Q. Assume you are a farmer thinking about buying weather insurance. The prob- ability of rain is 40% also if it rains you get 5$ worth of consumption. If it does not rain you get 2$ worth of consumption. The utility from consuming C dollars is log(C).

a) Write down the expected utility of the farmer.

b) Assume the farmer buys insurance that pays 3$ if it doesn't rain but costs 2$. Illustrate what is their consumption when it rains? When it doesn't rain?

c) Illustrate what is the expected utility of consumption with insurance?

d) Elucidate how much would the farmer be willing to pay for insurance that paid 3$?