Economists often make use of an exponential utility function for money

Economists often make use of an exponential utility function for money

(a) (4 points) Assume Mary has an exponential utility function with R=400. Mary is given the choice between receiving $400 with certainty (probability 1) or participating in a lottery that has a 60% probability of winning $5000 and a 40% probability of winning nothing. Assuming Mary acts rationally, which option would she choose? Show how you derived your answer.

(b) (5 points) Consider the choice between receiving $100 with certainty (probability 1) or participating in a lottery that has a 50% probability of winning $500 and a 50% probability of winning nothing. Write the most simplified equation F that can be used to pproximate the value of R in an exponential utility function that would cause an individual to be indifferent to these two alternatives:

F(R) = 0

For simplicity, you can use the notation Exp(x) to denote e^x

^{SHOW ALL YOUR WORK}