Answer:
The risk premium is positive, indicating a preference for certainty over risk.
Explanation:
The risk premium is a measure of how much someone is willing to pay to avoid a risky situation or to insure against potential losses. It is the difference between the expected value of a gamble (or lottery) and the guaranteed (certain) outcome.
In this case, you're dealing with a decision maker who has initial wealth of 4 and faces the following lottery:
Option A: A loss of 2 with a probability of 1/2
Option B: A gain of 2 with a probability of 1/2
Let's calculate the expected value of this lottery:
Expected Value (EV) = (Probability of Option A) * (Value of Option A) + (Probability of Option B) * (Value of Option B)
EV = (1/2) * (-2) + (1/2) * (2)
EV = -1 + 1
EV = 0
The expected value of this lottery is 0. This means that, on average, the decision maker doesn't expect to gain or lose wealth; it's a fair game in terms of expected value.
Now, to calculate the risk premium, we compare this lottery to a certain outcome. In this case, the certain outcome is keeping the initial wealth of 4.
Risk Premium = Guaranteed Outcome - Expected Value of Lottery
Risk Premium = 4 - 0
Risk Premium = 4
The risk premium is 4, which means that the decision maker is willing to pay up to 4 to avoid taking this lottery. This is because the lottery is a risky proposition, and the decision maker values the certainty of keeping their initial wealth at 4 over the gamble, even though, on average, the gamble doesn't result in a gain or loss. Therefore, the risk premium is positive, indicating a preference for certainty over risk.