Exercise 16.15

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.

  1. Assume Mary has an exponential utility function with $R = $400$. Mary is given the choice between receiving 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.

  2. Consider the choice between receiving 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.)

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