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Problems 1. Decide whether each of the following statements is True, False, or Uncertain, and give a brief but clear explanation of your answer. (Most of the credit will be given for the explanation.) (a) If average cost is falling, marginal cost must be falling as well. (b) Paint prices have risen in the past year, largely due to oil price increases. When defining the market for paint, oil companies should be included.

2. With Hurricane Rob approaching, the market conditions for plywood to protect homes are given by: Demand: P = 30 – Qd Supply: P = 4 + Qs where Q is measured in tons and P is in thousands of dollars per ton. (c) Graph the supply and demand for plywood. Find the equilibrium quantity and price.

Calculate the consumer surplus. (d) Newspapers often report that retailers are taking advantage of consumers by charging high prices during these times of crisis. Consider if the local government passed a consumer protection law that set P=5. How much would be supplied? How would consumer surplus compare to part (a)? economicshomeworkhelper.com

3. A local franchise has a monopoly on Krispy Kreme doughnuts with daily demand and cost given by: Demand: P = 150 – 2Q Cost: C = 250 + 30Q where Q is hundreds of donuts, P=price per 100 donuts, and C is in dollars. (a) To maximize profits, how many doughnuts will be sold daily? At what price? What will daily profits be? (b) Concerned about rising health care costs of municipal employees, the local government raises Krispy Kreme’s real estate taxes, causing its daily fixed costs to increase from 250 to 350. How much will its daily sales change?

4. Old McAdams had a farm. … And on this farm, he grows some corn. … To grow corn, he needs a tractor. A new tractor costs $100,000. There is a very active resale market for tractors; a tractor that is one year old sells for $70,000 and a tractor that is two years old sells for $45,000. For simplicity, assume that all tractors three or more years old cannot be used to grow corn and sell for $0. These prices are expected to stay the same in the future. The variable cost of producing corn is the same regardless of whether you are using a tractor that is new, one year old or two years old. economicshomeworkhelper.com

(a) Old McAdams faces an interest rate of 10%. What is the user cost of capital associated with using a new tractor for one year? What is the user cost of capital associated with using a one year old tractor for one year? What is the user cost of capital associated with using a two year old tractor for one year? (b) Old McAdams is formulating a plan for growing corn for the next three years. What is the optimal arrangement for the necessary tractor input over the three years? (For instance, should he buy a new tractor and use it for three years, or something else?)

5. Your company produces a specialized pump, that sells at a price around $60. Your factory (A) can produce these pumps with the following cost structure: the first 5000 units are produced at a constant (marginal) cost of $15 a unit, and the next 5000 units are produced at a constant (marginal) cost of $45 a unit. Factory A has a fixed cost of C (specified below), and a sunk cost of $257,000 from initial factory set-up.

Demand is soaring; you expect to sell 8000 units. Because of this, you develop a new outsourcing division (B) that arranges for production of the pumps in Korea, at a constant cost of $20 per unit (including transportation and other fees), with no fixed costs. (a) Graph the marginal cost for Factory A. Graph the marginal cost for Division B. economicshomeworkhelper.com

(b) If there were no fixed cost (C = 0) in factory A, how much should you produce in factory A, and how much should you outsource to B? (c) Does your answer change if A’s fixed cost were C = $20,000? How would your answer change if A’s fixed cost were C = $45,000? (d) Consider the case above where C = $45,000.

You are worried about the international situation. In particular, depending on the outcome of the November elections, you feel there is a .5 probability that your outsource costs stay at $ 20 per unit, and that there is a .5 probability that your outsource costs double to $40 per unit, for all units. (You are risk neutral.)

Suppose you must decide whether to pay the $45,000 now to keep Factory A open.

Should you make the investment? (Show any calculations used to arrive at your answer.)

6. Short Answer. For many years, a large number of charter boats have operated out of Boston Harbor that take people out to fish. In this competitive market, the price of a full day’s fishing is $150 per person. Boats hold up to 12 people and will operate on any given day as long as at least 6 people sign up. On average, over the entire season, 8 people a day go out on each boat. The cost of a trip is the same regardless of the number of people on board. economicshomeworkhelper.com

In light of the information provided above, what can be said (numerically) about the variable cost of operating a fishing boat trip in Boston Harbor?

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Solutions 1a) False. If average cost is falling, marginal cost must be less than average cost, but marginal cost may be rising as average cost is falling

1b) False. Oil companies represent neither demand nor supply substitutes for paint.

That is, if paint companies increased the price, consumers could not substitute crude oil for the paint, and oil companies are unlikely to enter the paint market.

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2b) Quantity supplied = 1: 1 ton. Consumer surplus falls compared to part (a). The maximum amount of consumer surplus occurs when those with the highest valued use for plywood are able to purchase it (see graph below ).

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Choose Q to maximize profit by taking the derivative of profit with respect to Q & setting it equal to zero: 150 – 4Q – 30 = 0 Ù 150 – 4Q = 30 (Marginal Revenue = Marginal Cost) Solve for Q: Q = 30, or 3,000 donuts Price is then read off the demand curve: P = 150 – 2 * 30 = $90 per 100 donuts Daily Profits = 90 * 30 – (250 + 30*30) = 2700 – 1150 = $1550 3b) With FC=350, the revenues are still greater than the economic cost of production, and KK will not shut down. In other words, profits fall by $100 to $1450, but profits>0 implies that the firm will not shut down. Since marginal cost is unaffected by the increase in fixed costs, daily sales (and price per doughnut) will be the same as in 3a).

Common Mistakes: Part A: 1. The equation given was in the form of P as a function of Q. You can use the shortcut of “doubling the slope” of the demand curve to get MR only if the equation is written in this form. If the equation is in the form of Q as a function of P, you need to rearrange the equation. economicshomeworkhelper.com

2. MC is calculated by taking the first derivative of the cost function, so for (250 + 30Q), MC = 30. You can not use the shortcut of “doubling the slope” for the MC curve.

3. Profit is calculated as Total Revenue minus Total Costs. Total costs include fixed cost. If you want to use the following equation, don’t forget to subtract fixed costs: (P – MC)*Q – FC. Part B 1. FC do not affect the amount of quantity produced and price. However, FC do affect the company’s decision of whether or not to shut down. Thus, we also need to look at the change in profit as a result of the FC increase. If economic profit is negative, daily sales would change because the company should shut down instead of operating.

4) This problem is the same as a question on 2002’s midterm. a) The User Cost of Capital for each type of tractor is as follows: UCC for 1-year use of new tractor = (100,000 – 70,000) + 10%*100,000 = $40,000 UCC for 1-year use of 1-year-old tractor = (70,000 – 45,000) + 10%*70,000 = $32,000 UCC for 1-year use of 2-year-old tractor = (45,000 – 0) + 10%*45,000 = $49,500

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b) Since variable cost is the same for all types of tractors, and there is no cost of reselling, each year Old McAdams should use whatever tractor has the lowest UCC. Hence, the best plan is to purchase a 1 year old tractor at the start of each year and sell that tractor (now 2 years old) at the end of each year.

5b) With no fixed cost, you produce 5000 units in A at $15 each and outsource 3000 units in B at $20 each. Note that by producing the first 5000 in Factory A, you save (2015)*5000 = $25,000 in total costs.

5c) With the fixed cost of C = $20,000, you still save $25,000-$20,000 = $5,000 with the above scheme, so your answer doesn’t change.

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With the fixed cost of C = $45,000, if you produce 5000 units in factory A, you lose $20,000 = $45,000 - $25,000. Therefore you would outsource all units (and shut down factory A, avoiding the fixed cost).

5d) You should pay the $45,000, because the value of keeping it open is greater than this cost. To see this, we need to compute the value of having the option to use Factory A in the future.

The revenue side is the same regardless of the uncertainty. 3000 will be outsourced whether the marginal cost is $20 or $40. So, we can focus on the costs of the first 5,000 units. We need to calculate the expected cost with and without Factory A. First, consider the potential costs of outsourcing versus using Factory A: Outsource costs of 5000 units at $20: OC1 = 20*5000 = 100,000 Outsource costs of 5000 units at $40: OC2 = 40*5000 = 200,000 Cost of 5000 units in factory A after the investment of $45,000: 15*5000 = 75,000 Expected Costs for 5000 units without factory A: .5 * 100,000 + .5 * 200,000 = 150,000.

Expected Costs for 5000 units with factory A: 75,000 Therefore the option value of keeping Factory A open is: 150,000 – 75,000 = 75,000. economicshomeworkhelper.com

This is greater than the cost of purchasing the option ($45,000), so you should make the investment.

Note: If you used all 8,000 you get the same answer: Expected Costs for 8000 units without factory A: .5 * (8000*20) + .5*(8000*40) = $240,000 Expected Costs for 8000 units with factory A: .

5 * (5000*15 + 3000*20) + .5*(5000*15 + 3000*40) = $165,000 Therefore the option value of continuing to operate factory A is: 240,000 – 165,000 = 75,000 Note 2: If you used profits (and assumed P=60ÆRevenue of 60*8000=480,000), same answer: Expected Profit for 8000 without A: 480,000 – 240,000 = $240,000 Expected Profit for 8000 with A: 480,000 – 165,000 = $315,000 Option Value: $315,000 - $240,000 = $75,000.

Note 3: This is similar to the VHS/Beta example from lecture, calculating the expected value with and without Beta, here it is the expected costs with and without Factory A. Some students approached the problem as in problem set 3, question 3, where a more complicated option value question was asked. In that problem, the value of having the uncertainty resolved before making the investment was calculated. The investment decision here considers the value of flexibility due to the investment (the option of using Factory A if MCb=$40).

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6) A profit maximizing firm will not produce in the short run if it cannot cover its variable costs of production. Examples of such costs here would be fuel and labor—costs that vary with the running of a boat trip.

In this market, the firms will not produce on any given day if 5 (or fewer) people sign up, but will produce on any given day if 6 people do. If 5 people sign up, the firm would receive $750. If 6 people sign up, they receive $900. Therefore, the variable cost of operating a fishing boat trip must be between $750 and $900 a day. (Recognizing the cost of the trip as $750 or $900 was accepted).

Common Mistakes: -Recognizing the average cost in the competitive market is 8*150=1200, which will cover total cost, but not calculating the variable cost.

-Recognizing that the cost does not vary with the number of people, but not calculating the cost of operating the boat trip (regardless of the number of people).

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