Consider a consumer who earns $700 if it is sunny and nothing if it rains. Rain
ID: 1193307 • Letter: C
Question
Consider a consumer who earns $700 if it is sunny and nothing if it rains. Rain occurs with probability ¼. The consumer’s von Neumann-Morgenstern utility index is
U = Y1/2.
The consumer can buy an insurance policy that costs 40¢ for each $1 of coverage if it rains.
(a). Solve for the consumer’s optimal bundle of contingent claims to income if it is sunny (YS) and income if it rains (YR). How much insurance coverage will he buy? How much will he pay in insurance premium?
(b). If the price of insurance rises and the consumer adjusts his purchase of insurance, how will his bundle of contingent claims to income in the two states of the world change?
Explanation / Answer
a) Contigent claims to income if it rains = 700 *1/4 = 175
Contingent claims ot income if it is sunny 700 *3/4 = 525
he will buy insurance for 525 *1/2
262.50
He will pay premium equal to 262.50 *0.40 = 105
b) If the price of insurance rises and the consumer adjusts his purchase of insurance, then he will have to pay a higher premium for same coverage
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