16 Suppose my utility function for my asset position is u(x) x1/2. I have $10,000 at present. Consider the following lottery:

L: With probability 1 2

, L yields a payoff of $1,025.

L: With probability 1 2

, L yields a payoff of $199.

a If I don’t have the right to play L, find an equation that when solved would yield the amount I would be willing to pay for the right to play L. This is called the buying price of lottery L.

b If I have the right to play L, what is the least I would accept from somebody who wanted to buy the right to play L? (After someone else buys L, I can’t play L.) This is called the selling price of lottery L.

c Answer part

(b) for the case that I have $1,000.

d Suppose that my utility function for my asset position is u(x)  1  ex. Show that for all possible asset positions, the buying price of L and the selling price of L will remain the same. Show that for all asset positions,

†Based on Ellsberg (1961). the buying price of L will equal the selling price of L.