PS7a(09) - ECN 712 Fall 2009 Professor Schlee Problem Set...

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ECN 712 Fall 2009 Professor Schlee Problem Set VIIa, Additional Practice For problems 1 and 2, consider the insurance problem in MWG, exercise 6.C.1 , with the following change of notation: W is wealth in the absence of a loss, and L is the magnitude of a loss if it occurs, π 2 is the probability of a loss, I is the indemnity level, and r 2 ( π 2 , 1) is the price per dollar of coverage. The vN-M utility u is differentiable with u 0 > 0 and is strictly concave. 1. How does an increase in risk aversion affect insurance demand? If the household’s preferences satisfy decreasing absolute risk aversion, how does an increase in wealth affect insurance demand? 2. Demand for state-contingent consumption (a) Show that this insurance problem can be reformulated as follows (by substituting I out of the problem using the budget constraint which follows). The consumer has a state- contingent endowment of ω = ( W,W - L ). Let x = ( x 1 ,x 2 ), where x 1 is consumption in the no-loss state and x
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