I. True-False (2 Points Each)

Final Exam I

Intermediate Microeconomics

Fall 2005

I. True-False (2 points each)

1. Donald's utility function is U(x, y) = x+. Currently he is buying some of both goods. If his income rises and prices don't change, he will buy more of both goods.

2. If two goods x and y are perfect complements, then if the price of x falls, the entire change in the demand for x is due to the income effect.

3. If the elasticity of demand curve for millet is -0.50 at all prices higher than the current price, we would expect that when bad weather reduces the size of the millet crop, total revenue of millet producers will fall.

4. An economic situation is Pareto optimal only if there is no way to make someone better off.

5. The economist's distinction between long and short run captures the idea that quantities of some factor inputs can be varied in the short run but not in the long run.

6. If a profit-maximizing competitive firm has constant returns to scale, then its long run profits must be zero.

7. Price equals marginal cost is a sufficient condition for profit maximization.

8. If there are constant returns to scale in a competitive industry, then the long run industry supply curve for that industry is horizontal.

9. In the Bertrand model of duopoly, each firm sets its price, believing that the other's price will not change. When both firms have identical production functions and produce with constant returns to scale, the Bertrand equilibrium price is equal to marginal cost.

10. If the initial endowment is on the contract curve, then there must always be a competitive equilibrium in which no trade takes place.

II. Multiple Choice (2.5 points each)

1. If there are only two goods, if more of good 1 is always preferred to less, and if less of good 2 is always preferred to more, then:

(a) indifference curves slope downwards.

(b) indifference curves slope upwards.

(d) indifference curves could take the form of ellipses.

(e) None of the above.

2. Molly's utility function is U(x,y) = y + 4. She has 25 units of x and 12 units of y. If her consumption of x is reduced to 0, how many units of y would she need in order to be exactly as well off as before?

(a) 48 units. (b) 37 units.

(e) None of the above

3. Henri's utility function is min{x, 5y + 2z}. The price of x is 1, the price of y is 15, and the price of z is 7. Henri's income is 44. How many units of x does Henri demand?

(a) 9.78 (b) 11

(e) None of the above.

4. When the price of bananas is 50 cents a pound, the total demand is 100 pounds. If the price elasticity of demand for bananas is -2; what quantity would be demanded if the price rose to 60 cents a pound?

(a) 50 (b) 90

(e) 70

5. If the marginal cost of brewing beer is 40 cents and the profit maximizing price is 70 cents, then the price elasticity of demand is

(a) -0.66. (b) -1.8.

(e) -3.

6. The demand function for corn is q = 200 - p and the supply function is q = 50+0.5p. The government sets the price of corn at 150 and agrees to purchase and destroy any excess supply of corn at that price. How much money does it cost the government to buy this corn?

(a) 11,250 (b) 18,750

(e) 14,500

7. If the short run marginal cost of producing a good is $20 for the first 200 units and $30 for each additional unit beyond 200, then in the short run, if the market price of output is 29, a profit maximizing firm will:

(a) produce a level of output where marginal revenue equals marginal cost.

(b) produce as much output as possible since there are constant returns to scale.

(d) not produce at all, since marginal cost is increasing.

(e) produce exactly 200 units.

8. The production function is .where L is the number of units of labor and M is the number of machines. If the amounts of both factors can be varied, and if the cost of labor is $25 per unit and the cost of using machines is $16 per machine, then the total cost of producing 16 units of output is:

(a) 160. (b) 328.

(e) 80.

9. Mr. Dent Carr's total costs are 2 + 75s + 100. If he repairs 25 cars, his average variable costs will be:

(a) 125. (b) 129.

(e) 87.50.

10. A competitive firm has a long run total cost function c(y) = 5 + 1,280 for y > 0 and c(0) = 0. Its long run supply function is described as follows:

(a) y = p/10 if p > 160; y = 0 if p < 160.

(b) y = p/5 if p > 158; y = 0 if p < 158.

(d) y = p/10 if p > 163; y = 0 if p < 163.

(e) y = p/5 if p > 165; y = 0 if p < 155.

11. The cheese business in Lake Fon-du-lac, Wisconsin is a competitive industry. All cheese manufacturers have the cost function C = + 9; while demand for cheese in the town is given by = 120 - P. The long run equilibrium number of firms in this industry is

(a) 19 (b) 38

(e) 39

12. A monopoly has the demand curve q = 10,000 - 100p. Its total cost function is

c(q) = 1000+ 10q. The government plans to tax the monopoly's profits at a rate of 50%. If it does so:

(a) the monopoly will increase its price by 50%.

(b) the monopoly will increase its price by more than 50%.

(d) the monopoly will not change its price or the quantity it sells.

(e) none of the above.

13. A price-discriminating monopolist sells in two separate markets such that goods sold in one market are never resold in the other. It charges = 3 in one market and = 7 in the other market. At these prices, the price elasticity in the first market is -2.50 and the price elasticity in the second market is -0.80. Which of the following actions is sure to raise the monopolists profits?

(a) Lower. (b) Raise.

(e) Raiseand lower.

14. An industry has two firms. The inverse demand function for this industry is

p = 92 - 2. Both firms produce at a constant unit cost of $32 per unit. What is the Cournot equilibrium price for this industry?

(a) 32 (b) 34

(e) None of the above.

15. Suppose that the market demand curve for bean sprouts is given by

P = 3, 580 - 5Q; where P is the price and Q is total industry output. Suppose that the industry has two firms, a Stackleberg leader and a follower. Each firm has a constant marginal cost of $80 per unit of output. In equilibrium, total output by the two firms will be:

(a) 350. (b) 175.

(e) 87.50.

16. If the number of persons who attend the club meeting this week is X; then the number of people who will attend next week is 21+0.70X. What is a long run equilibrium attendance for this club?

(a) 21 (b) 30

(e) 49

17. According to the First Theorem of Welfare Economics:

(a) Every competitive equilibrium is fair.

(b) If the economy is in a competitive equilibrium, there is no way to make anyone better off.

(d) At a Pareto optimum, all consumers must be equally wealthy.

(e) None of the above.

18. In a two-person, two-good, exchange economy, both consumers have quasilinear utility functions, linear in Good 2. If quantities of Good 1 are measured horizontally and quantities of Good 2 are measured vertically in the Edgeworth box, the set of Pareto optimal allocations includes

(a) a horizontal line through the interior of the box.

(b) a vertical line.

(d) a curved line from the lower left to the upper right corner of the box.

(e) all four edges of the box.

19. Robinson Crusoe's preferences over coconut consumption, C; and leisure, R; are represented by the utility function, U(C,R) = CR. There are 48 hours available for Robinson to allocate between labor and leisure. If he works L hours, he will produce the square root of L coconuts. He will choose to work:

(a) 8 hours. (b) 12 hours.

(e) 24 hours.

20. A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (30+ J)C - 2and the profits of the jeweler will be ( 72 + C)J - 2. The clothing store gets to choose his amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend. The amount spent by the clothing store will be:

(a) 22. (b) 44.

(e) 33.

III. Essay

1. Suppose that the inverse demand function for wool is p = A/q for some constant A. Suppose that 1/4 of the world's wool is produced in Australia.

a) If Australian wool production increases by 1% and the rest of the world holds its output constant, what will be the effect on the world price of wool?

b) How is the marginal revenue to Australia from an extra unit of wool relate to the price of wool?

2. A competitive firm has a production function described as follows. "Weekly output is the square root of the minimum of the number of units of capital and the number of units of labor employed per week." Suppose that in the short run this firm must use 16 units of capital but can vary its amount of labor freely.

a) Write down a formula that describes the marginal product of labor in the short run as a function of the amount of labor used. (Be careful at the boundaries.)

b) If the wage is w = 1 and the price of output is p = 4; how much labor will the firm demand in the short run?

c) What if w = 1 and p = 10?

d) Write down an equation for the firm's short run demand for labor as function of w and p.

3. Two firms in a grimy Ohio town produce the same product in a competitive industry. Each has an old factory using an old technology. It still pays to operate these factories but it would not pay to expand them. The only variable factor used by either firm is labor. Each firm pollutes the other and thus reduces the output of the other firm. The production functions of firms A and B respectively are and where 5 and 5 are the square roots respectively of the amount of labor used by firms A and B. The wage rate of labor is 1 and the price of the firms' output is 12.

a) If the two firms each maximize profits independently, what is there total output and how much quasi-rents do their factories earn?

b) If someone buys them both and maximizes joint profits, how much quasi-rents are earned in total?

Ⅰ.True-False Answer：1. False 2. True 3. False 4. False 5. True 6. True 7. False 8. True 9. True 10. True

Ⅱ.Multiple Choice Answer：1.B 2.C 3.B 4.C 5.D 6.A 7.E 8.A 9.A 10.A 11.B 12.D 13.B 14.C 15.C 16.D 17.E 18.B 19.C 20.A

Ⅲ.Essay

1. Answer: a) Price will fall by about one fourth of one percent. b) Marginal revenue is three fourths of price.

2. Answer: a) MP = 1/(2) if L < 16; MP = 0 if L > 16. b) 4 ;c) 16; d) L =.

3. Answer: Each produces 48 and quasi-rents are 12 for each. Each produces 36 and quasi-rents total 40.