Consider the salary of Mary Sue Nelson, a sales agent for Plain Truth Advertising. She has an effort cost of C = e2 and a reservation wage of $1,500 so that her compensation package is W = 1,500 + 0.2 Q, where the CEO sets the incentive at 0.2 and Q = 200 e. Here effort is known only by the employee. There is a random shock to output each period whose mean is zero. (a) What is the optimal effort for Mary Sue Nelson? (b) On average, what total wage or salary will she earn each month? (c) On average, what is the output of sales contracts that she makes? (d) On average, what kind of profit will the CEO earn off of Nelson's work?
What will be an ideal response?
(a) Mary Sue's expected benefits are 1,500 + 0.2 Q = 1,500 + 0.2(200e) = 1,500 + 40e. Her marginal expected benefit from another hour of effort is therefore 40. Her marginal cost from effort is 2e. Therefore her optimal effort is 40 = 2e or e = 20 hours.
(b) She will earn E(W) = 1500 + 0.2(200(20)) = $2,300.
(c) Her output is E(Q) = 200(20) = $4,000 in sales revenue
(d) Expected profit for the company is E(Q ? W) = 4,000 ? 2,300 = $1,700.
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