JNU SSS 2011 Question 26: Choice under uncertainty

Suppose there is a consumer whose life is divisible into three periods which follow each other consecutively—youth, middle age and post-retirement age. The length of each period is 20 years and the consumer earns no labour income on post-retirement. In his youth the consumer earns labour income at the rate of Rs 2,500 per month. In his middle age the consumer's earnings are uncertain—there is a 25% probability that he will earn at the rate of Rs 5,000 per month, alternatively, he will earn at the rate of Rs 10,000 per month. The consumer gets to know what his rate of earnings in middle age will be at the end of his youth. Assume that the consumer expects to pay no taxes, the nominal rate of return on saving and the rate of interest is always zero and there is no inflation expected throughout his life.

Suppose the consumer's attitude towards risk is as follows : He prefers an alternative which promises him an amount of Rs $X$ with probability $p$ and an amount of Rs $Y(X > Y)$ with probability $1 - p$ to an alternative which promises him an amount of Rs $Z$ for sure if and only if $Z < Y + (2p/3)(X - Y)$. An insurance company approaches the consumer in his youth and offers to pay Rs 7,615 per month to the consumer in his middle age in exchange for his flow of income during that period. Will the consumer accept the offer?