Amanda recently graduated from college,and she has a job offer with uncertain income.There is a 70% probability that she will make $10,000 and a 30% probability that she will make $70,000.Suppose Amanda is offered another job with a certain income.All else equal,if she has a constant marginal utility of income,she will accept the second job offer only if it pays more than:
A)$40,000.
B)$28,000.
C)$10,000.
D)$21,000.

Question

Quizplus · Accepted Answer

To determine Amanda's expected utility from the uncertain job offer, we need to calculate the expected value of her income:
Expected value = (probability of $10,000 * $10,000) + (probability of $70,000 * $70,000)
= (0.70 * 10,000) + (0.30 * 70,000)
= 31,000

Next, we need to compare Amanda's expected utility from the uncertain job offer to the utility she would receive from the certain job offer. Since we know that Amanda has a constant marginal utility of income, we can use a simple utility function that assumes decreasing marginal utility of income:

Utility = ln(income)

Using this function, we can calculate that Amanda's utility from the uncertain job offer is:

Utility of uncertain offer = ln(31,000) = 10.34

If the certain job offer pays X, Amanda will accept it if and only if:

Utility of certain offer = ln(X) > 10.34

Solving for X, we get:

X > e^10.34 = $28,484.09

Therefore, Amanda will accept the certain job offer only if it pays more than $28,484.09. Since the only answer choice that is greater than $28,484.09 is B ($28,000), the correct answer is B.

Amanda Recently Graduated from College,and She Has a Job Offer