A salesperson works for a car dealership for 40 hours per week,but may choose not to work hard all of the time.The dealership's owner cannot observe the salesperson's effort,but can observe the number of cars sold.The salesperson's personal cost of working at the dealership is C(H)= 1,200 + H²,where H is the number of hours during which he works hard.The corresponding marginal cost of effort is MC = 2H.Without any effort,the salesperson will,on average,generate a profit of $1,200.With each hour of high effort,he has a 5 percent chance of selling a car.Each car sale generates a profit of $900.Which of the following is an incentive scheme that leads to the efficient effort level and allows the owner to keep all of the surplus? A) $900 in base pay with a $1,177.50 bonus for each car he sells B) $900 in base pay with a $900 bonus for each car he sells C) $600 in base pay with a $1,000 bonus for each car he sells D) $1,177.50 in base pay with a $900 bonus for each car he sells

Question

Quizplus · Accepted Answer

To find the efficient effort level, we need to compare the marginal cost of effort (MC) to the marginal benefit of effort (MB). The marginal benefit of effort is the probability of selling a car times the profit per car sale, which is 0.05 * 900 = $45 per hour of high effort. Setting MC = MB, we get:
2H = 45
H = 22.5
Therefore, the efficient effort level is 22.5 hours of high effort per week.

To design an incentive scheme that leads to this efficient effort level and allows the owner to keep all of the surplus, we need to offer the salesperson a base pay plus a bonus that equals the marginal benefit of effort for each hour of high effort, since that is the amount that makes the salesperson indifferent between working hard and not working hard. The base pay should equal the profit generated by not working at all, which is $1,200. So the total compensation should be:

Base pay + Bonus = $1,200 + ($45 * 22.5) = $1,177.50

Therefore, choice D is the only one that meets these criteria. The salesperson will receive a base pay of $1,177.50 and a $900 bonus for each car sold, which is exactly the efficient incentive for this scenario.

A Salesperson Works for a Car Dealership for 40 Hours