171 M2-5

171 M2-5 - Economics 171 Decisions Under Uncertainty...

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Economics 171: Decisions Under Uncertainty Solutions to Midterm 2: Winter 2009 1. (24 pts) Amy’s utility function is ( ) 2 100 ux x x = . a. For what values of x is Amy’s utility function increasing? ( ) '1 0 0 2 0 50 x x =− > < b. Calculate her coefficient of absolute risk aversion. ( ) () '' 2 21 0 0 2 5 0 x x x λ = c. Write the equation that you could solve to find her certainty equivalent for the lottery ($20, 0.2; $40, 0.8). (You do not need to solve for this certainty equivalent.) () ( ) () () 22 2 $20,0.2;$40,0.8 100 0.2 100 20 20 0.8 100 40 40 ux EU xx = ⎡⎤ −= + ⎣⎦ d. How many solutions will your equation for (c) have? Explain intuitively. The graph of u ( x ) might help. Two. The utility function is an upside down parabola. Two x values will have the appropriate level of utility. e. Is she nonincreasingly (decreasingly), constantly, or nondecreasingly (increasingly) risk averse? Briefly explain. 11 0 50 50 x x =− − = > ⎢⎥ −− (except when x = 50) She is none of these. She is nondecreasingly risk averse when 0 < x < 50 and when x > 50. But her coefficient decreases if we go from x < 50 to x > 50. (It’s fairly acceptable to say she is nondecreasingly (increasingly) risk averse.)
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2. (24 pts) Conan is a risk averse, von Neumann-Morgenstern expected utility maximizer. His utility function satisfies our usual assumptions.
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This note was uploaded on 06/08/2010 for the course ECON 171 taught by Professor Newhouse during the Spring '07 term at UCSD.

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171 M2-5 - Economics 171 Decisions Under Uncertainty...

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