toughMicroEcon

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Print Your Name:___________________________________ Your Section #:____________ True-False Questions: Answer A for “True” and B for “False”. Each correct answer is worth 2 points. Each wrong answer is worth zero points. Answers left blank are worth 1 point. 1. If the production function 1 2( , )f x x exhibits increasing-returns-to-scale, it is possible

that the marginal product of 1x diminishes as 1x increases. 2. In a given game, if a strategy profile is a Nash equilibrium, then it is also a dominant

strategy equilibrium. 3. Since a monopoly charges a price higher than marginal cost, it will produce an inefficient

amount of output. 4. In an exchange economy where both consumers have well-behaved preferences, the

competitive equilibrium allocation will always be Pareto efficient. 5. A profit-maximizing firm may lose money in the short-run. 6. The cost function C(y) = 10 + 3y has marginal cost less than average cost for all levels of

output. 7. A competitive, cost-minimizing firm has the production function f (x, y) = x + 2y and uses

positive amounts of both inputs. If the price of x doubles and the price of y triples, then the cost of production must go up by more than double.

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8. The market for a good is in equilibrium when the government unexpectedly imposes a quantity tax of $2 per unit. In the short run, the price will rise by $2 per unit so that firms can regain their lost revenue and continue to produce.

9. A Stackelberg follower will necessarily make at least as much profit as he would if were a

Cournot duopolist. 10. If a profit-maximizing competitive firm has constant returns to scale, then its long-run profit must

be zero. Multiple-Choice Questions: Select the best answer. Each correct answer is worth 5 points. Each wrong answer is worth zero points. Answers left blank are worth 1 point. 11. A firm has two variable factors and a production function, 1/3 1/31 2 1 2( , ) f x x x x . The price

of output is 1, the price of factor 1 is 1w , and the price of factor 2 is 2w . What is the profit-maximizing level of input 1x ?

A) 2 21 21/ (9 )w w B) 21 21/ (9 )w w C) 21 21/ (27 )w w D) 21 21/ (15 )w w E) 21 21/ (27 )w w 12. Suppose that the production function is 1 2 3 1 2 3( , , ) ( ) f x x x x x x

    , where  ,  , and  are positive constants. For what positive values of  ,  , and  are there increasing returns to scale?

A) 1 B) / 1  C) 1   D) 1     E) None of the above.

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13. Two firms, Firm 1 and Firm 2, sell a homogeneous product in a single market. Firm 1 moves first and decides to produce 1q units of output. After observing Firm 1’s decision, Firm 2 decides to produce 2q units of output. Firm 1 produces output with zero marginal cost. Firm 2’s cost function is 2 2( ) 2c q q . The inverse market demand function is given by 10 p Q , where 1 2 Q q q . What is the market price of the product in equilibrium?

A) 5 B) 4 C) 6 D) 3 E) 2 14. Consider the following game, where each player has three possible strategies.

Player B

Player A

B1 B2 B3 A1 5, 4 3, 0 4, 2 A2 3, 3 8, 4 2, 4 A3 5, 0 0, 0 0, 0

How many Nash equilibria does this game have? A) 0 B) 1 C) 2 D) 3 E) 4 15. Allen is considering producing widgets in a competitive industry. If he chooses to

produce a positive number of widgets, then he must buy a widget mold which costs $60. Allen may only buy one mold, which can produce up to 80 widgets. The first 20 widgets cost $5 each to produce, the next 30 cost $10 each, and the next 30 after that cost $5 each. If the market price of widgets is $8, what will be Allen’s profit when he produces the optimal number of widgets?

A) 0 B) 30 C) 60 D) 90 E) 120

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16. Consider a 2 good, 2 consumer exchange economy in which good 2 is the numeraire. If the current price of good 1 is 1 10p and the net demand for good 1 is 10, what is the net demand for good 2?

A) 10 B) -10 C) 100 D) -100 E) Cannot be determined from the information given. 17. Suppose a profit-maximizing cider mill operating in a perfectly competitive market has

the following cost curves, and it is currently producing a positive quantity. Then the market price is at least ________ and the mill will produce at least _______ pints of cider.

Pints of Cider

Price ($/pint)

MC

ATC

AVC

120 250 370 400

5

11

23

26

35

A) 5, 120 B) 11, 250 C) 11, 370 D) 23, 370 E) 35, 120

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18. A firm has the production function 1/2 1/21 2 1 2f (x , x ) x x . On the diagram below, 1x is on the horizontal axis and 2x is on the vertical axis. Suppose we drew some isoquants. Now suppose we draw a straight line on the graph and we notice that wherever this line meets an isoquant, the isoquant has a slope of -3. The straight line we drew

x1

x2

A) is vertical. B) is horizontal. C) is a ray through the origin with slope 3. D) is a ray through the origin with slope 2. E) has a negative slope. 19. Hilda runs a cookie factory. Her cookies are made with sugar, peanut oil, and lard. The

number of boxes of cookies that she produces is f (s, p, l) = min{s, p + 2l}, where s is the number of bags of sugar, p the number of canisters of peanut oil, and l the number of canisters of lard that she uses. The price of a bag of sugar is $12. The price of a canister of peanut oil is $6. The price of a canister of lard is $9. If Hilda makes cookies in the cheapest way possible, how much does it cost to make 200 boxes of cookies?

A) $2400 B) $3300 C) $3600 D) $4200 E) $4500

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20. Roberta runs a dress factory where she produces 50 dresses per day. She uses a combination of labor and electricity to produces the 50 dresses per day in the cheapest possible way. She can hire as much labor as she wants at a cost of 20 cents per minute. She can use as much electricity as she wants at a cost of 10 cents per minute. Her production isoquants are smooth curves without kinks and she uses positive amounts of both inputs.

A) The marginal product of a kilowatt-hour of electricity is twice the marginal product

of a minute of labor. B) The marginal product of a minute of labor is twice the marginal product of a

kilowatt-hour of electricity. C) The marginal product of a minute of labor is equal to the marginal product of a

kilowatt-hour of electricity. D) The marginal product of a minute of labor plus the marginal product of a

kilowatt-hour of labor must equal 50 / (20 10) . E) There is not enough information to determine the ratio of marginal products. 21. When Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of

fertilizer is 1 N / 200 bushels of corn. If the price of corn is $4 per bushel and the price of fertilizer is $1.20 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?

A) 140 B) 280 C) 74 D) 288 E) 560 22. The production function of a competitive firm is described by the equation 1/2 1/21 2y 4x x .

The factor prices are p1 = $1 and p2 = $36 and the firm can hire as much of either factor it wants at these prices. The firm’s marginal cost is

A) decreasing and then increasing as y increases. B) constant for all values of y . C) always decreasing as y increases. D) increasing and then decreasing as y increases. E) always increasing as y increases.

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23. Mr. Dent Carr’s total costs are 2s2 + 45s + 30. If he repairs 15 cars, his average variable costs will be

A) $77 B) $75 C) $150 D) $105 E) $52.50 24. The bicycle industry is made up of 100 firms with the long-run cost curve

2c(y) 2 y / 2  , and 120 firms with the long-run cost curve 2c(y) y / 4 . No new firms can enter the industry. What is the long-run industry supply curve at prices greater than $2?

A) y = 170p B) y = 360p C) y = 240p D) y = 340p E) y = 375p 25. The town council of Frostbite, Ontario, is trying to decide whether to build an outdoor

skating rink which would cost $1 million and last for only one season. Operating costs would be zero. Yearly passes would be sold to anyone who wanted to use the rink. If p is the price of the pass in dollars, the number demanded would be q = 1200 – 0.6p. The council has asked you to advise them on building the rink. Your report should say that

A) revenue won’t cover construction costs at any ticket price. There is no way to

increase total consumer surplus by building the rink. B) if the rink is built and price is set to maximize profits, the town makes a profit and

consumers will be better off. C) if the rink is built and price set to maximize profits, the town makes a profit but

consumers are worse off than without a rink. D) there is no price at which ticket revenues still cover costs, but total consumer surplus

from the rink exceeds costs. E) None of the above.

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26. Suppose that Grinch and Grubb go into the wine business in a small country where wine is difficult to grow. The demand for wine is given by p = $420 – .2Q, where p is the price and Q is the total quantity sold. The industry consists of just the two Cournot duopolists, Grinch and Grubb. Imports are prohibited. Grinch has constant marginal costs of $60 and Grubb has marginal costs of $30. How much Grinch’s output in equilibrium?

A) 275 B) 550 C) 825 D) 1,100 E) 1,650 27. Charlie can work as many hours as he wishes at a local fast-food restaurant for a wage of

$4 per hour. Charlie also does standup comedy. Since Charlie lives in a quiet, rather solemn Midwestern town, he is the town’s only comedian and has a local monopoly for standup comedy. The demand for comedy is Q = 40 – P, where Q is the number of hours of comedy performed per week and P is the price charged per hour of comedy. When Charlie maximizes his utility, he spends at least 1 hour per week working at the restaurant and he gets at least 1 hour of leisure time. His utility depends only on income and leisure. How many hours per week does he perform standup comedy?

A) 36 B) 40 C) 18 D) 20 E) There is not enough information to answer this question. 28. The Fabulous 50s Decor Company is the only producer of pink flamingo lawn statues.

While business is not as good as it used to be, in recent times the annual demand has been Q = 700 – 5P. Flamingo lawn statues are handcrafted by artisans using the process Q = min{L, G/4} where L is hours of labor and G is gallons of pink plastic. WL = 20 and WG = 2. What would be the profit-maximizing output and price?

A) Q = 265 and P = 87 B) Q = 330 and P = 74 C) Q = 300 and P = 80 D) Q = 530 and P = 34 E) Q = 280 and P = 84

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29. The demand for a monopolist’s output is 2 6,000q

(p 7) 

 , where p is its price. It has

constant marginal costs equal to $5 per unit. What price will it charge to maximize its profits?

A) $33 B) $12 C) $26 D) $17 E) $5 30. The marginal cost of thwips is 0, but people love them. Demand in the United States is

given by Q1 = 7,200 – 300p1, where p1 is the price in the United States, and demand in England is given by 3,600 – 200p2, where p2 is the price in England. Suppose that resale between England and the United States is prohibited. Then the difference between the price charged in the United States and the price charged in England will be

A) 3 B) 6 C) 0 D) 13 E) 9 31. If a monopolist faces an inverse demand curve, p(y) = 100 – 2y and has constant marginal

costs of $4 and zero fixed costs and if this monopolist is able to practice perfect price discrimination, its total profits will be

A) $24 B) $3,456 C) $2,304 D) $1152 E) $576

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32. The demand for a good y is given by 2y 256 / p . Only two firms produce y. They have identical costs 2c(y) y . If they agree to collude and maximize their joint profits, how much output will each firm produce?

A) 2 B) 5 C) 10 D) 12 E) 16 33. Roach Motors is the dominant used-car dealer in a small Midwestern city. After paying

$10,000 for overhead, Roach Motors’ cost per car is $500. There are 5 other small used-car lots in this town, but since they are not large enough to purchase cars through the same discount sources as Roach, each firm faces the cost function

2C(y) 1000y 5y  . The total market demand for used cars is Q 1000 P /10  . Assuming Roach is aware of its competitors’ costs, what price should Roach set for a used car?

A) $1,250 B) $800 C) $970 D) $1,140 E) $1,500 34. A profit-maximizing firm produces output using input x. The production function of the

firm is given by

3 0 5

( ) 2 5 5 10 15 10

        

x if x f x x if x

x if x .

When the price of output is 2 and the price of input x is 3, what is the profit-maximizing

amount of input x? A) 5 B) 10 C) 7.5 D) 0 E) None of the above.

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35. A competitive firm’s production function is 1 2 1 2f (x , x ) max{x , x } , and factor prices are 1 2(w , w ) (3, 4) . What is the firm’s cost function?

A) c(y) 3y B) 2c(y) 7y C) 2c(y) 4y D) c(y) 7y E) 2c(y) 3y 36. Any firm in the industry for cherry pies has cost function 2c(y) 4y 8y 256   .

Demand for cherry pies is given by D(p) 104 p  . What is the price in the long-run competitive equilibrium for this industry?

A) 6 B) 8 C) 56 D) 82.67 E) None of the above. 37. Consider a 2 good, 2 consumer exchange economy in which good 2 is the numeraire. If

the current price of good 1 is 1p 10 and the net demand for good 1 is 10, what is the net demand for good 2?

A) 10 B) -10 C) 100 D) -100 E) Cannot be determined from the information given.

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38. LeBron and Tom participate in a pure exchange economy. LeBron has utility function L L L L L 31 2 1 2U (x , x ) x (x ) and endowment

L L 1 2( , ) (10,10)   . Tom has utility

function T T T T 3 T1 2 1 2U (x , x ) (x ) x and endowment T T 1 2( , ) (10,10)   . Which of the

following could be the competitive equilibrium prices? A) 1 2(p , p ) (3,3) B) 1 2(p , p ) (3,1) C) 1 2(p , p ) (1,3) D) 1 2(p , p ) (2,6) E) 1 2(p , p ) (2,1)

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