Question

A farmer believes that the probability that the next harvest season will be a rainy one is 50%, and that it will be normal is 50%. The farmer's utility function is: u (y) = (y)^1/2, where y is income. Yields appear in the table below:

Y in normal state	Y rainy season
$ 40,000	$ 10,000

Consider the following insurance plans:

Plan 1. Full coverage at an actuarially fair insurance premium.

Plan 2. An actuarially fair partial coverage of $20,000.

Plan 3. Partial coverage of $15,000 at a price per unit of coverage of $0.60.

2.1 Write the probability distributions of the three insurance policies

2.2 Calculating the expected utility, what is the best insurance plan to the farmer?

2.3 Find the optimal coverage of the farmer if the price per dollar of coverage is $0.60.

Answer 1