Prelim%202%20Solutions%20%20--%20Nov%2023

Prelim%202%20Solutions%20%20--%20Nov%2023 - Economics 3010...

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Unformatted text preview: Economics 3010 Fall 2009 Professor Daniel Benjamin Cornell University EXAM #2 SOLUTIONS I. True / False / Uncertain. Make sure to explain how you reached your conclusion. (5 points) 1) According to the Efficient Markets Hypothesis, it is possible to predict future movements in a stock’s price based on recent past movements in that stock’s price. False. 2 points: The Efficient Markets Hypothesis states that stock prices already reflect all available information. 2 point: Hence stock price changes are unpredictable. 1 point: If recent past movements in a stock’s price contained information relevant to predicting future stock price movements, that information would already be incorporated into the stock’s price; otherwise, there would be an arbitrage opportunity (which would violate the no‐arbitrage principle). (5 points) 2) An employee whose portfolio is largely invested in her own employer’s company stock is poorly diversified, and the extra risk will not be compensated by a higher expected return. True. 2 points: Diversification is undertaking many risky activities, each on a small scale, rather than a few risky activities on a larger scale. 1 point: The employee could diversify much better by holding many stocks on a small scale (e.g., by holding an index fund that invests broadly in the stock market). 2 points: The part of a stock’s risk that is compensated by a higher expected return is the part that cannot be diversified away, i.e., the covariation between the stock’s return and the market return (the return on a portfolio composed of all stocks). (This is a key lesson of the Capital Asset Pricing Model.) [Additional note: Having a large investment in your own company’s stock is even more risky than holding a large investment in some other company’s stock because if the company does badly, not only will your stock wealth decline, but you may lose your job, as well! In the jargon of economics, we’d say that if you invest heavily in your own company’s stock, you are making the return on your human capital highly correlated with the return on your financial capital (which is the opposite of diversifying).] II. Brief Problem (5 points) Consider the following scene from the recent Batman movie, The Dark Knight. There are two ships floating in the harbor, one whose passengers are convicts, and one whose passengers are civilians. The Joker has put explosives on both ships. The Joker tells the passengers that the only way to save themselves is to trigger the explosives on the other ship; otherwise he will destroy both at midnight. This situation can be modeled as a two‐player game, where the players are the convicts and the civilians, and the available actions are {trigger the explosives, don’t trigger the explosives} . Suppose that survival gives a payoff of 100, and death gives a payoff of 0 (and assume that neither player cares about the well‐being of the other). Draw the normal form of this game, and pure‐strategy Nash equilibrium (or equilibria, in case there is more than one). Make sure to explain why your situation fits the definition of a Nash equilibrium. 2 points: The normal form of the game is: Convicts Trigger Don’t Trigger Civilians Trigger 0 , 0 100 , 0 Don’t Trigger 0 , 100 0 , 0 2 points: There are 3 Nash equilibria in Pure Stategies: (Trigger, Trigger), (Don’t Trigger, Trigger) and (Trigger, Don’t Trigger) (Note: Triggering the explosives is not a (strictly) dominant strategy because, if the other player triggers, the player is indifferent between triggering or not. In this case, we say triggering is a weakly dominant strategy.) 1 point: A Nash equilibrium is a strategy profile such that each player’s strategy is optimal, taking as given the strategies of the other players. For example, here, the strategy profile (Trigger, Trigger) is a Nash equilibrium because if one player plays the strategy Trigger, there is no strategy that gives a higher payoff to the other player than Trigger. 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. The amount of copying services per day (y) a copy store can provide depends on the number of industrial copy machines (K) and number of labor hours (L) according to the production function: y = f(K, L) = K1/2 L1/2. The rental rate of an industrial copy machine is $100 per day, and the wage rate is $12 per hour. Suppose that industrial copy machines are leased on annual contracts, so the store’s number of industrial copy machines is fixed at 4 in the short run. This entire question except for part (e) is about the short run. (3 points) (a) Write down the store’s short run cost minimization problem, and show that the store’s daily cost function is c(y) = 400 + 3y2. (Hint: The algebra here is straightforward; there is no need to set up a Lagrangian.) 2 point: The store’s cost minimization problem is c(y) = minL, 12L + 100(4) s.t. 41/2 L1/2 = y 1 point: Substituting L = y2/4 from the production function into 12L + 100(4) gives c(y) = 400 + 3y2. (7 points) (b) Suppose the store is a monopolist in a small town, where the daily demand for copy services is y = 80 – p. Draw the demand curve, the marginal revenue curve, and the marginal cost curve on the same graph (please label the curves clearly), and mark where the profit‐maximizing output and price are. Show that the profit‐maximizing level of output is 10. What price does the monopolist charge? 1 point: The inverse demand curve is p = 80 – y, so revenue as a function of output is R(y) = (80 – y)(y) = 80y – y2. Marginal revenue is MR(y) = ∂(80y – y2) / ∂y = 80 – 2y. 1 point: The marginal cost curve is given by MC(y) = ∂c(y) / ∂y = 6y. 2 points: [Accurate diagram plotting the (inverse) demand curve, MR(y), and MC(y).] 1 point: The profit‐maximizing level of output solves MR(y) = MC(y). (Accurate depiction on the diagram is sufficient for full credit.) 1 point: The firm charges the price corresponding to the profit‐maximizing level of output on the demand curve. (Accurate depiction on the diagram is sufficient for full credit.) 1 point: Solving MR(y) = 80 – 2y = 6y = MC(y) gives y = 10. (1 point) (c) What price does the monopolist charge? 1 point: Substituting y = 10 into the demand curve, the monopolist charges p = 80 – 10 = 70. (2 points) (d) If the store produces the profit‐maximizing level of output, how many labor‐hours will it hire? 2 points: From the production function, L = y2/K. Since y = 10 and K = 4, L = (10)2/4 = 25. (2 points) (e) Will the store’s profit be higher in the short run or the long run (assuming the demand curve is the same in the both cases)? Explain. (No need for calculations here; verbal intuition will suffice.) 1 point: The store’s profit will be higher in the long run. 1 point: By definition, in the long run, the firm can adjust its capital input as well as its labor input. Hence, for any given level of output, the firm can always produce that output at least as cheaply in the long run. ...
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This note was uploaded on 12/28/2011 for the course ECON 3010 at Cornell University (Engineering School).

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