12-1. 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 key question is what
happens to the wage in the time-rate firm. Presumably this wage will also fall by half to $17.50 per hour.
If it falls by half, then the sorting of workers to the two firms remains unchanged.
12-2. 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 industry?
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
12-3. 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
MC = 4N
number of bicycles assembled per hour.
Donna’s marginal cost is
MC = 6N
(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 assembly’s, 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.
Likewise, as Donna’s marginal cost of the first assembly is $6, the second is $12, and the third is $18;