Economists often make use of an exponential utility function for money: U(x) = −e^x/R, where R is a positive constant representing an individual’s risk tolerance. Risk tolerance reflects how likely an individual is to accept a lottery with a particular expected monetary value (EMV) versus some certain payoff. As R (which is measured in the same units as x) becomes larger, the individual becomes less risk-averse.

a. Assume Mary has an exponential utility function with R = $500. Mary is given the choice between receiving $500 with certainty (probability 1) or participating in a lottery which has a 60% probability of winning $5000 and a 40% probability of winning nothing. Assuming Marry acts rationally, which option would she choose? Show how you derived your answer.

b. Consider the choice between receiving $100 with certainty (probability 1) or participating in a lottery which has a 50% probability of winning $500 and a 50% probability of winning nothing. Approximate the value of R (to 3 significant digits) in an exponential utility function that would cause an individual to be indifferent to these two alternatives. (You might find it helpful to write a short program to help you solve this problem.)