Chapter 11 - Incentive Pay
11-1. Suppose there are 100 workers in an economy with two firms. All workers are worth
$35 per hour to firm A but differ in their productivity at firm B. Worker 1 has a value of
marginal product of $1 per hour at firm B; worker 2 has a value of marginal product of $2
per hour at firm B, and so on. Firm A pays its workers a time-rate of $35 per hour, while
firm B pays its workers a piece rate. How will the workers sort themselves across firms?
Suppose a decrease in demand for both firms’ output reduces the value of every worker to
either firm by half. How will workers now sort themselves across firms?
Workers 1 to 34 work for firm A as a time rate of $35 is more than their value to firm B, while
workers 36 to 100 work for firm B. Worker 35 is indifferent. More productive workers, therefore,
flock to the piece rate firm. After the price of output falls, firm A values all workers at $17.50 per
hour, while worker 1’s value at firm B falls to 50 cents, worker 2’s value falls to $1 at firm B, etc.
The question is what happens to the wage. Presumably wage also fall, to $17.50 per hour in firm
A. If it falls by half, then the sorting of workers to the two firms remains unchanged.
11-2. Taxicab companies in the United States typically own a large number of cabs and
licenses; taxicab drivers then pay a daily fee to the owner to lease a cab for the day. In
return, the drivers keep their fares (so that, in essence, they receive a 100 percent
commission on their sales). Why did this type of compensation system develop in the taxicab
Imagine what would happen if the cab company paid a 50 percent commission on fares. The cab
drivers would have an incentive to misinform the company about the amount of fares they
generated in order to pocket most of the receipts. Because cab companies find it almost
impossible to monitor their workers, they have developed a compensation scheme that leaves the
monitoring to the drivers. By charging drivers a rental fee and letting the drivers keep all the
fares, each driver has an incentive to not shirk on the job.
11-3. A firm hires two workers to assemble bicycles. The firm values each assembly at $12.
Charlie’s marginal cost of allocating effort to the production process is 4
number of bicycles assembled per hour.
Donna’s marginal cost is 6
(a) If the firm pays piece rates, what will be each worker’s hourly wage?
As the firm values each assembly at $12, it will pay $12 for 1 assembly, $24 for 2 assemblies, etc.
when offering piece rates. As Charlie’s marginal cost of the first assembly is $4, the second is $8,
the third is $12, and the fourth is $16; Charlie assembles 3 bicycles each hour and is paid an
hourly wage of $36.
As Donna’s marginal cost of the first assembly is $6, the second is $12, and
the third is $18; Donna assembles 2 bicycles each hour and is paid an hourly wage of $24.
(b) Suppose the firm pays a time rate of $15 per hour and fires any worker who does not