This question requires writing some code.

Suppose that you have a consumer who earns income of 20 units of consumption but faces a probability that they will suffer a loss of 10 units of consumption. Utility is logarithmic, and the expected utility function is additively separable across states (as in class). There will also be an insurance premium and an amount of coverage purchased, .

a) Write a function for the expected utility as a function of ,, and the insurance premium.

b) Suppose there is a risk neutral insurer. Define a function to compute the expected utility for the consumer who purchases any amount insurance from zero up to full insurance and plot this.

c) Now repeat (a) and (b) for a general CRRA utility function: ()=11(>0,1)......(1)

Compute the expected utility function as described in (b) for 3 values of (you can pick any you like) and plot all three of these functions along with the one for log utility on the same graph.