Prelim%202 - Economics 3010 Fall 2008 Professor Daniel...

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Unformatted text preview: Economics 3010 Fall 2008 Professor Daniel Benjamin Cornell University EXAM #2 You have 75 minutes for this exam. No calculators are allowed. There are 65 points on the exam, and you should plan to spend approximately as many minutes per question as they are worth in points. This should leave you five minutes at the beginning to read over the test and five minutes at the end to check your answers. Please do all of the questions on this exam. Use a separate blue book for each part of the exam (I, II, and III), three in total. On the cover of each blue book, please write your name, your TA’s name, your section time, and the part of the exam answered in that book. Read over the whole test before starting. To keep the test as fair as possible, we will only answer questions during the first ten minutes. Some advice: Complete answers will include definitions of relevant terms and verbal intuition (in addition to graphs or formulas, if those are appropriate). Do not get hung up on calculations when answering a question. If you get the formulas and explanation correct, little credit will be deducted for mistakes in calculation. The questions vary in difficulty, so try to keep moving through the exam; if you are having trouble with something, it is probably a good idea to skip it and come back later. Good luck! I. True / False / Uncertain Your grade on these questions will depend on the generality, completeness, and persuasiveness of your explanation, not simply on whether the “true” or “false” is correct. The objective here is to provide an answer that convinces; not merely an answer that is “not wrong.” At the very least, make sure that you give clear definitions for the relevant economic terms used in the question. Please use a separate blue book for this section. (5 points) 1) Moral codes and charities are among the private solutions to the externality problem. (5 points) 2) If the production function is smooth and the solution to the firm’s cost‐minimization is interior (i.e., not a corner solution), the technical rate of substitution is equal to the factor price ratio. (5 points) 3) In a perfectly competitive industry, every firm earns an economic profit of zero in both the short run and the long run. (5 points) 4) A firm with production function f(K, L) = K0.9 L0.8 has increasing returns to scale and decreasing marginal product of labor. (5 points) 5) According to the Second Fundamental Theorem of Welfare Economics, any Walrasian equilibrium is Pareto efficient. II. Brief Problem (5 points) Every year for as long as anyone can remember, Mr. Wu has decorated his lawn every holiday season with a spectacular winter scene. Tourists would come from far and wide just to see, admire, and photograph his lawn show. This year, Mr. Wu has decided to retire his lawn show because, even though he personally gets $500 worth of enjoyment from it, it now costs him $600 worth of effort to put the scene together (since he isn’t getting any younger). If there were one “large” tourist – say a local TV station – that received $200 of benefit from the show and could bargain with Mr. Wu at low cost, what would the Coase theorem predict? (To receive full credit, make sure you state the Coase theorem.) Why might the Coase theorem not apply if, instead of one “large” tourist, there were 100 “small” tourists – say families – each of whom received $20 of benefit from the lawn show? III. Multi‐Part Problem Note: This question is designed so that if you skip part of the question, you still have enough information (stated explicitly earlier in the question) to answer later parts of the question. Please answer as many parts as you can. Suppose the market for New York City taxicabs is perfectly competitive. Each firm requires a car to use as a taxi (capital K), but then the amount of taxi services provided depends on the number of hours worked as a driver (labor L). Specifically, each firm in the industry has production function: if K = 1 q(K, L) = { 2 L1/2 { 0 if K = 0, where q is taxi services per day, K is the presence or absence of a car, and L is number of hours worked as a driver. The rental rate of a car is $100 per day, and the wage rate is $1. Daily market demand for taxi services is D(p) = 2,000 – 10p, where p is the price. It takes time to sign a rental contract on a car, and firms that are currently renting cars are stuck in annual contracts that cannot be cancelled on short notice. In the short run, there are 75 firms that are currently renting cars. (We will assume for simplicity that each firm can have only zero cars or one car, but not more than one car.) (5 points) (a) Show that a firm in this industry has the following short run cost function: SRTC(q) = 100 + (q2 / 4) for any q ≥ 0. (6 points) (b) What is the firm’s short run average cost (SRAC) function? Short run average variable cost (SRAVC) function? Show that the firm’s short run marginal cost function is SRMC(q) = q / 2 for any q ≥ 0. (c) Graph the firm’s SRAC, SRAVC, and SRMC curves. With reference to your graph, (5 points) explain why no firm will ever shut down in the short run, regardless of the output price. (3 points) (d) Show that each firm’s short run supply function is Sfirm(p) = 2p and that the short‐ run market supply function is Smkt(p) = 150p. (3 points) (e) Show that the short run equilibrium market price is pSR = 12.5 and that each firm produces qSR = 25. At the short run equilibrium, what is a representative firm’s profit? (5 points) (f) In the long run, new firms can rent cars, and old firms can get out of their rental contracts. Explain why the long run cost function is LRTC(q) = { 100 + (q2 / 4) if q > 0 { 0 if q = 0. LR Show that the long run equilibrium price is p = 10 and that each firm produces qLR = 20. (4 points) (g) Draw a supply and demand diagram depicting the long run equilibrium, and explain why the long run supply curve is a horizontal line (i.e., perfectly elastic) at the long run equilibrium price. Show that the long run equilibrium market quantity of taxi services provided is QLR = 1900. What is the long run equilibrium number of firms? (4 points) (h) Suppose that production of each unit of taxi services causes $5 of pollution damage (due to car exhaust) so that the marginal social cost of production is $5 higher than the marginal private cost at every level of output. Draw a supply and demand diagram depicting the demand curve (i.e., the marginal benefit curve), the long run marginal private cost curve, and the long run marginal social cost curve. Show that the socially optimal market quantity of taxi services provided is Qsocial = 1850. ...
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