This problem unpacks risk aversion and the value of insurance. An individual with wealth $100 considers the following gamble: win $50 (and consume $150) with 50% probability, lose $50 (and consume the remaining $50) with 50% probability. The individuals utility function over final consumption is u(c)=c^(1/2) .

A) Write down the individuals expected utility using the figures provided. Calculate the expected utility over the gamble (use a calculator).

B) What is the individuals expected consumption E[c]?

C) How does the individuals expected utility compare to their utility over the expected consumption?

D) Repeat the above, picking different numbers for the payoffs (other than gain $50 lose $50). Repeat again with different numbers for the probabilities (other than 50/50). So long as the probabilities sum to 100% and consumption (c) is not negative, you should always get the same answer you got in part c. Draw a graph that explains why this occurs. Explain what all this has to do with the concept of risk aversion.