Question

Suppose that a decision maker’s risk attitude toward monetary gains or losses x given by the utility function u(x)=(10,000+x)^0.5 Suppose that a decision maker has been given a lottery ticket for free. Suppose that the lottery winning is $500,000, and the chance of winning is one in a thousand. What is the minimum price that the decision maker would be willing to sell the ticket for?

Answer 1

SOLUTION:

From given data,

The utility function u(x)=(10,000+x)^0.5

The  lottery winning is $500,000

The expected utility from the lottery for the decision maker would be:

EU = 0.001 * U(500,000) + 0.999 *U(0)

because there is a 0.001 chance of winning 500,000 and 0.999 chance of not winning anything.

therefore we get,

EU = 0.71414 + 99.9

EU = 100.61414

Now,

Let the price for which he would let the ticket sell be k.

Then the expected utility from this k amount should be equal to that of the expected utility from the ticket that is we get,

U(k) = 100.61414

squaring on both sides then we get,

Therefore ,$123.2 is the answer.

The minimum price that the decision maker would be $123.2 willing to sell the ticket