Question

An individual owns two assets: an initial wealth of $20, and a lottery ticket which will pay a prize of $10 with probability 0.5 and nothing with probability 0.5.

Find the minimum price at which the individual is willing sell his lottery ticket if his utility function is:

a. u(x) = x
b. u(x) = x2
c. How do you reconcile the difference between the answers found for (a) and (b)?

Answer 1

He will sell at 5

Explanation:

Compute expected utility with the ticket:

1) EU = (0.5 × 30)+ (0.5 × 20) = 25 utils

We have to find the wealth level that provides the same utility as we have with the ticket:

Since U(x) = x

x = 25

He will sell at = 5

2) EU = 0.5 ×
`(30)^(2)` + 0.5 ×
`(20)^(2)`

= 650 utils

since U(x) =
`x^(2)`

or x =
`√(U)`

x =
`√(650)`

x = 25.495