• 6. Rose has the following exponential utility function $U(x) = 1 - e^{-x/R}$ with R being the risk tolerance. In the following gamble: there is a 50% chance of a gain of $500,000 and a 50% chance of a loss of one third of $500,000. She prefers to do nothing over this gamble. Which of the following values of R yields a utility function that is the most consistent with her preference? (12 points)
\$50,000;
\$100,000;
\$250,000;
\$350,000.