Midterm Exam II.docx

Answers to Final Exam (B)Intermediate MicroeconomicsJanuary 11,2007You have 2 hours to solve the exam set. The whole exam set is worth 100 points:(1 )Notice how many points each question is worth and allocate your time appropriately.(2)To get full credit on answers, you must be clear and rigorous: Define your variables, thoroughly label any graph, and interpret your graph or math in words.I. True-False (2 points each)If the supply is perfectly elastic, then an upward shift of the demand curve will lead to a higher price and quantity in equilibrium.Correct Answer: FalseSupply and demand theory shows us that the burden of a sales tax is shared equally by suppliers and demanders whether the tax is collected from the sellers or collected from the buyers.Correct Answer: FalseIn a private-values auction with rational bidders, we can expect the same outcome from an English auction as from a Vickrey auction.Correct Answer: TrueIt is possible to have decreasing marginal products for all inputs, and yet have increasing returns to scale.Correct Answer: TrueIf there are increasing returns to scale, then average costs are a decreasing function of output.Correct Answer: TrueIf the average cost curve is U shaped, then the marginal cost curve must cross the average cost curve at the bottom of the U.Correct Answer: TrueA firm produces one output, using one input, with the production function f(x) = 2x13 where x is the amount of input. The cost function for this firm is proportional to the price of the input times the cube of the amount of output.Correct Answer: TrueIf a profit-maximizing competitive firm has constant returns to scale, then its long run profits must be zero.Correct Answer: TrueA natural monopoly occurs when a firm gains ownership of the entire stock of some natural resource and thus is able to exclude other producers.Correct Answer: FalsePrice equals marginal cost is a sufficient condition for profit maximization.Correct Answer: FalseMultiple Choice (3 points each)1. Daily demand for gasoline at Billy-Bobs Mobile Station is described by Q = 776 -200p where Q are gallons of gasoline sold and p is the price in dollars. Billy-Bobs supply is Q =890 + 1500p. Suppose the state government places a tax of 20 cents on every gallon of gasoline sold. What is the deadweight loss resulting from this tax?(a) 3.53 dollars.(b) 3.11 dollars.(c) 0.42 dollars.(d) 96.12 dollars.(e) 34.59 dollars.Correct Answer: AA competitive firms production function is /(xrx2)= 4xi +1*；”. prjce of factor 1 is 1 and the price of factor 2 is 1. The price of output is 2. What is the profit-maximizing quantity of output?(a) 116232(b) 112244(c) 104Correct Answer: A2. The production function is given by ”(匕)=6 Suppose that the cost per unit of labor is 12 and the price of output is 6, how many units of labor will the firm hire?(a) 168(b) 424(c) None of the above.Correct Answer: B)/ )/ )/ )/ )/a b c d e/()/ )/ )/ )/ )/a b c d e/(3. A competitive firm has the short run cost function c(y) = 3y3 - 36y2 + 128y + 35. The firm will produce a positive amount in the short run if and only if the price is greater than: 10.23.19.Correct Answer: CTwo firms constitute the entire doghouse industry. One has a long run cost curve of3 + 4y2 3 and the other has a long run cost curve of 10 + y2/10. If no new firms enter the industry, at which of the following prices will exactly one firm operate?(a) 13(b) 57(c) None of the above.Correct Answer: BA profit-maximizing monopolist faces the demand curve, q = 100-3p. It produces at a constant marginal cost of $20 per unit. A quantity tax of $10 per unit is imposed on the monopolists product. The price of the monopolists product:(a) rises by $5.(b) rises by $10.(c) rises by $20.(d) rises by $12.(e) stays constant.Correct Answer: AA profit-maximizing monopolist sets:(a) price equal to average cost.(b) price equal to marginal cost.(c) price equal to marginal cost plus a pro-rated share of overhead.(d) price equal to marginal revenue.(e) marginal revenue equal to marginal cost.Correct Answer: EA monopolist has the total cost function, c(q) = 1300+ 7q. The inverse demand function is 110 - 2q; where prices and costs are measured in dollars. If the firm is required by law to meet demand at a price equal to its marginal cost:(a) the firms profits will be zero.(b) the firm will lose $650.(c) the firm will make positive profit, but not as much profit as it would make if it were allowed to choose its own price.(d) the firm will lose $1,300the firm will lose $780Correct Answer: DA price-discriminating monopolist sells in two separate markets such that goods sold in one market are never resold in the other. It charges Pi = 3 in one market and p= 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 P2.(b) Raise P2.(c) Raise Pi and lower 2.(d) Raise both Pi and P2.(e) Raise 2 and lower 乃.Correct Answer: BSuppose that the market demand curve for bean sprouts is given by P = 3580 - 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.(c) 525.(d) 700.(e) 87.50.Correct Answer: CAccording 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.(c) A competitive equilibrium always exists.(d) At a Pareto optimum, all consumers must be equally wealthy.(e) None of the above.Correct Answer: ERobinson Crusoes 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.(c) 16 hours.(d) 20 hours.(e) 24 hours.Correct Answer: CA 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 一 2C2 and the profits of the jeweler will be ( 72 + C)J 一 2J2. 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.(c) 66.(d) 11.(e) 33.Correct Answer: AIf 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(c) 42(d) 70(e) 49Correct Answer: D4. 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 includesa horizontal line through the interior of the box.(a) a vertical line.(b) a straight line from the lower left to the upper right corner of the box.(c) a curved line from the lower left to the upper right corner of the box.(d) all four edges of the box.Correct Answer: BBig Pig and Little Pig have two possible strategies, Press the Button, and Wait at the trough. If both pigs choose Wait, both get 2. If both pigs press the button then Big Pig gets 7 and Little Pig gets 3. If Little Pig presses the button and Big Pig waits at the trough, then Big Pig gets 10 and Little Pig gets 0. Finally, if Big Pig presses the button and Little Pig waits, then Big Pig gets 6 and Little Pig gets 1. In Nash equilibrium,(a) Little Pig will get a payoff of 1 and Big Pig will get a payoff of 6.(b) Little Pig will get a payoff of 3 and Big Pig will get a payoff of 7.(c) Both pigs will wait at the trough.(d) Little pig will get a payoff of zero.(e) The pigs must be using mixed strategies.Correct Answer: ETamara and Julio consume only bread and wine. They trade only with each other and there is no production. They both have strictly convex preferences. Tamaras initial endowment of bread and wine is the same as Julios.(a) At the initial endowment their marginal rates of substitution must be the same.(b) In a competitive equilibrium, the ratio of the two prices must be 1.(c) In a competitive equilibrium, they must consume identical consumption bundles.(d) If they have identical utility functions, then the initial allocation is Pareto optimal.(e) None of the above.Correct Answer: DA parent has two children living in cities with different costs of living. The cost of living in city B is 4 times the cost of living in city A. The child in city A has an income of 5000 and the child in city B has an income of 20000. The parent wants to give a total of $4000 to her two children. Her utility function is U(Ca, Cb) = CaCb, where Ca and Cb are the consumptions of the children living in cities A and B respectively. She will choose to:(a) give each child 2000, even though this will buy less goods for the child in city B.(b) give the child in city B 4 times asmuchmoney as the childincity B.(c) Give the child in city A 4 times asmuchmoney as the childincity B.(d) Give the child in city B 2 times asmuchmoney as the childincity A.(e) Give the child in city A 2 times asmuchmoney as the childincity B.Correct Answer: AA mountain village owns a common pasture where villagers graze their goats. The cost to a goat owner of owning and caring for a goat is 4 groschens. The pasture gets overgrazed if too many goats share the pasture. The total revenue from all goats on the common pasture is f(g) = 48g - 2g2, where g is the number of goats on the pasture. The town council notices that total profit from the pasture is not maximized if villagers are allowed to pasture goats for free. The council decides to allow a goat to use the common pasture only if its owner buys it a goat license. To maximize total profit (of villagers and council), how many groschens per goat should the council charge?(a) 1220(b) 2426(c) 22Correct Answer: E5. In Rustbucket, Mi there are 200 used cars for sale, half of them are good and half of them are lemons. Owners of lemons are willing to sell them for $100. Owners of good used cars are willing to sell them for prices above $1100 but will keep them if the price is lower than $1100. There is a large number of potential buyers who are willing to pay $200 for a lemon and $1,700 for a good car. Buyers cant tell good cars from bad, but original owners know.(a) There will be an equilibrium in which all used cars sell for $ 950.(b) The only equilibrium is one in which all used cars on the market are lemons and they sell for 200.(c) There will be an equilibrium in which lemons sell for 100 and good used cars sell for 1,100.(d) There will be an equilibrium in which all used cars sell for 600.(e) There will be an equilibrium in which lemons sell for 200 and good used cars sell for1,700.Correct Answer: AEssay 1 (total 10). Suppose that the inverse demand function for wool is p = A/q for some constant A. Suppose that 1/4 of the worlds wool is produced in Australia.a(5). 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(5,). How is the marginal revenue to Australia from an extra unit of wool relate to the price of wool?Answer: a) Price will fall by about one fourth of one percent.b) Marginal revenue is three fourths of price.2 (total 10). 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 Qa = L! - (2/3)Q/, and0 =玲5-(1/3)0 where 我and 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 (5s). If the two firms each maximize profits independently, what is there total output and how much quasi-rents do their factories earn?b (5). If someone buys them both and maximizes joint profits, how much quasi-rents are earned in total?Answer: a) Each produces 48 and quasi-rents are 12 for each.b) Each produces 36 and quasi-rents total 40.