Microeconomics Goolsbee 1st Edition Test Bank
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1. Which of the following statements is TRUE?
I. Accounting profit = total revenue – accounting cost.
II. Economic cost = accounting cost – opportunity cost.
III. Economic profit = accounting profit + opportunity cost.
IV. Economic profit = total revenue – economic cost.
A) I and IV
B) I, II, III, and IV
C) II and IV
D) I, III, and IV
2. Lilly's Lumber Yard had the following revenues and costs last year:
If Lilly did not own a lumber yard, she would earn $115,000 per year as a store manager for Home Depot. Lilly's lumber yard had an economic cost of ______ and an economic profit of ______.
A) $225,000; – $75,000
B) $400,000; $35,000
C) $405,000; – $5,000
D) $210,000; $0
3. Debbie, a popular wedding photographer, is able to photograph a wedding every Saturday of the year. She charges couples $4,000 for a complete set of photographs that cost her $2,200 to print and develop. Suppose that on one Saturday Debbie photographs her niece's wedding without charge, but her niece insists on paying Debbie $2,200 to cover her printing and developing costs. What is Debbie's economic cost of photographing her niece's wedding?
A) $0
B) $1,800
C) $2,200
D) $4,000
4. A landscaping company is considering renting a backhoe at a fixed cost of $12,000 for the season. The variable cost of completing a landscaping project with the use of the backhoe is $500. Alternatively, without the use of the backhoe, the company would incur a variable cost of $1,000 per landscaping project and no fixed costs. If the landscaping company plans to complete more than ______ projects, the total cost of landscaping projects will be lower ______.
A) 24; with the use of the backhoe
B) 18; with the use of the backhoe
C) 44; without the use of the backhoe
D) 12; without the use of the backhoe
5. A fixed cost is a cost that:
A) does not change with the level of the firm's output.
B) is associated with the firm's variable inputs.
C) decreases as the firm increases output.
D) captures the wear and tear of using capital in the production process.
6. Which of the following statements is TRUE?
I. The firm's total cost is the sum of its fixed and variable costs.
II. Over longer time horizons, the costs of the firm's inputs tend to become fixed.
III. In the long run, the firm can adjust the use of all of its inputs.
A) II only
B) I only
C) I and III
D) I, II, and III
7. The presence of capital rental markets gives firms:
A) the ability hire more labor in periods of high demand by keeping capital costs fixed.
B) reduced flexibility in substituting among various labor and capital inputs.
C) the ability to hire more capital in periods of high demand by keeping capital costs fixed.
D) the flexibility to adjust their capital usage based on output levels, making capital costs variable.
8. Suppose that you close down your coffee shop and sell your coffee maker for $500. If you originally bought the coffee maker for $4,000 and it lost $1,000 because of depreciation (i.e., age and use), the sunk cost of the coffee maker is:
A) $3,500.
B) $3,000.
C) $2,500.
D) $1,500.
9. Which of the following is an example of a sunk cost fallacy?
A) “I paid $85 for this wool sweater, but it is too scratchy on my skin, so I think I'll give it to my mother-in-law.”
B) “I'm not going to allow the sacrifice of 2,527 troops who have died in Iraq to be in vain by pulling out before the job is done.”
C) “I will not buy an Under Armour hoodie until it goes on sale for at least 25% off.”
D) “I'm going to buy another bag of popcorn because this popcorn is burnt.”
10. An entrepreneur gathers the following information to make a decision on whether to stay open for business or to shut down permanently:
Future operating revenues = $18 million
Future operating costs = $14 million
Sunk costs = $8 million
What should the entrepreneur do?
A) The entrepreneur should continue to operate the business, because the operating revenues exceed the operating costs.
B) The entrepreneur should shutdown the business, because the operating revenues are insufficient to cover the operating costs and sunk costs.
C) The entrepreneur should shutdown the business, because the sunk costs are greater than zero.
D) The entrepreneur should continue to operate the business to help pay off the sunk costs.
11. A business anticipates future operating revenue of $200 million, future operating costs of $150 million, and sunk costs of $60 million. This business should:
A) permanently shut down operations because the value of staying open is negative.
B) continue operations because the sunk costs are less than the future operating revenues.
C) continue operations because the future operating revenues are greater than the future operating costs.
D) permanently shut down operations because the ratio of future revenues to future costs is less than 2.
12. Corporate bankruptcy restructuring allows a firm to treat its debt payments as:
A) average fixed costs.
B) sunk costs.
C) marginal costs.
D) depreciation expenses.
Use the following to answer questions 13-14:
Figure 7.1
A) $200.
B) $100.
C) $300.
D) $500.
A)
B) $200; $250
C) $200; $150
D) $250; $200
15. Which of the following statements is TRUE?
I. If TC = $40,000 and FC = $18,000, then VC = $58,000.
II. Because fixed cost does not vary with output, the fixed cost curve is a vertical line.
III. The total cost and variable cost curves always have the same shape and slope.
IV. When output is zero, total cost equals fixed costs.
A) I, II, and III
B) III only
C) II, III, and IV
D) III and IV
Use the following to answer question 16: Figure 7.2
16. (Figure 7.2) Consider a firm with the following cost structure:
Which of the preceding represents the cost curves of the firm?
A) panel (a)
B) panel (b)
C) panel (c)
D) panel (d)
Use the following to answer question 17: Figure 7.3
17. (Figure 7.3) The firm's total cost is given by curve ______ on the following graph.
A) A B) B
C) C D) D
Use the following to answer question 18: Figure 7.4
18. (Figure 7.4) What could cause the movement from TC1 to TC2?
A) a decrease in the firm's fixed costs of production
B) economies of scale
C) a technological change that increases the productivity of inputs
D) an increase in input prices
19. A firm is producing 50 units of output at a total cost of $1,000, with a per-unit variable cost of $8. What is the firm's average fixed cost?
A) $12
B) $4
C) $20
D) $28
Use the following to answer question 20: Table
20. (Table 7.1) Which of the following is correct at 4 units of output?
A) AFC = 70; AVC = 21; ATC = 91
B) AFC = 17.50; AVC = 52.50; ATC = 70
C) AFC = 0.06; AVC = 0.02; ATC = 0.08
D) AFC = 280; AVC = 840; ATC = 1,320
Use the following to answer questions 21-22: Figure 7.5
21. (Figure 7.5) The firm's average total cost curve appears in which of the following?
A) panel (a)
B) panel (b)
C) panel (c)
D) panel (d)
22. (Figure 7.5) Which of the following statements is TRUE?
I. At point A, ATC > MC.
II. At point B, ATC = MC.
III. At point C, ATC < MC.
A) I and II
B) I, II, and III
C) III only
D) I only
Use the following to answer question 23:
Figure 7.6
I. The slope of the TC curve at 2 units of output is 8.
II. The slope of the TC curve between 2 and 5 units of output is negative.
III. The slope of the TC curve at 9 units of output is 12.
A) I and II
B) II only
C) III only
D) I only
24. Which of the following statements is TRUE?
I. MC = TC/Q
II. MC = VC/Q
III. Marginal cost falls as diminishing returns to labor set in.
A) I, II, and III
B) I and II
C) II and III
D) I and III
Use the following to answer question 25:
Figure 7.7
I. At Q = 3, the marginal cost is $2.33.
II. At Q = 8, the marginal cost is $1.80.
III. The slope of the total cost (TC) curve at Q = 3 is $2.33.
A) II only
B) I and III
C) II and III
D) I only
Use the following to answer question 26:
26. (Table 7.2) Carl's Detailing is a small business that travels to people's homes to meticulously clean their high-end sports cars. Carl hires detailers (labor) at a wage of $80 per day per worker. A van that is used to carry cleaning supplies to client homes has a fixed cost of $20 per day. The table shows the relationship between the number of cars cleaned and the number of detailers. The marginal cost of cleaning the first car is ______, and the marginal cost of cleaning the third car is ______.
A) $80; $480
B) $80; $240
C) $100; $260
D) $100; $300
27. A firm is producing 4 units of output at an average total cost of $40. When the firm produces 5 units of output, average total cost rises to $50. What is the marginal cost of the fifth unit of output?
A) $10
B) $30
C) $90
D) $120
28. Which of the following statements is TRUE?
I. If marginal cost is rising, the average total cost must be rising.
II. The marginal cost curve intersects both the average total and average variable cost curves at their minimum points.
III. If marginal cost is less than average variable cost, the average variable cost curve is negatively sloped.
A) I, II, and III
B) I and III
C) II only
D) II and III
29. Suppose a firm's total cost is given by TC = 100 + 4Q + 2Q2. Which of the following statements is TRUE?
I. AVC = 4Q + 2Q2
II. AFC = 100/Q
III. ATC = 2Q + 4 + 100/Q
IV. FC = 100 + 4Q
A) I and II
B) II and III
C) III only
D) I and IV
30. Suppose a firm's total cost and marginal cost functions are given by TC = 18 + Q + 2Q2 and MC = 1 + 4Q, respectively. What is the output level that minimizes average total cost?
A) 5
B) 3
C) 4.45
D) 6
31. Suppose a firm's total cost and marginal cost are given by TC = 192 + 10Q + 3Q2 and MC = 10 + 6Q. What is the output level that minimizes average total cost?
A) 8
B) 1.5
C) 21
D) 4
32. Suppose a firm's total cost and marginal cost are given by TC = 150 + 0.50Q +1.5Q2 What is the firm's average variable cost of producing 10 units of output?
A) $5.55
B) $15.50
C) $15
D) $17
Use the following to answer question 33: Figure 7.8
A) $43; $3,010
B) $11; $560
C) $0.10; $7
D) $7; $490
Use the following to answer question 34: Figure 7.9
A) not be able to because capital is fixed.
B) move to point W in the short run and point Z in the long run.
C) move to a point between W and Z in the short run.
D) move to point Z in the short run and point W in the long run.
Use the following to answer question 35:
Figure 7.10
35. (Figure 7.10) Suppose the firm is currently producing at point Z and wants to reduce its output to Q1. Which of the following statements is TRUE?
A) In the short run, the firm will move to point A, where total costs of production are higher than at point C.
B) The firm will move along its long-run expansion path from point Z to point A.
C) In the short run, the firm will move to point A, where total costs of production are lower than at point C.
D) In the long run, the firm will move to point A, where total costs of production are lower than at point C.
Use the following to answer question 36:
Figure 7.11
36. (Figure 7.11) The short-run total cost curve is represented by the letters ______, and the long-run total cost curve is represented by the letters ______.
A) WXA; ZXY
B) ZXA; WXY
C) WXY; ZXA
D) ZXY; WXA
Use the following to answer question 37: Figure 7.12
37. (Figure 7.12) The short-run average total cost curve is given by ______, and the long-run average total cost curve is given by______.
A) CZW; AZY
B) CZY; AZW
C) AZY; CZW
D) AZW; CZY
38. Which of the following statements is TRUE?
A) Short-run average total cost curves intersect the long-run average total cost curve at its minimum point.
B) It is not possible for two short-run average total cost curves to cross.
C) The long-run average total cost curve is derived by tracing out all of the firm's short-run average total cost curves.
D) The long-run average total cost curve indicates that it is more costly to produce output in the long run, especially when input prices are rising because of inflation.
39. Charlie's Umbrellas has a production function given by Q = 10K0.5L0.5, where MPL =
5K0.5/L0.5 and MPK = 5L0.5/K0.5. Charlie is using 9 units of capital (K) in the short run. The wage (W) is $80 per day and the rental rate per unit of capital (R) is $5 per day. What is Charlie's total cost of producing 60 umbrellas?
A) $445
B) $365
C) $108
D) $276
40. A firm's production function is given by Q = KL, where MPL = K and MPK = L. The wage rate (W) = $50 and the rental rate per unit of capital (R) is $12.50. In the short run, capital (K) is fixed at 10 units. The short-run average total cost of producing 100 units of output is ______, and the long-run average total cost of producing 100 units of output is ______.
A) $14.75; $8.80
B) $6.25; $5
C) $6.25; $4.20
D) $14.75; $9
41. Which of the following statements is TRUE?
I. If a firm experiences economies of scale, long-run average total cost rises with increases in output.
II. Diseconomies of scale are associated with the portion of the long-run average total cost curve that slopes upward.
III. For the long-run average total cost curve to slope downward, the total cost of production must increase less than proportionately with output.
IV. A firm may experience economies of scale despite a production function with constant returns to scale.
A) I, II, and III
B) II, III, and IV
C) II and III
D) I only
42. A firm is producing 10,000 units of output at a total cost of $5,000. If the firm increases output by 5,000 units and its total costs rise by $2,000, the firm is experiencing:
A) economies of scale.
B) economies of scope.
C) constant returns to scale.
D) diseconomies of scale.
43. The firm's long-run total cost is given by 2 1 10010 3 LTCQQ=−+ and long-run marginal cost is given by LMC = 100 – 20Q + Q2. At what output level does the firm experience economies of scale?
A) Q < 15
B) Q < 175
C) Q < 4,000
D) Q < 88
44. The firm's long-run total cost is given by LTC = 5,000Q – 100Q2 + Q2 and its long-run marginal cost is given by LMC = 5,000 – 200Q + 3Q2. At what output level does the firm experience diseconomies of scale?
A) Q > 30
B) Q > 50
C) Q > 245
D) Q < 245
45. Suppose a firm with a production function Q = KL (where MPL = K and MPK = L) is producing 125 units of output by using 5 workers and 25 units of capital. The wage rate (W) per worker is $10 and the rental rate per unit of capital (R) is $2. What happens to the firm's long-run average total cost if it decreases output to 45 units?
A) Long-run average total cost rises from $1.80 at 125 units of output to $2 at 45 units of output.
B) Long-run average total cost rises from $0.80 at 125 units of output to $1.33 at 45 units of output.
C) Long-run average total cost falls from $0.80 at 125 units of output to $0.60 at 45 units of output.
D) Long-run average total cost falls from $1.80 at 125 units of output to $1.15 at 45 units of output.
Use the following to answer question 46: Figure 7.13
46. (Figure 7.13) ______ of scale occur between ______ units of output.
A) Economies; 4 and 6
B) Diseconomies; 1 and 5
C) Diseconomies; 5 and 9
D) Economies; 5 and 9
47. Suppose the total cost of producing goods Q1 and Q2 jointly is given by TC = 100 + 50Q1Q2 – (Q1Q2)0.5. The total cost of producing Q1 and Q2 in two separate facilities is given by TC = 75 + 3,000Q1 + 1,000Q2 + + . If the firm produces Q1 = 40 and Q2 = 100, the firm should produce the goods ______ because of ______ of scope.
A) jointly; economies
B) in separate facilities; diseconomies
C) jointly; diseconomies
D) in separate facilities; economies
48. A firm produces two goods Q1 and Q2. For economies of scope to exist, it must be TRUE that:
A) TC(Q1,0) + TC(0,Q2) > TC(Q1,Q2).
B) TC(Q1,0) + TC(0,Q2) < TC(Q1,Q2).
C)
D) (TC(Q11,0) + TC(0,Q12))/(TC(Q11, Q12)) < 1.
49. A firm's long-run total cost curve is given by 22 1 2,000 3 LTCQQQ =−+ , where long-run marginal cost is given by LMC = 2,000
20Q + Q2. What is the quantity of output that minimizes long-run average total cost?
A) 15
B) 165
C) 500
D) 210
50. Producing 200 units of good Y and 100 units of good X in the same factory costs the firm $50,000. In contrast, producing 200 units of good Y in one factory and 100 units of good X in another factory costs the firm $75,000. So if the firm produces the two goods together, it experiences:
A) quadratic returns to scale.
B) diseconomies of scope.
C) economies of scope.
D) diseconomies of scale and diseconomies of scope.
51. Menard quit his high-school teaching job, which paid $60,000 per year, to start a business that prepares students for the SAT exam. His first year in business generated the following revenues and costs:
a. What is Menard's economic cost of his SAT-preparation business?
b. What is Menard's accounting profit?
c. What is Menard's economic profit?
52. Stan started a lawn-fertilizing business and is considering purchasing a powered fertilizer spreader or a self-propelled spreader. The powered spreader has a fixed cost of $4,000 for the season, whereas the self-propelled spreader has a fixed cost of only $100 for the season. The variable costs of fertilizing a lawn with the powered spreader and self-propelled spreader are $7 and $15, respectively.
a. Draw the total cost curves of fertilizing lawns using the powered spreader and the self-propelled spreader.
b. If Stan is expected to fertilize 400 lawns for the season, which production method should he choose?
c. How many lawns does Stan have to fertilize for it to make sense to use the powered spreader?
53. Jim owns Nickelback Bar, a bar located in a strip mall that is dedicated to the rock band Nickelback. Jim pays a $3,000 monthly lease to operate out of the strip mall. If Jim breaks the lease before the end of the calendar year, he is required to pay $2,000 for each of the remaining months. Jim purchased $40,000 of Nickelback-themed bar fixtures; the fixtures have absolutely no value in any alternative use. Each weekend Jim contracts with a security company that provides four security guards for $1,200.
a. Does the $1,200 payment to the security firm represent a variable cost, sunk cost, or avoidable fixed cost? Explain your answer.
b. Suppose that at the end of August Jim permanently shuts down his bar. What are Jim's sunk costs?
54. Answer the following questions.
a. Marcie is enrolled in a Principles of Microeconomics class but mistakenly buys a macroeconomics book from eBay that cannot be returned. She paid $80 for the book. Marcie's friend tells Marcie to read the macroeconomics book or otherwise she will have lost her $80. Explain whether you agree with Marcie's friend.
b. Peter is taking Intermediate Economics and decides to drop the course after the second midterm. Peter paid $180 for the course's textbook, which can be resold for $70 on barnesandnoble.com. What is Peter's sunk cost for the textbook?
55. Fran is considering permanently closing down her beauty salon. A consultant advises her that if she stays open for business, she will have future operating revenues of $300,000 and future operating costs of $280,000. In addition, Fran has paid $40,000 for salon fixtures that, if necessary, can be resold for $15,000 after closing the beauty salon.
a. What is the value of Fran's beauty salon if it remains open?
b. What is the value of Fran's beauty salon if she closes it permanently?
c. Explain whether Fran should close down the beauty salon permanently.
Use the following to answer question 56: Figure 7.14
56. (Figure 7.14) Complete the following table:
57. A firm with a production function Q = KL (where K is units of capital and L is units of labor) has an expansion path that is given by K = 2L. The wage rate (W) is $20 and the rental rate of capital is $10. Complete the following table, assuming that the firm is using the optimal mix of inputs for any given output level.
Use the following to answer question 58:
Figure 7.15
58. (Figure 7.15) Graph the firm's total cost curve as it corresponds to points A, B, and C.
59. Suppose that a windshield business changes from paying its workers an hourly wage rate to a piece rate system (i.e., paying workers for each windshield installed). The new compensation scheme increases worker productivity by 44%, with only a negligible effect on worker earnings. Graphically illustrate how the change in worker compensation affects the total cost of windshield installation.
Use the following to answer question 60:
Figure 7.16
60. (Figure 7.16) Answer the following questions.
a. Complete the following table.
b. Based on your answers in the preceding table, graph the firm's ATC curve.
61. Amy owns Accurate Accounting, Inc. and her business costs for the year are as follows:
Building rent = $30,000
Accounting staff = $200,000 Supplies (paper, pencils, paperclips, ink and toner, etc.) = $10,000
Annual software license = $15,000
Accurate Accounting, Inc. prepared 600 corporate tax returns for the year. Complete the following table.
62. Answer the following questions.
a. If TC = 1,500 + 7.5Q + Q2, derive the cost functions for VC, FC, ATC, AVC, and AFC.
b. If VC = 50Q and FC = 800, derive the cost functions for TC, ATC, AVC, and AFC.
c. If ATC = derive the cost functions for TC, FC, VC, AVC, and AFC.
63. Complete the following table.
64. Determine whether each of the following statements is TRUE or FALSE.
a. The slope of the total cost curve is equal to marginal cost or the change in variable cost divided by the change in output.
b. AFC = ATC – AVC
c. The average total cost cannot equal marginal cost.
d. Total cost can increase from an increase in variable cost.
65. Dillon operates Ducks Unlimited, a farm that raises mallard ducks to sell to dog food companies. Dillon leases the land for $5,000 per month and hires workers at $1,000 per month per worker. Complete the following table, which shows how the number of workers varies with the number of ducks raised.
66. Suppose a firm's total cost function is given by TC = 6,000 + 2Q + 0.25Q2, where MC = 2 + 0.5Q
a. What is the output level that minimizes total cost?
b. What is the output level that minimizes average total cost?
Use the following to answer question 67: Figure 7.17
67. (Figure 7.17) Graphically illustrate the firm's MC, ATC, and AVC curves in one diagram. You should indicate the minimum points on the AVC and ATC curves. In a separate diagram, show the firm's AFC curve.
Use the following to answer question 68:
Figure 7.18
68. (Figure 7.18) Where the firm is currently producing at point Y:
a. graph the firm's short-run average total cost curve, showing the total cost at 10, 20, and 30 units of output.
b. graph the firm's long-run total cost curve, showing the total cost at 10, 20, and 30 units of output.
c. graph the firm's short-run ATC curve, showing the ATC at 10, 20, and 30 units of output.
d. graph the firm's long-run ATC curve, showing the ATC at 10, 20, and 30 units of output.
69. A firm has a production function of Q = KL + L, where MPL = K + 1 and MPK = L. The wage rate (W) is $100 per worker and the rental rate (R) is $100 per unit of capital.
a. In the short run, capital (K) is fixed at 4 and the firm produces 100 units of output. What is the firm's total cost?
b. In the long run, what is the total cost of producing 100 units of output?
70. Suppose that a firm is currently producing 100 units of output at a total cost of $20,000.
a. Give a numerical example of this firm experiencing economies of scale as it expands output.
b. Give a numerical example of this firm experiencing constant economies of scale as it expands output.
c. Give a numerical example of this firm experiencing diseconomies of scale as it expands output.
71. A firm's long-run total cost function is given by LTC = 115,000Q – 500Q2 + Q3, where long-run marginal cost is given by LMC = 115,000 – 1,000Q +3Q2. At what range of output does this firm experience economies of scale?
Use the following to answer question 72:
72. Consider the preceding table. What important characteristic describes this firm's production process?
73. Answer the following questions.
a. Define economies of scope using these cost functions: TC(Q1,Q2), TC(Q1,0), and TC(0,Q2).
b. Why do economies of scope arise?
Answer Key
51. a. Economic cost = accounting cost + opportunity costs
Accounting costs = $30,000 + $15,000 + $55,000 = $100,000
Menard's opportunity cost is $5,000, the difference in salary between teaching and operating the tutoring business.
Economic cost = $105,000
b. Accounting profit = revenues – accounting costs = $120,000 – $100,000 = $20,000.
c. Economic profit = $120,000 – $105,000 = $15,000. 52. a.
b. The total cost of the powered spreader = $4,000 + 7(400) = $6,800. The total cost of the self-propelled spreader = $100 + 15 × (400) = $6,100. Stan should buy the self-propelled spreader because his total costs will be lower.
c. The total cost of the powered spreader = $4,000 + 7Q, and the total cost of the self-propelled spreader = $100 + 15Q. Set both total cost equations equal to each other and solve for Q.
4,000 + 7Q = 100 + 15Q
8Q = 3,900
Q = 487.5
Stan's total costs of production are lower with the powered spreader if he fertilizes more than 487.5 lawns.
53. a. There is no indication that the payment for security guards is a variable cost, depending on the number of drinks or patrons served. The payment is not a sunk cost because if Jim closes down his business he will no longer have to hire security guards. Therefore, the payment for security guards represents an avoidable fixed cost, a type of fixed cost that the firm no longer has to pay if it stops operating.
b. Jim's sunk costs equal $48,000 the $2,000 per month lease payment from September through December and the $40,000 of bar fixtures that cannot be sold.
54. a. You should disagree with Marcie's friend. The $80 that Marcie paid for the wrong book is a sunk cost. The $80 has already been spent (or lost) and cannot be recovered, regardless of whether Marcie reads the book.
b. Peter's sunk cost is $110, the nonrecoverable portion of the book's cost.
55. a. Value of staying open = future operating revenues – future operating costs –sunk costs = $300,000 – $280,000 – $25,000 = –$5,000. Note that the $25,000 sunk cost = $40,000 – $15,000.
b. Value of shutting down = future operating costs – future operating revenues – sunk costs = $280,000 – $300,000 – $25,000 = –$45,000.
c. Fran should stay open because the value of staying open is greater than the value of shutting down. Alternatively, because future operating revenues exceed future operating costs, Fran should keep her business open. 56.
32. Total cost = WL + RK = 4(20) + 8(10) =
increases in compensation), making it possible to install any number of windshields at a lower cost.
AVC = 50
AFC = 800/Q
c. If ATC = TC/Q, then TC = ATC × Q
TC = Q = 72,000 + 5Q + 0.50Q2 .
FC = 72,000
VC = 5Q + 0.50Q2
AVC = 5 + 0.50Q
AFC = 72,000/Q
63. At zero units of output, TC = FC, so FC = $1,000 regardless of output. At 2 units of output, TC = 690 × 2 = $1,380. At 3 units of output, VC = 200 × 3 = $600. At 5 units of output, TC is $350 (the marginal cost of the fifth unit) more than at 4 units of output.
67. The MC curve will intersect the minimum points on the ATC and AVC curves.
69. a. First, find the number of workers hired when Q = 100 and K = 4. Plugging Q = 100 and K = 4 into the production function gives:
100 = 4L + L
5L = 100
L = 20
TC = WL + RK = $100(20) + $100(4) = $2,400.
b. In the long run, the firm uses the optimal mix of inputs, where the marginal product per dollar of labor equals the marginal product per dollar of capital.
MPL/W = MPK/R
(K + 1)/100 = L/100
K + 1 = L
K = L – 1 (plug into production function) 100 = (L – 1)L + L
L2 = 100
L = 10
K = 10 – 1 = 9
TC = $100(10) + $100(9) = $1,900
70.
a. At 100 units of output, ATC = 20,000/100 = $200. For economies of scale to exist, ATC must fall with output. For example, if the firm increases output to 150 and total cost rises to $28,000, ATC = 28,000/150 = $186.67. Notice that output expanded by 50%, but total cost increased by only 40%.
b. At 100 units of output, ATC = 20,000/100 = $200. For constant economies of scale to exist, ATC must not change with output. For example, if the firm increases output to 150 and total cost rises to $30,000, ATC = 30,000/150 = $200. Output and total cost increased proportionately, or both by 50%.
c. At 100 units of output, ATC = 20,000/100 = $200. For diseconomies of scale to exist, ATC must fall with output. For example, if the firm increases output to 150 and total cost rises to $35,000, ATC = 35,000/150 = $233.33. Total cost increased disproportionately to output.
71. First, find the lowest point on the long-run ATC, which occurs where LATC = LMC.
LATC = LTC/Q = 115,000 – 500Q + Q2 .
LATC = LMC 115,000 – 500Q + Q2= 115,000 – 1,000Q + 3Q2
2Q2 = 500Q
Q = 250
Economies of scale occur for output levels less than 250.
72. This firm has economies of scope. It is cheaper for this firm to produce two goods jointly ($192,000) than each good separately ($240,000 = $96,000 + $144,000).
73. a. TC(Q1,Q2) < TC(Q1,0) + TC(0,Q2)
b. Economies of scope may arise because the production of two or more goods may share a common input. For example, beef and hides share the common input of cattle, so there will be cost savings from producing the two goods together rather than separately. Heating oil and kerosene are byproducts of refining oil. A steel company can produce different types of steel in the same furnace, which will be cheaper than trying to produce each type of steel in its own separate facility.