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HE+ANS+to+HW3+-+Spring+2010 - Department of Economics...

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Department of Economics Prof. Derek DeLia Health Economics 220:316:01 Spring 2010 ANSWERS TO HOMEWORK #3 QUESTION 1 : a. Yes, the consumer is risk averse because the second derivative is negative for all positive wealth levels. b. $205.65 c. $5.65 QUESTION 2 : a. For the consumer to be risk averse we must have 0<c<1, b>0, and a can be any number. b. $5.19 c. The answer to part b would be unchanged. The number a would cancel out on both sides of the equation. d. I will go over the diagram in the review session. QUESTION 3 : a. Since 0<c<1, the consumer is risk averse. We proved in class that a risk averse consumer will choose to fully insure if the premium is actuarially fair. Therefore, the optimal value of a is 1. b. After setting up the objective function and setting the first derivative to zero, we have a=0.43. Since the consumer is risk averse, we know the objective function is concave. Therefore, this gives the consumer maximum utility. c. the answers to a and b would not change at all since adding a constant does not affect the derivatives or the optimal value of a.
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