Consider the salary of Mary Sue Nelson, a sales agent for Plain Truth Advertising. Her wage package is W = 1,000 + .4Q, where Q is her dollar volume of sales. Her productivity is Q = 200e + , where e denotes her hours of effort and m is a random variable with mean 0. She has an effort cost of C = e². Under this contract, her choice of effort will be: A) 0 hours per week. B) 20 hours per week. C) 40 hours per week. D) 80 hours per week.

Question

Quizplus · Accepted Answer

To find the optimal choice of effort, we need to maximize Mary Sue's utility, which is given by her wage package minus the effort cost:

U = W - Ce = (1000 + 0.4Q) - Se^(1/2) = (1000 + 0.4(200e + 11m)) - Se^(1/2)

Taking the derivative of U with respect to e and setting it equal to 0, we get:

dU/de = 88Se^(-1/2) - 0.4S = 0

Solving for e, we get:

e = (220/S)^(2)

Now we need to check if this choice of effort is feasible, i.e. if the cost of effort is less than the expected increase in income due to increased sales:

Ce = Se^(1/2) = S(220/S) = 220 < 400

Since the cost of effort is less than the expected increase in income, Mary Sue will choose to work 40 hours per week (i.e. e = 4400/S).

Consider the Salary of Mary Sue Nelson, a Sales Agent