Realized income into the pool

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Reference no: EM13770758

1. Demand for Insurance

Consider the utility function u(x) = log x.

(a) Set up the individual's expected utility maximization problem. Derive the first-order condition.

(b) Find the optimal insurance coverage, C*, when insurance is actuarially fair (i.e. q = p).

(d) Comparative Statics. Use the first order condition from part (a) to find change in C* = C(W; L; q; p) with respect to

(a) Probability

(b) Loss

2. Supply of Insurance

Suppose there are two risk averse individuals, Cate and Dirk. They both face an identical independent risky prospect: each individual has a 50% chance of earning $100 and a 50% chance of earning $10. Let u(x) = log x be the utility function.

(a) Find Dirk's expected utility from this prospect.

(b) Suppose Cate and Dirk decide to pool their incomes. They pay their realized income into the pool and they each get half of the total income of the pool. Find Dirk's expected utility under the pooling scheme. (Hint: Since the two prospects are identical and independent, there are four possible outcomes).

Reference no: EM13770758

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