Question

Certainty Equivalent and Risk Premium. Suppose an individual with zero initial wealth and utility function u(W)=√W is confronted with the gamble (16,4,0.5) i.e., it pays of 16with probability 0.5 and 4 with probability 0.5.

What is the certainly equivalent for this gamble?

Answer 1

The certainty equivalent for this gamble is $9.

Step-by-step explanation:

The certainty equivalent is the amount of a guaranteed outcome that an individual would be willing to accept instead of taking a risky alternative. To find the certainty equivalent for this gamble, we need to determine the amount of money that would provide the same level of utility as the gamble.

Using the utility function u(W) = √W, we can calculate the utility of each outcome of the gamble:

Utility of $16: √16 = 4

Utility of $4: √4 = 2

The probability-weighted utility of the gamble can be calculated as follows: (0.5 × 4) + (0.5 × 2) = 3

To find the certainty equivalent, we need to solve the equation √CE = 3, where CE is the certain amount of money that provides the same utility as the gamble's expected utility.

Taking the square of both sides of the equation, we get CE = 9.