# Homework 7 Answers - 1 The previous analysis is illustrated...

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ECO 301: Intermediate Microeconomics Marco A Castaneda Homework 7: Answers 1. ANSWER We have the distributions over the income of the individual: = 2 / 1 100 2 / 1 w/p 0 x A) = 3 / 1 100 3 / 2 w/p 25 x B) a) For each distribution, the expected income of the individual is: A) 50 ) 100 )( 2 / 1 ( ) 0 )( 2 / 1 ( ] x [ E = + = B) 50 ) 100 )( 3 / 1 ( ) 25 )( 3 / 2 ( ] x [ E = + = b) The preferences of the individual are described by the utility function 2 / 1 ) x ( ) x ( u = Therefore, to determine which distribution the individual would prefer, we compute the expected utility from each distribution: A) 5 ) 100 )( 2 / 1 ( ) 0 )( 2 / 1 ( )] x ( u [ E 2 / 1 2 / 1 = + = B) 3 / 20 ) 100 )( 3 / 1 ( ) 25 )( 3 / 2 ( )] x ( u [ E 2 / 1 2 / 1 = + = Therefore, the individual would prefer the distribution (B). Intuitively, both distributions have the same expected income, but the individual is risk averse and there is a sense in which the distribution (B) involves less risk than the distribution (A).

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Unformatted text preview: 1 The previous analysis is illustrated in the graph: u 2. ANSWER We have the probability distribution over income and the preferences of the individual = 2 / 1 400 2 / 1 w/p 100 x and 2 / 1 ) x ( ) x ( u = a) The expected income is 250 ) 400 )( 2 / 1 ( ) 100 )( 2 / 1 ( ] x [ E = + = b) The expected utility is 15 ) 400 )( 2 / 1 ( ) 100 )( 2 / 1 ( )] x ( u [ E 2 / 1 2 / 1 = + = c) The certainty equivalence is the income with certainty which provides the same utility as the distribution, namely u(x CE ) = E[u(x)]. Therefore, we have (x CE ) 1/2 = 15 x CE = 225 10 25 x E B [u(x)] 50 75 100 E A [u(x)] 2 3 u d) The answers are illustrated in the graph: 20 10 100 x E[u(x)] 200 300 400 E[x]...
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## This note was uploaded on 04/13/2008 for the course ECON 301 taught by Professor Castaneda during the Spring '08 term at Tulane.

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Homework 7 Answers - 1 The previous analysis is illustrated...

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