Question

A dairy farmer is concerned about the outbreak of disease in her dairy herd. She is wondering whether to insure against a possible outbreak of the disease. Describe the steps involved in applying expected utility theory to this problem to determine whether the farmer should insure or not insure.

Do you think applying this theory is a reasonable approach to predicting whether the farmer will in fact take out insurance? Why or why not? Explain.

Answer 1

From a completely rational and economic point of view, the farmer will take out the insurance if the expected benefit of the insurance is higher than its cost. Lets understand ths in steps.

First, the farmer must know the cost of insurance. This is pretty straight forwards as all insurance companies clearly show that cost.

Now that the she knows the cost of the insurance, she must know that this cost will reduce her utility. This is because lets say she was earning 100USD earlier and the utlity from that was X. Now that she is earning 100-cost of insurance, her utility will be lesser than X. This reduction in utility is important. Lets say the reduction in utility is Y. So, in case she takes the insurance, her utility will be X-Y

Now lets come to the benefit of insurance. The insurance will make sure that the loss because of the outbreak is covered by the insurance. Lets say there is a 50% chance of the disease. Lets say this disease will reduce her utility X by Z amount. So, in case the disease occurs, her utility will be X-Z.

Her expected utility without insurance is.

.5*X+.5*(X-Z)           (because there is 50% chance of the disease).

Her Utility with insurance is

X-Y.

She should take the insurance as long as the utility from insurance is at least as much as the utility without insurance. In other words

(X-Y)>=.5*X+.5*(X-Z)

This makes intuitive sense too. Why take insurance if its utility is lower than utility when not taking insurance?

Now that we have described the theory, lets see if its reasonable to use this?

Clearly, the usability of the theory hinges on a lot of things. The first is that the farmer must know the probability of the disease actually happening. Then only she can calculate the expected utility. Second, she must also know the utility function (after all, cost and utility are two separate things) that she has. Finally, she must know the cost of the insurance.

It is hard to know the probability of the disease. Historical data and experience may give us some idea, but thats about it. Its also hard to know the exact utility we will get out of something.

So, in practicality, this theory is usable only if we are reasonably certain about all these things. If we arent, then its not practical to use this theory.

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