Final answer:
To determine how much one would pay to avoid a risky gamble with a logarithmic utility function, we evaluate their certain equivalent wealth that provides the same utility as the expected utility of the gamble. This calculation is performed for two levels of wealth, $10,000 and $1,000,000.
Step-by-step explanation:
The question involves calculating the amount a person with a logarithmic utility function for wealth would pay to avoid a risky gamble. Given the utility function U(W) = ln(W), the expected utility for a 50/50 chance of winning or losing $1,000 when the current wealth is $10,000 can be calculated as:
0.5 * ln($10,000 + $1,000) + 0.5 * ln($10,000 - $1,000) = 0.5 * ln($11,000) + 0.5 * ln($9,000).
We then compare this expected utility to the utility of certain wealth level W (i.e., without taking the risk) that gives the same utility. This certain wealth is what the person would pay, denoted C, so U(W-C) = Expected Utility. We then solve for C.
For $1,000,000 wealth, the calculations follow the same process. Since marginal utility decreases as wealth increases, the amount they would be willing to pay to avoid the risk may be different.