Now suppose you wish to estimate the utility of $5,000. You are indifferent between (a) receiving $10,000 for sure and (b) receiving $40,000 with probability p and $5,000 with probability 1 ? p , where p = 1/3. Use this to calculate the utility of $5,000.
Hint. Suppose, in general, that you fix utilities for salaries Q 1 and Q 2 (here, $10,000 and $40,000, respectively) and wish to calculate the utility of some salary Q that is less than $10,000. If you are indifferent between (a) receiving Q 1 and (b) a lottery in which you receive Q 2 with probability p and Q with probability 1 ? p , then
This allows you to solve for u ( Q )in terms of u ( Q 1 )and u ( Q 2 ).