Suppose your utility function for your asset position is u(x) =x^1/2 and you have $1,000,000 at present. KFC, a well-known fast food chain, is offering you the chance to buy a franchise for the next year which yields the following probabilistic payoffs: With probability 0.5, the franchise yields a payoff of $102,500. L: With probability 0.5, the franchise yields a loss of -$19,900.

1. What is the maximum you are willing to pay for this franchise?

2. Suppose now you already own that franchise, and you would like to sell it given the above probabilistic payoffs. What is the minimum selling price that makes you happy.

3. Suppose you don’t have $1,000,000 instead, your asset position is $100,000, how much will be your selling price. In two lines, comment on your findings of part 2 and 3.