Rose is a risk-averse decision-maker and faces a decision involving the oil rights on a piece of land. A decision analyst helps her determine an appropriate utility function by asking her to consider what she would do in some hypothetical situations. In the first hypothetical situation, she is given the opportunity to take the following gamble: there is a 50% chance of a gain of $200,000 and a 50% chance of a loss of $100,000. In this situation, she would prefer the gamble to doing nothing. In the second hypothetical situation, she is given the opportunity to take the following gamble: there is a 50% chance of a gain of $500,000 and a 50% chance of a loss of $250,000. In this situation, she does NOT prefer the gamble: she prefers to do nothing. If she will model her utility with the following exponential utility function
U(x)=1-e^(-x/R), then which of the following values of the risk tolerance R yields a utility function that is consistent with her preferences: $50,000, $100,000, $400,000, or $800,000?