mid_ans_F06

mid_ans_F06 - Department of Economics University of...

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Page 1 of Three Department of Economics Economics 202A Fall 2006 University of California, Berkeley Akerlof/Halac There are three questions. Answer all parts to all questions. 1. Inventory-Sales Problem [40 points] You hold an inventory of one bushel of wheat. The bushel costs you s to store per period. The price per bushel, p, randomly varies over time and is i.i.d. Your goal is to sell the wheat to maximize your discounted profits. Assume that the discount rate for this problem is 0. A. Explain why, if a price p is observed in the first period, the current value of the bushel of wheat, is: V(p) = max {p, [-s + E V(p´)]}, where V(p´) is the value of the wheat, conditional on observing a price p´ one period from now. E represents expectations. Using intuition, explain why the solution to this problem is a “threshold rule”: sell, if p > p* wait, if p ± p*. Also, explain why the threshold rule satisfies the equality : p* = - s + E V (p). B. Assume that p is distributed uniformly between 0 and 1, and that s ±² . Show that: p* = 1 - [(1 - (1 -2s) ] ² . What is the value of p* as the cost of storage, s , approaches zero? Give an intuitive explanation for your answer.
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Page 2 of Three 2. A Taylor Model [40 points] Consider an economy with two competing firms, i = { A , B }, whose prices are fixed over one- year intervals. Firm A sets its prices in January and Firm B sets its prices in July. Let t be six-month periods, so that A sets its prices at t = 0, 2, 4, etc. and B at t = 1, 3, 5, etc. Assume that the ideal price for firm i at time t is equal to the money supply at time t : p i * t = m t The price set by a firm at time t , x t , is an average of the ideal price at t and the expected ideal price at t + 1 (with the expectation taken at time t ): x t = ± p i * t + ± E t p i * t+1 Regarding expectations, the firm setting the price at time t knows the money supply at that time. The aggregate price level is:
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This note was uploaded on 08/01/2008 for the course ECON 202A taught by Professor Akerlof during the Fall '07 term at Berkeley.

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mid_ans_F06 - Department of Economics University of...

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