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Consider an expected utility maximizing individual who has initial wealth $W_0$. Two states of the world are possible. For any wealth level $W$, the utility

Consider an expected utility maximizing individual who has initial wealth $W_0$. Two states of the world are possible. For any wealth level $W$, the utility functions in states 1 and 2 are $u_1(W)$ and $u_2(W)$ respectively, and they are both strictly increasing and strictly concave. In state 2 the individual incurs a loss equal to $L$, while in state 1 she incurs no loss. The probability of state 2 is $\pi$. The individual can buy insurance coverage against the possible loss; if the amount of insurance coverage she buys is $C$, the consumer will receive this amount from the insurance company if and only if a loss occurs. Insurance coverage has a price equal to $p$ for each unit of coverage she buys; so, buying coverage equal to $C$ will cost the consumer the amount $pC$. This question is about the optimal amount of coverage $C^*$. For the next two parts only: assume that $p = \pi$, and also assume that $u_1'(W) > u_2'(W)$. Calculate the slope of the agent's indifference curves where they cross the certainty line (remember, the certainty line is the set of all points where the consumer's wealth is the same in all states)

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