Question

Consider a lottery with three possible outcomes: 

The maximum amount that a risk-neutral person would be willing to pay to play the above lottery is INR ____________.

Hint:

For a risk-neutral person, the maximum amount they would be willing to pay for a lottery is equal to the expected value of the lottery, which is the weighted average of the possible rewards, where the weights are the probabilities.

Answer 1

To find the maximum amount a risk-neutral person would be willing to pay, we calculate the expected value of the lottery.

The expected value \( E(X) \) of the lottery is given by the sum of the products of the probabilities and rewards for each outcome:

\[ E(X) = (P_1 \times R_1) + (P_2 \times R_2) + (P_3 \times R_3) \] Where:
\( P_1, P_2, P_3 \) are the probabilities of outcomes I, II, and III, respectively.
\( R_1, R_2, R_3 \) are the rewards corresponding to outcomes I, II, and III, respectively.

Substitute the given values:

\[ E(X) = (0.2 \times 25) + (0.3 \times 50) + (0.5 \times 100) \] \[ E(X) = 5 + 15 + 50 = 70 \]

Thus, the maximum amount a risk-neutral person would be willing to pay to play the lottery is INR 70.