1. 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 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 $\$100$ 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.)

Economists often make use of an exponential utility function for money:
$U(x) = -e^{-x/R}$, where $R$ is a positive constant representing an
individualâ€™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 $\$400$ 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 $\$100$ 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.)