eco204_summer_2009_HW_11 - University of Toronto,...

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain HW 11 Please help improve the course by sending me an email about typos or suggestions for improvements Question 1 We've examined firms competing as rivals in a Cournot oligopoly. In this question you will examine what happens if the firms cooperate instead. Ajax Microchip Corporation (AMC) manufactures and sells microchips. AMC's cost function is: C = 100 + 38 q1 where q1 ( note the subscript 1) is in `000s of units (i.e. 1,000 units would be q = 1). Assume AMC has the capacity to produce 10,000 microchips a month. Market demand is estimated to be P = 170 20Q where Q, the total market output, is in `000s of units and P is in dollars. Suppose AMC cooperates with another identical microchip manufacturer Murdock Microchip Company (MMC). Compare the first order condition for optimal output with the case of Cournot rivalry. How many microchips will each company produce and what will the market price be? How much profit will each company earn? Show all calculations. Hint: Now that the firms cooperate, what is their objective (think back to the franchisor/franchisee problem)? Question 2 Consider a "gamble" with three possible outcomes: $125 will be received with probability 0.2, $100 with probability 0.3, and $50 with probability 0.5. (a) What is the expected value of the gamble? (b) What would a riskneutral person pay to play the gamble? Question 3 The CEO of "Alberta Sandbox" an oil drilling company must decide whether to drill a site and, if so, how deep. It costs $160,000 to drill the first 3,000 feet at which there is a 0.4 chance of 1 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain striking oil. If oil is struck, the net profit is $600,000. If oil is not struck, the CEO can drill another 2,000 feet at an additional cost of $90,000. The chance of finding oil between 3,0005,000 feet is 0.2 and the net profit (after all drilling costs) from a strike at this depth is $400,000. What action should the CEO take to maximize profit? Question 4 (20072008 Final Exam Question) You're a dealer for a brand of luxury cars "LambbooGenie" 1 Sales of LambbooGenie cars are procyclical: in a growing (G) economy, sales increase and in a recessionary (R) economy, sales decrease. You have to place an order tomorrow afternoon for either 50 or 100 cars. Your profits depend on the state of the economy: LambbooGenie Dealership Profits Growth (G) $225m $350m Order Size 50 Cars 100 Cars Recession (R) $100m $150m (a) Suppose the probability of growth is P(G) = 0.6. How many cars should you order? Assume you're a risk neutral decision maker. To help decide how many cars to order, you pay money to acquire some information about the stock market which better informs you whether the economy will grow or contract. The following table gives the probability of stocks rising and falling and the economy growing and contracting: Table of Probabilities Growth (G) Recession (R) 0.4875 0 0.1125 0.4 0.6 0.4 Stock Market Stocks Rise (+) Stocks Fall () Total Total 0.4875 0.5125 1.000 (b) What is the value of your decision if you use the stock market as a "test" for whether the economy will grow or go into a recession? How much is the stock market information above worth to you? Again, assume you are risk neutral. Show all calculations clearly. Question 5 A company must decide whether to drill for oil. The outcome of not drilling is $0. The outcomes from drilling are the following net profits (i.e. revenues minus cost) and corresponding probabilities: 1 No relation to HLamborghiniH. 2 University of Toronto, Department of Economics, ECO 204 Summer 2009 S. Ajaz Hussain {$600m, $200m, $0m, or $120m; 0.2, 0.18, 0.32, 0.30}. (a) Draw the decision tree for this problem. (b) If the company is risk neutral, what is the decision? (c) Now suppose the company is risk averse. Suppose the board of directors decides that: U($600, $200; 1, 0) = U($600) U($600, $200; 0.7, 0.3) = U($200) U($600, $200; 0.5, 0.5) = U($0) U($600, $200; 0.25, 0.75) = U($120) Suppose you're now risk averse. Should the company drill for oil? Hint #1: the statement U($600, $200; 0.7, 0.3) = U($200) means "the utility of $200 is the expected utility of a gamble between $600 and $200 with probabilities 0.7 and 0.3 respectively". Put another way, the board of directors intuited their utility of $200 by the certainty equivalence of the gamble {$600, $200; 0.7, 0.3}. Hint #2: The maximum number in this question even though it's not in the tree is $600; similarly, minimum number in this question even though it's not in the tree is $0 what do you know about the utility of the max and min amounts? (d) Can you reduce the uncertainty for drilling for oil: ($600, $200, $0, $120; 0.2, 0.18, 0.32, 0.30) to a gamble between $600 and $200? By doing this question, you're reducing the drilling option ($600, $200, $0, $120; 0.2, 0.18, 0.32, 0.30) to an "equivalent risk". This is a technique used by risk managers to transform and understand risk in terms of some benchmark uncertainty. Hint: Exploit certainty equivalence. 3 ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto- Toronto.

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