Suppose you are a farmer thinking about buying weather insurance. The prob- ability of rain is 40%, and 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) Suppose the farmer buys insurance that pays 3$ if it doesn't rain but costs 2$. What is their consumption when it rains? When it doesn't rain?
c) What is the expected utility of consumption with insurance?
d) How much would the farmer be willing to pay for insurance that paid 3$?