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Unformatted text preview: Kata Bognar [email protected] Economics 142 Probabilistic Microeconomics UCLA Fall 2008 Homework Assignment 4. Solutions  1. ‘At the southernmost point of the United States are the Florida Keys, a string of [20] small islands held together by a concrete causeway.’ Two of these remote coral islands are Key Largo and Key West. Both islands have 50 inhabitants. Each year, early fall a hurricane passes by the area hitting one or the other island with equal probability and destroying 75% of the wealth on that (but not on the other) island. Suppose that every habitant of Key Largo has $10 , 000 from last year tourism. Then, if the hurricane hits Key Largo each habitant looses $7 , 500 . Similarly, suppose that every habitant of Key West has $10 , 000 and if the hurricane hits Key West each habitant looses $7 , 500 . The habitants of the Keys are expected utility maximizers with vNM utility function u ( x ) = √ x. (a) What are the relevant states of nature in this situation? Answer: There are two relevant states of nature here, one is when the hurricane hits Key Largo and the other is when the hurricane hits Key West. Let us call the state in which the hurricane hits Key Largo state 1 and the other state 2. SInce it is equally likely that the hurricane hits either island the probability of each states is 1/2. Notice that defining one state as the hurricane hits and the other as the hurricane does not hit is not correct. Then the ‘hurricane’ state includes both the event that the hurricane hits Key Largo and the event that the hurricane hits Key West. However, they are quite different for the habitants, i.e. lead to different payoffs. (b) Pick a representative habitant from both islands and use an Edgeworth Box to show their endowments. What is the expected utility of the habitants? Justify that this allocation is not Pareto efficient. 1 (State 1) 12500 (State 2) 12500 Key Largo Key West • Endowment 10000 2500 Answer: The endowment for a habitant of Key Largo is basically an act with a payoff 10000 with probability 1/2 and a payoff 2500 with probability 1/2. The expected utility of the endowment for a habitant of Key Largo is the expected utility from this act given the vNM utility u ( x ) = √ x. So that is 1 2 √ 2500 + 1 2 √ 10000 = 75 ....
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This note was uploaded on 01/25/2010 for the course ECON ECON 142 taught by Professor Bognar during the Fall '09 term at UCLA.
 Fall '09
 Bognar
 Microeconomics

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