Most people are risk averters and therefore they buy insurance to avoid risk.

Now an important question is how much money or premium a risk-averse individual will pay to the insurance company to avoid risk and uncertainty facing him.

Suppose the individual buys a house which yields him income of Rs. 30 thousands per month. But if the house catches fire and due to the damage caused, his income from it falls to Rs. 10 thousands per month and thus he suffers a loss of income. For the sake of simplifying analysis suppose there is 50 per cent chance of the house catching fire. Then they expect value of income in this risky and uncertain situation is

E (X) = 0.5 X 30,000 + 0.5 x 10,000

= 15,000 + 5,000

= 20,000

It is important to note that expected income of Rs. 20,000 is the weighted average of the two uncertain alternatives (30 thousands and 10 thousands) using their probabilities as weighty Different probabilities of the occurring of these incomes (30 and 10 thousands) would yield different expected income. Further note that the expected income is not the actual income that a person would get; it is weighted average of the two uncertain outcomes.

The utility function OU with a diminishing marginal utility of money income of a risk- averse individual is shown in Fig. 17.7. With money income of Rs. 30 thousands, his utility is 75 and with his lower income of 10 thousands his utility is 45. Given that there is probability of 0 5 for each outcome, expected utility of the two outcomes is given by

E (U) = 0.5 U (30,000) + 0.5 U (10,000)

= 0.5×75 + 0.5 x 45

= 37.5 + 22.5

= 60