

0

P 0

Q’’2 1

2

3

4

5 Quantity

F

E

Q’’1 6

7

8

9

10

Figure 3: Two-Part Tariff: Price Lower than Marginal Cost

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2 Bundling

2

4

Bundling

Bundling means packaging two or more products, for example, vacation travel

usually has a packaging of hotel, airfare, car rental, etc.

Assume there are two goods and many consumers in the market, and the con­

sumers have different reservation prices (willingness to pay).

See Figure 4 and 5. The coordinates are the reservation prices of the two goods

respectively.

If the firm sells the goods separately with prices P1 and P2 (see Figure 4),

• when r1 > P1 , and r2 > P2 , the consumer will buy both good 1 and 2; • when r1 > P1 , but r2 < P2 , the consumer will only buy good 1; • when r2 > P2 , but r1 < P1 , the consumer will only buy good 2; • when

r1 < P < 1,

and

r2 < P < 2,

the consumer will buy neither good 1 nor 2. If the firm sells the two goods in a bundle and charges price PB , • if

r1 + r2 > PB ,

the consumer will buy the bundle; • if

r1 + r2 < PB ,

the consumer will not buy the bundle.

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2 Bundling

5

10

r2

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2

r1

1

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0

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Figure 4: Price without Packaging.

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r2

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6

5

4

3

2

r1

1

0

0

1

2

3

4

5

6

7

8

Figure 5: Price with Packaging.

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2 Bundling

6

10

r2

9

8

7

6

(5,5) .

.(4,4)

5

4

3

2

.(1,1)

1

0

0

1

.(2,2) r1 2

3

4

5

6

7

8

9

10

Figure 6: Bundling Example 1. Bundling Example 1: the four points in Figure 6 represent the four con­ sumers’ reservation values. Consider two pricing strategies – one is that the two goods are sold separately with prices P1 = 3 and P2 = 3, and the other is that the two goods are sold in a bundle with price PB = 6. Without bundling, the revenue is R = 12, and with bundling, the revenue is R = 12; bundling does not do better. Bundling Example 2: Consider the other four consumers shown in Figure 7 and the firm chooses between the two pricing strategies mentioned before. With­ out bundling, the revenue is R = 12, and with bundling, the revenue is R = 24; obviously, bundling strategy benefits the producer in this case Conclusion: bundling works well when • the consumers are heterogeneous; • price discrimination is not possible; • the demand for different goods are negatively correlated. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


3 Monopolistic Competition

7

10

r2

9

8

7

6

.

(1,5)

5

.

(2,4) 4

3

.(4,2)

2

.(5,1)

1

0

0

1

2

3

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5

r1 6

7

8

9

10

Figure 7: Bundling Example 2.

3

Monopolistic Competition

In monopolistic competition, • there are many firms; • there is free entry and exit; • products are differentiated but close substitutes. Thus • each firm faces a distinct demand, which is downward sloping and elastic; • there is no profit in long run (see Figure 8 and 9); • price is higher than marginal cost because firms have some monopoly power, and thus there is some deadweight loss.

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3 Monopolistic Competition

8

10

9

8

7

MC 6

P

P

S

5

PROFIT

AC

4

3

2

1

0

0

1

2

DS=AR

MR

QS

S

3

4

5 Q

6

7

8

9

10

Figure 8: Short Run in Monopolistic Competition Market.

10

9

8

7

MC

P

6

5

AC

4

PL

3

2

1

0

DL=AR

QL MRL 0

1

2

3

4

5 Q

6

7

8

9

10

Figure 9: Long Run in Monopolistic Competition Market.

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1 Game Theory

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

November 21, 2007

Lecture 27

Game Theory and Oligopoly Outline 1. Chap 12, 13: Game Theory 2. Chap 12, 13: Oligopoly

1

Game Theory

In monopolistic competition market, there are many sellers, and the sellers do not consider their opponents’ strategies; nonetheless, in oligopoly market, there are a few sellers, and the sellers must consider their opponents’ strategies. The tool to analyze the strategies is game theory. Game theory includes the discussion of noncooperative game and coopera­ tive game. The former refers to a game in which negotiation and enforcement of binding contracts between players is not possible; the latter refers to a game in which players negotiate binding contracts that allow them to plan joint strate­ gies. A game consists of players, strategies, and payoffs. Now assume that in a game, there are two players, firm A and firm B; their strategies are whether to advertise or not; consequently, their payoffs can be written as πA (A� s strategy, B � s strategy) and πB (A� s strategy, B � s strategy) respectively. Now let’s represent the game with a matrix (see Table 1). The first row is the situation that A advertises, and the second row is the situation that A does not advertise; the first column is the situation that B advertises, and the second column is the situation that B does not advertise. The cells provide the payoffs under each situation. The first number in a cell is firm A’s payoff, and the second number is firm B’s payoff. Dominant strategy is the optimal strategy no matter what the opponent does. If we change the element (20, 2) to (10, 2), no matter what the other firm does, advertising is always better for firm A (and firm B). Therefore, both firms have a dominant strategy. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Oligopoly

Firm A

2

Advertise Not Advertise

Firm B Advertise Not Advertise 10,5 15,0 6,8 20,2

Table 1: Payoffs of Firm A and B. When all players play dominant strategies, we call it equilibrium in dominant strategy. Now back to original case, B has dominant strategy, but A does not, because • if B advertises, A had better advertise; • if B does not advertise, A had better not advertise. So we see that not all games have dominant strategy. However, since B has dominant strategy and would always advertise, A would choose to advertise in this case. Now consider another example. Two firms, firm 1 and firm 2, can produce crispy or sweet. If they both produce crispy or sweet, the payoffs are (−5, −5); if one of them produces crispy while the other produces sweet, the payoffs are (10, 10).

Firm 1

Crispy Sweet

Firm 2 Crispy Sweet -5,-5 10,10 10,10 -5,-5

Table 2: Payoffs of Firm 1 and 2. There is no dominant strategy for both firms. We define another equilibrium concept – Nash equilibrium. Nash equilibrium is a set of strategies such that each player is doing the best given the actions of its opponents. In this case, there are two Nash equilibriums, (sweet, crispy) and (crispy, sweet).

2

Oligopoly

Small number of firms, and production differentiation may exist.

Different Oligopoly Models 1. Cournot Model: firms produce the same good, and they choose the pro­ duction quantity simultaneously. 2. Stackelberg Model: firms produce the same 3. Bertrand Model: firms produce the same good, and they choose the price. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2.1

2.1

Cournot Model

3

Cournot Model

Example. Market has demand P = 30 − Q, with two firms, so Q = Q1 + Q2 , and assume that there is no fixed cost and marginal cost, M C1 = M C2 = 0. Firm 1 would like to maximize its profit P × Q1 , or (30 − Q1 − Q2 ) × Q1 ; from the

d ((30 − Q1 − Q2 ) × Q1 ) = 0, dQ1

we have firm 1’s reaction function Q1 = 15 −

Q2 , 2

in which the Q2 is the estimation of firm 2’s production by firm 1. In the same way, firm 2’s reaction function is Q2 = 15 −

Q1 , 2

in which the Q1 is the expectation of firm 1’s production by firm 2. At equilibrium, firm 1 and firm 2 have correct expectation about the other’s production, that is, Q1 = Q1 , Q2 = Q2 . Thus, at equilibrium, Q1 = 10, and Q2 = 10.

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1 Stackelberg

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

November 26, 2007

Lecture 28

Oligopoly Outline 1. Chap 12, 13: Stackelberg 2. Chap 12, 13: Bertrand 3. Chap 12, 13: Prisoner’s Dilemma In the discussion that follows, all of the games are played only once.

and

1

Stackelberg

Stackelberg model is an oligopoly model in which firms choose quantities se­ quentially. Now change the example discussed in last lecture as follows: if firm 1 pro­ duces crispy and firm 2 produces sweet, the payoff is (10, 20); if firm 1 produces sweet and firm 2 produces crispy, the payoff is (20, 10) (see Table 1).

Firm 1

Crispy Sweet

Firm 2 Crispy Sweet -5,-5 10,20 20,10 -5,-5

Table 1: Payoffs of Firm 1 and 2. �

� −5, −5 10, 20 20, 10 −5, −5 This is an extensive form game; we use a tree structure to describe it. Firm 1 Crispy

Sweet Firm 2

Firm 2 Crispy

Sweet

Crispy

Sweet

(-5,-5)

(10,20)

(20,10)

(-5,-5)

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2 Bertrand

2

Start from the bottom using backward induction, namely, solve firm 2’s decision problem first, and then firm 1’s. If firm 1 chooses crispy, firm 2 will choose sweet to get a higher payoff. If firm 2 chooses sweet, firm 2 will choose crispy. Knowing this, firm 1 will choose sweet in the first place. In this case, going first gives firm 1 the advantage. Now consider the case we discussed for the Cournot model, but firm 1 chooses Q1 first, and firm 2 choose Q2 later. For firm 2, the first order condition d (30 − Q1 − Q2 ) × Q2 = 0 dQ2 gives that Q2 (Q1 ) = 15 −

Q1 . 2

For firm 1, d (30 − Q1 − Q2 (Q1 ) × Q1 = 0 dQ1 gives that Q1 = 15. Thus, the result will be Q1 = 15, π1 = 112.5; Q2 = 7.5, π2 = 56.25. In this case, firm 1 also has advantage to go first.

2

Bertrand

The Bertrand model is the oligopoly model in which firms compete in price. First assume that two firms produce homogeneous goods and choose the prices simultaneously. Assume two firms have the same marginal cost M C1 = M C2 = 3; consumers buy goods from the firm with lower price. If P1 = P2 = 4, the two firms share the market equally, but this is not the equilibrium. The reason is that one firm can get whole demand by lowering the price a little; therefore, the equilibrium will be P1 = P2 = 3,

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2 Bertrand

3

when the price is equal to the marginal cost. Now we check if P1 = 3 is the best choice for firm 1 given P2 = 3. When P1 = 3, π1 = 0; if P1 > 3, consumers will not buy firm 1’s goods, thus π1 = 0; if P1 < 3, the price is lower than the marginal cost, thus π1 < 0. It follows that P1 = 3 is optimal for firm 1; by analogy, we can get the same conclusion for firm 2. Therefore, P1 = P2 = 3 = M C in a Bertrand game with homogeneous goods. This is like the competitive market. Suppose the goods from the two firms are heterogeneous, but substitutes. Firm 1 and firm 2 face the following demands: Q1 = 12 − 2P1 + P2 , and Q2 = 12 − 2P2 + P1 . Firm 1’s and firm 2’s reaction functions are P1 = 3 +

P2 , 4

P2 = 3 +

P1 . 4

and

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3 Prisoner’s Dilemma

4

At equilibrium, P1 = P 1 , and P2 = P 2 ; so P1 = P2 = 4, Q1 = Q2 = 8, and π1 = π2 = 32. Consider the case when the firms choose prices sequentially. Supposing firm 2’s first order condition d (12 − P2 + P1 ) × P2 = 0 dQ2 and firm 1’s first order condition d (12 − 2P1 + P2 (P1 )) × P1 = 0. dQ1 From the first equation P1 , 4 and then substitute it into the second equation, we obtain P2 (P1 ) = 3 +

2 P1 = 4 . 7 Therefore,

1 π1 = 32 ; 4 1 P2 = 4 , 14

and

15 . 98 In this case, we can see that the firm who goes first has disadvantage, when competing in price. π2 = 33

3

Prisoner’s Dilemma

Criminals A and B cooperated, and then got caught. However, the police have no evidence; so they have to interrogate A and B separately, trying to make them tell the truth.

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3 Prisoner’s Dilemma

Firm A

5

Betray Silent

Firm B Betray Silent -3,-3 0,6 -6,0 -1,-1

Table 2: Payoffs of Firm A and B. The above matrix shows A and B’s payoffs. Given the payoffs, A and B choose to tell the truth (betray) or keep silent. We can see that, if they both keep silence, the result (−1, −1) is best for them; nonetheless, if one of them betrays another, he will be free but his companion will have payoff -6; moreover, if both of them betray, they will face the result (−3, −3). Consider what A thinks. Whether B keeps silence or betrays him, A will always be better off if he betrays; so will B. Therefore, the result of this problem is (−3, −3), namely, both prisoners betray.

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1 Collusion – Prisoners’ Dilemma

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

November 28, 2007

Lecture 29

Strategic Games Outline 1. Chap 12, 13: Collusion – Prisoners’ Dilemma 2. Chap 12, 13: Repeated Games 3. Chap 12, 13: Threat, Credibility, Commitment 4. Chap 14: Maximin Strategy

1

Collusion – Prisoners’ Dilemma

Last time we talked about the prisoners’ dilemma. The conclusion is that they will betray the other. Now apply it to the cases of Cournot and Bertrand models. In the Cournot model, the demand is P = 30 − Q1 − Q2 . The equilibrium will be Q1 = Q2 = 10, with π1 = π2 = 100. However, to maximize their total profits, they should choose a total quantity Q so that d (Q(30 − Q)) = 0, dQ which follows that Q = 15. If they share profit equally, Q1 = Q2 = 7.5, and π1 = π2 = 112.5.

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1 Collusion – Prisoners’ Dilemma

2

10

9

8

Q2(Q1)

7

6

5

4

3

Q1(Q2)

2

1

0

0

1

2

3

4

5

6

7

8

9

10

Figure 1: Reaction Curves in Cournot Model. Obviously, the latter case will make both of them better off. But given the opponent produces 7.5, each of them can increase the profit by producing more (see Figure 1). In Bertrand model, demand functions for firm 1 and firm 2 are Q1 = 12 − 2P1 + P2 , and Q2 = 12 − 2P2 + P1 . Equilibrium is P1 = P2 = 4, with π1 = π2 = 32. However, firms can choose P1 and P2 together to maximize the total revenue π = P1 (12 − 2P1 + P2 ) + P2 (12 − 2P2 + P1 ). By first order condition, we obtain 12 − 4P1 + 2P2 = 0, and 12 − 4P2 + 2P1 = 0.

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2 Repeated Games

3

Thus P1 = P2 = 6, with π1 = π2 = 36. But in this case, each firm has incentive to lower its price given the other firm’s price (see Figure 2).

10

9

8

P2(P1)

7

6

5

P1(P2)

4

3

2

1

0

0

1

2

3

4

5

6

7

8

9

10

Figure 2: Reaction Curves in Bertrand Model.

2

Repeated Games

Back to the prisoners’ problem. If suspect A and B will cooperate for infinite periods, and they are both patient, they care about future payoffs. Because if one of them betrays this time, the opponent will lose the trust and betray in the future; the payoff changes from −1 to −3 for each time. Therefore, both A and B would like to keep silence. But if they are impatient, and only consider today’s payoff, they will still betray. Now move on to the case that A and B will cooperate for finite number times which is fairly large. We deduce from the last time they cooperate; the answer is that they will betray for the last time, so will they for other opportunities. Therefore, the collusion between A and B succeed only if they will be cooperative forever and are patient.

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3 Threat, Credibility, Commitment

3

4

Threat, Credibility, Commitment

Back to the crispy-sweet question.

Firm 1

Crispy Sweet

Firm 2

Crispy Sweet

-5,-5 10,20 20,10 -5,-5

Table 1: Payoffs of Firm 1 and 2. Firm 1 Crispy

Sweet

Firm 2 Crispy (-5,-5)

Firm 2 Sweet

Crispy

Sweet

(10,20)

(20,10)

(-5,-5)

In order to get the largest 20 by producing sweet, firm 2 tries to make firm 1 believe that firm 1 should choose crispy by claiming that it always produces sweet no matter what firm 1 produces. However, firm 1 can ignore firm 2’s announcement because once firm 1 choose sweet, firm 2 will produce crispy. Suppose that firm 2 will advertise and so change the payoffs.

Firm 1

Crispy Sweet

Firm 2

Crispy Sweet

-5,-5 10,35 20,10 -5,10

Table 2: Payoffs of Firm 1 and 2. Firm 1

Crispy

Sweet

Firm 2

Firm 2

Crispy

Sweet

Crispy

Sweet

(-5,-5)

(10,35)

(20,10)

(-5,10)

In this case, firm 2 feels indifferent between choosing crispy or sweet when firm 1 produces sweet, and chooses sweet when firm 1 produces crispy. So it is credible if firm 2 claims that it always chooses sweet, and then firm 1 had better choose crispy. This example tells us that firm 2 had to do something to make the announcement credible. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


4 Maximin Strategy

4

5

Maximin Strategy

See Table 3. Firm B has dominant strategy: advertise. Therefore, the equilibrium should be both A and B advertise. However, if firm B does not choose the rational option, the minimum payoff of A is 5 if A advertises, and 8 if A does not advertise. The maximin strategy is the strategy that renders the highest minimum payoff. When A cannot tell whether B is rational or not, A might use maximin strategy. In this case, the maximin strategy of A is:

Firm A

Advertise Not Advertise

Firm B Advertise Not Advertise 10,5 5,0 8,8 15,2

Table 3: Payoffs of Firm A and B.

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1 Dominant Firm Model

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

November 30, 2007

Lecture 30

Dominant Firm Model and Factor Market Outline 1. Chap 12, 13: Dominant Firm Model 2. Chap 14: Factor Market

1

Dominant Firm Model

The dominant firm model is the model that in some oligopolistic markets, one large firm has a major share of total sales, and a group of smaller firms supplies the remainder of the market. The large firm has power to set a price that maximizes its own profits. A dominant firm exists because it has lower marginal cost than the other fringe firms. Assume the fringe firms’ total supply is SF , the market demand is DM , then the dominant firm’s demand is (see Figure 1) D D = D M − SF . Knowing DD , we can derive M RD . The dominant firm produces at a quantity QD that satisfies M RD = M CD . Correspondingly, the price is P ∗ . The fringe firm’s supply curve thus shows QF . Furthermore, the total quantity is QT = QF + QD . Example (OPEC). OPEC is an example of a successful cartel, which can be regarded as a dominant firm. Cartels are more likely to succeed if • demand is inelastic, and • supply of non-Cartel producers is inelastic.

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2 Factor Market

2

10

9

8

P*

MCD

DM

7

DD

P

6

5

SF

4

3

MRD

2

1

0

QF 0

1

2

QD 3

QT 4

5 Q

6

7

8

9

10

Figure 1: Dominant Firm Model.

2

Factor Market

The last chapters were about product market, or output market, in which • individuals are buyers, and • firms are producers; we start to discuss factor markets, or input markets, in which • individuals are producers, and • firms are buyers.

Firms need labor and capital to produce.

Outline 1. Demand of Labor 2. Supply of Labor

2.1

Demand of Labor

Demands of labor are different in short run and long run markets, and condi­ tional and unconditional market (see Table 1). Firms use labor and capital as input. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2.1

Demand of Labor

Conditional Unconditional

3

Short Run Output price fixed Other factors fixed Output Price varies Other input factors fixed

Long Run Output price fixed Other input factors vary Output Price varies Other Inputs vary

Table 1: Demand of Labor. Short Run Demand of Labor. Only labor is variable. The prices for L and K are w and r respectively.

Define marginal revenue product of labor M RPL to be additional revenue

from an additional unit of labor.

M PL is the additional output obtained from an additional unit of labor;

M R is the additional revenue from an additional unit of output. Therefore,

M RPL =

dR dR ∂Q = = M R × M PL . dL dQ ∂L

Firm chooses Q such that w = M RPL (L), so the marginal revenue and marginal cost at hiring one more unit of labor are the same. • If output market is competitive, MR = P; if it is not competitive, MR < P (see Figure 2 and 3). • Given w, we derive the firm’s demand for labor from w = M RPL (L). M RPL decreases in L; therefore, M RPL is the firm’s short run de­ mand curve. Long Run Demand of Labor. Both K and L are variable. w decreases then M C decreases, Q increases, and L increases. With higher L, M PK increases, so the firm uses more K, and then M PL increases further, and the firm hires more labor. Thus, the demand of labor is more elastic than that in short run (see Figure 5).

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2.1

Demand of Labor

4

10

9

8

7

P

6

5

MPL× P

4

MPL× MR

3

Competitive

Not Competitive

2

1

0

0

1

2

3

4

5 L

6

7

8

9

10

Figure 2: Marginal Revenue Product of Labor.

10

9

8

7

W

6

5

DL=MPL× MR

4

3

2

1

0

0

1

2

3

4

5 L

6

7

8

9

10

Figure 3: Marginal Revenue Product of Labor in Competitive Market.

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2.1

Demand of Labor

5

10

9

8

7

W

6

DL

5

4

3

2

1

0

0

1

2

3

4

5 L

6

7

8

9

10

Figure 4: Marginal Revenue Product of Labor Increases in Price.

10

9

MRP,L

8

7

W

6

MRPL

5

DL

4

3

2

1

0

0

1

2

3

4

5 L

6

7

8

9

10

Figure 5: Marginal Revenue Product of Labor in Long Run.

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2.1

Demand of Labor

6

10

9

8

7

W

6

MRP,L

5

DL MRPL

4

3

2

1

0

0

1

2

3

4

5 L

6

7

8

9

10

Figure 6: Unconditional on Output Market Price. Unconditional on Output Market Price. The discussion before was based on the assumption that the output price is fixed. Now consider the case when the output price is unconditional so that it is not fixed. If w decreases, L increases and Q increases, and so P decreases; with

M RPL decreases, Q and L decrease.

The demand is less elastic than when output P is fixed (see Figure 6).

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1 Supply of Labor

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

December 3, 2007

Lecture 31

Factor Market Outline 1. Chap 14: Supply of Labor 2. Chap 14: Demand of Labor

1

Supply of Labor

We derive the supply of labor by solving consumers’ utility maximization prob­ lems. Two variables determining the utility are leisure (L), which is measured by hours, and income (Y ); the prices are w and 1 respectively. To maximize u(L, Y ), we have ∂u ∂L ∂u ∂Y

= w.

If w increases, on one hand, higher wages encourage people to work more (point A to point B), which is a substitution effect; on the other hand, higher wages allow the worker to purchase more goods, including leisure, which reduces work hours (point B to point C), which is an income effect (see Figure 1). When the wage is higher, if the substitution effect exceeds the income effect, labor supply increases, and leisure decreases; if the income effect exceeds the substitution effect, labor supply decreases, and leisure increases (see Figure 2). Like product markets, competitive, monopolistic, and monopsonistic mar­ kets are types of factor markets. In a competitive factor market, if the product market is also competitive, M RPL = P × M PL . If the product market is monopolistic, M RPL = M R × M PL = P (1 −

1 ) × M PL . |ed |

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1 Supply of Labor

2

10

9

8

7

C Y

6

B

5

4

A

Income Effect

3

2

1 Substitution Effect 0

2

3

4

5

6

7 L

8

9

10

11

12

Figure 1: Substitution Effect and Income Effect of Labor Supply.

10

9

8

7

Wage

6

Supply of Labor Income Effect > Substitution Effect

5

Income Effect < Substitution Effect

4

3

2

1

0

3

3.5

4

4.5

5 5.5 6 Hours of Work per Day

6.5

7

7.5

8

Figure 2: Backward-Bending Supply of Labor.

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1.1

Factor Competitive

3

10

9

8

SL

7

w

6

w*

5

4

3

DL=P× MPL

2

1

0

L* 0

1

2

3

4

5 L

6

7

8

9

10

Figure 3: Competitive Factor Market.

1.1

Factor Competitive

Competitive market is most efficient, and there is no deadweight loss (see Fig­ ure 3). When M R < P , both w and L decrease; the market is then not as efficient as competitive market, and has deadweight loss (see Figure 4).

1.2

Factor Monopsony

Marginal Value equals the demand. Marginal Expenditure ME =

∂PS (Q)Q ∂PS = Q + PS > PS . ∂Q ∂Q

Because L is determined by M E = M V, we can see that

w < w∗ , and

L < L∗ (see Figure 5). One example of factor monopsonist is the government hiring soldiers.

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1.2

Factor Monopsony

4

10

9

8

SL

7

w

6

w*

5

P× MPL

w,

4

3

2

1

0

L, L* 0

1

2

3

4

DL=MR× MPL

5 L

6

7

8

9

10

9

10

Figure 4: Noncompetitive Factor Market.

10

9

ME 8

S=AE

7

w

6

w*

5

4

w,

3

D=MV 2

1

0

L, 0

1

2

3

L* 4

5 L

6

7

8

Figure 5: Monopsonistic Factor Market.

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1.3

1.3

Factor Monopoly

5

Factor Monopoly

An example of monopoly power in factor markets involves labor unions. Economic rent is the difference between payments to a factor of production and the minimum payment that must be spent to obtain the factor; it is like producer surplus in a product market (see Figure 6).

10

9

8

SL

7

6

w

w 5

Economic Rent

4

3

2

1

0

0

0.5

1

1.5

2 L

2.5

3

3.5

4

Figure 6: Economic Rent. When some workers lose their jobs, remaining workers have higher wages. If the union tries to maximize the number of workers hired, it should set the wage and labor employed w∗ and L∗ ; if the union tries to maximize economic rent, it should set the wage and labor employed w1 and L1 . w1 > w∗ , and L1 < L∗ (see Figure 7). It is hard to say which one is better for the workers. Now consider a model of union workers and non-union workers. Assume the demand for union workers is DU , and the demand for non-union workers is DN U . The total market demand DL = DU + DN U is fixed.

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1.3

Factor Monopoly

6

10

9

8

SL

w,

7

w

6

w*Economic

5

Rent 4

3

DL

MR 2

1

0

L, 0

1

2

3

L* 4

5 L

6

7

8

9

10

Figure 7: Monopoly Power of Sellers of Labor. When a monopolistic union raises the wage rate in the unionized sector of the economy from w∗ to wU , employment in that sector falls; for the total supply of labor to remain unchanged, the number of non-union workers increases and the wage in the non-unionized sector must fall from w∗ to wN U (see Figure 8). Assume the total supply of workers is 60; the demands for nonunion and union workers are 1 wN U = 30 − LN U , 2 wU = 30 − LU . • When the union does not intervene, wN U = wU = w. Thus

LN U = 60 − 2w,

and

LU = 30 − w.

Then

L = 90 − 3w = 60,

which gives

w = 10,

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1.3

Factor Monopoly

7

10

9

wU

8

SL

7

DU

w

6

DNU

w*

5

4

3

wNU

2

DL

1

0

0

1

2

3

4 5 6 Number of Workers

7

8

9

10

Figure 8: Wage Discrimination in Labor Market. and therefore

LU = 20,

LN U = 40. • When the union maximizes the total wage of union workers as a monop­ olist, the first order condition is d d (wU × LU ) = (30 − LU ) × LU = 0. dLU dLU Then

30 − 2LU = 0,

LU = 15;

thus

wU = 15.

For the nonunion workers,

LN U = 45,

wN U = 7.5.

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2 Demand of Supply

2

8

Demand of Supply

In competitive factor market, assume Q = 10L − L2 , and P = 1. M RPL = M PL × M R = 10 − 2L. w is marginal cost of hiring labor, thus w = 10 − 2L, then LD =

10 − w . 2

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1 Present Discount Value

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

December 5, 2007

Lecture 32

Investment, Savings, Time and Capital Markets Outline 1. Chap 15: Present Discount Value 2. Chap 15: Bond 3. Chap 15: Effective Yield 4. Chap 15: Determine Interest Rate

1

Present Discount Value

Present discount value (PDV) determines the value today of a future flow of income. Payment A Payment B

Today 100 20

1 year 100 100

2 year 0 100

Table 1: Two Payments. Consider the two payments, A and B, in Table 1.

Because the present value of 1 dollar in n years is

1

, (1 + r)n where r is the interest rate, the present values of A and B are 100 + and 20 +

100 , 1+r

100 100 + , 1 + r (1 + r)2

respectively. • If r is low, P V of B is larger than P V of A. • If r is high, P V of A is larger than P V of B. Several examples are provided in Table 2. Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].


2 Bond

2

Value of r P V of A P V of B

0.05 195.24 205.94

0.10 190.90 193.54

0.15 186.96 182.57

Table 2: Present Values.

2

Bond

A bond is a contract in which a borrower (issuer) agrees to pay the bondholder (the lender) a stream of money. For instance, a payment consists of a coupon payment of 100 dollars per year for 10 years, and a principal payment of 1000 dollars in 10 years. P V of the bond is PV =

100 100 100 1000 + + ... + + . 1 + r (1 + r)2 (1 + r)10 (1 + r)10

With a higher interest rate, the present discount value is lower (see Figure 1).

10

9

8

7

PDV

6

5

4

3

2

1

0

2

3

4

5

6

7 r

8

9

10

11

12

Figure 1: Present Discount Value and Interest Rate. Perpetuity is a bond that pays a ďŹ xed amount of money each year forward: PV =

100 100 100 + + ... = . 2 1 + r (1 + r) r

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3 Effective Yield

3

3

Effective Yield

Effective yield is the interest rate that equates the present value of a bond’s payment stream with the bond’s market price. Riskier bonds have higher yields. An effective yield equals risk-free interest rate plus risk premium. When we choose between projects, we can compare the present value, or compare the yield rate, and choose the higher one. Time (Year) Project A (Dollar) Project B (Dollar)

0 -50 -20

1 5 4

2 55 24

Table 3: Two Projects. Assume

r = 15%.

P V of A is -4, and P V of B is 11. P V of B is higher; thus firm should invest in B. Now calculate the yield rates. For project A, 5 55 50 = + , 1 + rA (1 + rA )2 rA = 10%. For project B, 20 =

4 24 + , 1 + rB (1 + rB )2 rB = 20%.

Here yield rate of B is higher. Firm should invest in B again. In this case, the results of both criteria are consistent; however, they are not always consistent.

4

Determine Interest Rate

The interest rate is the price that borrowers pay lenders to use their funds. It is determined by supply and demand for loanable funds. Demand for loanable funds comes from firms and governments that want to make capital investments. Supply of loanable funds comes from household savings (see Figure 2). Suppose a consumer only lives for two periods, intertemporal utility function u(C1 , C2 ) will be maximized, under the budget constraint P V = Y1 +

Y2 C2 = C1 + , 1+r 1+r

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4 Determine Interest Rate

4

10

9

8

Savings 7

Interest Rate

6

5

4

3

Investment

2

1

0

0

1

2

3

4 5 6 Quantity of Loanable Funds

7

8

9

10

Figure 2: Supply and Demand of Funds. in which C1 and C2 stand for consumptions in period 1 and 2, and Y1 and Y2 are incomes in period 1 and 2 respectively. When the consumer’s utility is maximized ∂u ∂C1 ∂u ∂C2

= 1 + r.

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1 Adverse Selection

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

December 7, 2007

Lecture 33

Asymmetric Information Outline 1. Chap 17: Adverse Selection 2. Chap 17: Moral Hazard

1 1.1

Adverse Selection Used Car Market

Buyers do not know the quality of each car but know quality distribution. Assume there are three cars, and their prices are 0, 5, and 10, respectively. The consumer’s willingness to pay is 5, so the seller of 10 will leave the market. As a result, the consumer’s willingness to pay decreases to 2.5; thus the seller of 5 will leave the market. Finally, the willingness to pay decreases to 0; market fails, and only car stays is the worst one. This is called the Lemon Problem.

1.2

Insurance Market

Insurance companies do not know how healthy each person is. For instance, the probabilities of getting sick of A and B are shown in Table 1. When one is sick, the insurance company gives him 10 dollars to cover medical expense.

A B

Sick 0.1 0.5

Healthy 0.9 0.5

Table 1: Probability of Health. Thus the expected expense for A is 1, and that for B is 5.

Since the company cannot tell who is healthy, it sets a premium of 3.

Those healthy people who are risk-averse enough would accept the $3 pre­

mium; those who are not risk-averse enough would reject the $3 premium. If

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2 Moral Hazard

2

only unhealthy people accept the insurance contract, the insurance company has to adjust the premium to $5. Solve this problem by requiring people to do a physical examination before buying insurance – the examination works as a certificate, like credit history for banks.

2

Moral Hazard

Moral hazard occurs when the insured party whose actions are unobserved by the insurer can affect the probability or magnitude of a payment associated with an event. For example, it often occurs in insurance: if my home is insured, I might be less likely to lock my doors or install a security system. Assume jewelry is worth $10. The probability to be stolen is 0.5. If the owner spend $2 to hire a guard, the probability decreases to be 0.1. Because 10 × 0.9 + 0 × 0.1 − 2 = 7, 10 × 0.5 + 0 × 0.5 = 5, one will hire a guard. If the owner asks for insurance, and the insurance will pay $10 if the jewelry is stolen. If the owner hires a guard, the actuarially fair insurance premium is p = 10 × 0.1 = 1. However, the owner buys the insurance, he will not hire a guard. If the insurance company only cover $4.9 when stolen; and the insurance premium is P : Hiring a guard, the owner’s payoff is 10 × 0.9 + 4.9 × 0.1 − 2 − P = 7.49 − P ; not hiring a guard, the owner’s payoff is 10 × 0.5 + 4.9 × 0.5 − P = 7.45 − P. Thus, the owner will hire a guard, and the actuarially fair insurance premium is P = 4.9 × 0.1 = 0.49.

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1 Efficient Wage Theory

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

December 10, 2007

Lecture 34

Externalities, Market Failure and Government Outline 1. Chap 17: Efficient Wage Theory 2. Chap 18: Externalities 3. Chap 18: Property Rights 4. Chap 18: Common Property Resources

1

Efficient Wage Theory

Use the efficient wage theory to explain the presence of unemployment. Suppose the wage is w, and workers can choose to work or shirk provided a benefit of S. The unemployment rate is u, and the workers get caught and fired with a probability p. If a worker shirks, he can get S + (1 − p)w + p(1 − u)w = S + w(1 − pu), if a worker does not shirk, he gets w. Therefore, a worker will work if w � S + w(1 − pu), that is, w�

S . pu

This is called nonshirking constraint. Without information asymmetry, the market wage is wC , and full employ­ ment exists at LC . With information asymmetry, the nonshirking constraint and the demand of labor determine the wage w∗ and labor L∗ (see Figure 1). With greater asymmetric information, the probability that shirking is de­ tected, P decreases, and thus the nonshirking constraint rises. The wage and ′ labor are w and L′ respectively (see Figure 1). Thereby

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2 Externalities

2

10

9

Nonshirking Constraint SL

8

7

w

6

w’ w*

5

4

3

wC

2

DL

1

L’ 0

0

1

2

3

LC

L* 4

5 L

6

7

8

9

10

Figure 1: Unemployment in a Shirking Model. • w∗ > wC , L∗ < LC ; •

w > w∗ , ′

L < L∗ .

2

Externalities

Externalities are the effects of production and consumption activities not di­ rectly reflected in the market. They can be negative or positive. Negative Externalities. Action by one party imposes a cost on another party. Example (Pollution). Pollution is not reflected in market because at mar­ ket, residents do not demand firm pay for that cost. Positive Externalities. Action by one party benefits another party. Example (Beautiful Garden). If your neighbor has a beautiful garden, you are happier, but you do not pay your neighbor.

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2 Externalities

3

Negative Externality An example is steel plant dumping waste in the river as it makes steel. That imposes cost on fisherman downstream. Marginal external cost (M EC) is the increase in this cost for each additional unit of steel production. Marginal social cost (M SC) is M C plus M EC. Given the market price P , a firm chooses to produce q1 , but if taking external cost into account, a firm should produce at q ∗ (see Figure 2).

10

9

MSC 8

7

MC

P

6

5

4

3

2

0

q1

q*

1

0

1

2

3

4

5 Q

6

7

8

9

10

Figure 2: A Firm with Negative Externality. In a competitive market, the equilibrium price and quantity are P1 and q1 , but the efficient outcome should be P ∗ and q ∗ (see Figure 3). The failure to incorporate external cost creates deadweight loss.

Positive Externality Landscaping generates external benefits to the neighbors. Like the example above, the marginal social benefit (M SB) is the sum of private benefit (which is the demand) and the marginal external benefit (M EB). The quantity q1 consumed in the market is less than the efficient level q ∗ (see Figure 4).

Solution to Externality Here are some solutions with government intervenes.

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2 Externalities

4

10

9

MSC 8

DWL

7

MC

6

P

P* 5

4

P1

3

D

2

1

0

0

q1

q* 1

2

3

4

5 Q

6

7

8

9

10

Figure 3: The Whole Industry with Negative Externality.

10

9

8

7

P

6

P1

5

MC

4

3

2

MSB

1

0

q1 0

1

2

D

q* 3

4

5 Q

6

7

8

9

10

Figure 4: External BeneďŹ ts.

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3 Property Rights

5

• Tax each unit produced by M EC. The marginal cost of the firm is M C + T = M C + M EC = M SC,

then the firm will choose efficient output.

• Create a standard and monitor pollution. Control the quantity produced or pollution emission.

3

Property Rights

When property rights are well-specified, economic efficiency may be achieved without government intervention. • Factory can install a filter. • Fishermen can pay for a treatment plant to intercept and clean up factory waste. Factory No Filter Filter No Filter Filter

Fishermen No Treatment No Treatment Treatment Treatment

Factory’s Profit 500 300 500 300

Fishermen’s Profit 100 500 200 300

Total Profit 600 800 700 600

Table 1: Profits Under Alternative Emissions Choices. In this case (see Table 1), the most efficient result is that factory installs filter and fishermen do not pay for treatment. • If fishermen own the river, they can sue the plant for damages $400. The factory has two options. – The factory do not install the filter and pay damages. Profit 500 − 400 = 100. – The factory install filter. Profit is 300.

Thus the factory will install the filter.

• If factory owns the river, fishermen have three options. – Fishermen put in treatment plant. Profit is 200. – Fishermen pay the cost of filter installation to the factory. Profit 500 − 200 = 300.

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4 Common Property Resources

6

– No plant, no filter. Profit is 100. A payment to the factory by the fisherman results in an efficient outcome and is in their own interest. Theorem (Coase Theorem). When parties can bargain without cost and to their mutual advantage, the outcome will be efficient, regardless of how the property rights are specified.

4

Common Property Resources

Everyone has free access to a renewable resource, for example, lake, forest, and so on. Without control, the quantity consumed is q1 where private cost is equal to marginal benefit (demand). However, the efficient level of quantity is q ∗ where M SC = M B(D) (see Figure 5).

10

9

MSC

8

Private Cost

7

P

6

5

P1

4

3

D (MB)

2

1

0

q1

q* 0

1

2

3

4

5 Q

6

7

8

9

10

Figure 5: Common Property Resources. Some measures to prevent from consuming too much: • Government puts restrictions on production quantity. • Set private ownership and the owner sets fees for use of resources.

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1 Public Goods

1

14.01 Principles of Microeconomics, Fall 2007

Chia-Hui Chen

December 12, 2007

Lecture 35

Public Goods Outline 1. Chap 18: Public Goods

1

Public Goods

Characteristics of public goods: Nonrival. For any given level of production, the marginal cost of providing it to an additional consumer is zero: enjoy it rather than use it up. Nonexclusive. People cannot be excluded from consuming the good. Difficult to charge for its enjoyment. Example (Roads). Example (Streetlight). Once streetlight is setup, everyone can see the light (nonexclusive). It is more efficient to have government provide public goods. Government provides and imposes tax. Free-rider problem. Consumer need to pay for public goods, and they tend to understate the value. Example (Streetlight). Assume cost of building a street light is 1. A’s and B’s reservation values for the street light are both 1, but they are not known by government. Then government asks A and B to announce their value. The street light will be built if VA + VB � 1, and people who have value share the cost. Their payoffs are shown in Table 1). Therefore, A and B will both announce the value as 0. The result is inefficient: consumers wait for others to pay for the public goods.

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1 Public Goods

2

B

A

Announce Value as 0 Announce Value as 1

Announce Value as 0 0,0 0,1

Announce Value as 1

1,0 1/2,1/2

Table 1: PayoďŹ&#x20AC;s of A and B.

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Macroeconomics