Question

Based on your reading and our discussion in class, the demand for health insurance (actually other insurances, too) is related to several important factors. Explain the following using graphs:

A) How is demand for health insurance related to the degree (level) of risk aversion.

B) How is demand for health insurance related to the size of potential “loss”. In this case, consider “loss” as the financial loss or cost that may incurred if a negative health event happens.

Answer 1

Almost all people are risk averters and hence they buy insurance to avoid risk.

The important question arises on how much money or premium an individual person for risk-averse will pay to the insurance company to avoid risk and uncertainty approaching him/her.

For example: a person purchases a house which yields him 30,000 income per month. But on someday unfortunately, if the house catches fire and due to the damages, his income falls to Rs. 10,000 from 30,000 per month and so then he suffers a loss of income. In simpler analysis, suppose there is a 50% chance of the house catching fire, then expected income in this risky situation is that the utility function OU is a diminishing marginal utility of money income for a risk averse individual, as is shown in the below figure. With the regular income of Rs. 30,000 his utility is 75 and with the lower income of Rs. 10,000 his utility is 45.  

Suppose if there is a probability of 0.5 for each of the outcome, expected utility of the two outcomes would be as:  

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

= 0.5×75 + 0.5 x 45, = 60

As seen in the figure, that there is a straight-line AB joining both the utilities I.e.; 75 and 45. On this straight-line AB, the amount of expected utility will be corresponding to the expected value of income in the present risky situation as it can be seen from figure that on this straight-line AB and corresponding to the expected value of income of Rs. 20,000, the expected utility is 60 which is shown as the point D on the line AB.

But from the individual’s utility function - OU, it can be seen that utility of 60 equals a certain and assured income of Rs. 16,000. So, the person with the expected income of Rs. 20,000 will not mind to let go Rs. 4,000 to gain a guaranteed income of Rs. 16,000 as per the expected Utility of the uncertain but expected income of Rs. 20,000 will be equal to the utility of a fixed income of Rs. 16,000.

To sum up, it means that if the person gives up Rs. 4,000 from the uncertain expected regular income, he will get the same utility of 60, which is similar to what he would get with a certain income of Rs. 16,000. Risk premium will be the amount of Rs. 4,000 which is equal to distance DC in the above figure.  

Hence, the risk premium is that amount of money which a risk-averse person will be ready to pay in order to avoid the unexpected risk. By paying the risk premium this individual insures himself against any large losses that might occur due to any natural disasters and get an assured or fixed income. It is clear from the above illustration that why people prefer to buy insurance for uncertainties such as life, fire, accident, and ill health.