Exercise 2- Attitudes towards risk and fair bets

The following graph represents Mike's marginal utility of income (not the utility but the marginal utility):

Marginal Utility

MU(I)

Income

We know that Mike's income I is greater than $20, but we do not know his exact income. Alejandro offers Mike

the following bet: Alejandro will roll a 6 sided dice (all numbers equally likely). If it is 1 or 2, Mike pays Alejandro

$20. Otherwise, if it is 3, 4,5 or 6, Alejandro pays Mike $10.

a) Is this a fair bet?

b) Will Mike accept or reject the bet? Do your answer depend on Mike's initial wealth? (assuming he can

always pay the $20 if he loses)