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Unformatted text preview: Homework 5 1. On Homework 2 (the Bonus question) you were asked to write the FOC for corner solutions. a) Use those conditions to write the demand functions associated with the utility function u(x,y)= x + y. b) Illustrate in an indifference curve diagram the best bundle when P x = 2, P y = 1 and I = 10. a) Similar for x b) Plug in the demand the values, (x,y)=(5,0) 2. If you saw the movie The Perfect Storm then you know that commercial fishing is a risky venture. In particular a fishing boat cannot be assured of finding a sufficient number of fish to make any money on the trip. Suppose that there are two fishermen, George and Mark, who are each setting off on fishing trips in the morning. Both are experienced fishermen so they each know where the fish are likely to be. However they also know that they cannot be absolutely sure that they will be successful. If they find a large school of fish then the fishing trip will earn a profit for each of them of $50,000. However if they cannot find a large school of fish then they will earn no profits on the trip (we will assume that they can find enough fish to cover the costs of the trip). Each fisherman knows that the likelihood that he will find a large school of fish is .9 so that the probability that he will not find a large school is .1. a) What are the expected profits of each of the fishing trips? b) Suppose that the night before they sail George proposes that they pool their risks. In particular he proposes that if only one of them find a large school of fish then they will share The thick line is the budget constraint while the thin indifference curves. I/Py the profits of the successful trip equally (if neither finds the large school or if both find the large school then they exchange no money). What are the expected profits of each of the fishing trips? If both fishermen are risk averse then will Mark accept the proposal? Explain your answer. c) Suppose that Georges preferences can be represented by the utility function ( 29 1 2 ( ) .002 u x x = . What is the certainty equivalent to his original situation (ie where he does not pool risks with Mark)? What is the risk premium? Illustrate the certainty equivalent and the risk premium in a diagram. 3. Suppose that you own a bar near the University of Nevada at Las Vegas. Every time the basketball team wins a home game, business is brisk and you clear $200 for the day. When it loses, business is slow and on those days you clear only $50. Let 1 be the probability that the basketball team wins. The problem is, you don't like risk; you would prefer a certain income to an uncertain one. Fortunately for you, gambling is legal in Nevada and there are many people who like to bet on sporting events. Thus you can hedge against low profit days by betting against the home team....
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 Winter '09
 chudnovsky

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