# ECO101H1 Chapter Notes - Chapter 12: Flight Attendant, Profit Sharing, Southwest Airlines

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Published on 1 Nov 2012
School
UTSG
Department
Economics
Course
ECO101H1
Page:
of 5
84
CHAPTER 12
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
the job.
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, where N is the
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;
Donna assembles 2 bicycles each hour and is paid an hourly wage of \$24.
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(b) Suppose the firm pays a time rate of \$15 per hour and fires any worker who does not assemble
at least 1.5 bicycles per hour. How many bicycles will each worker assemble in an 8 hour day?
As working is painful to workers, each will work as hard as necessary to prevent being fired, but that is
all. Thus, each worker assembles 1.5 bicycles each hour, for a total of 12 bicycles in an eight hour day.
12-4. All workers start working for a particular firm when they are 20 years old. The value of each
worker’s marginal product is \$18 per hour. In order to prevent shirking on the job, a delayed-
compensation scheme is imposed. In particular, the wage level at every level of seniority is
determined by:
Wage = \$10 + (.4 × Years in the firm).
Suppose also that the discount rate is zero for all workers. What will be the mandatory retirement
age under the compensation scheme? (Hint: Use a spreadsheet.)
To simplify the problem, suppose the workers works 1 hour per year. (The answer would be the same
regardless of how many hours are worked, as long as the number of hours worked does not change over
time). Some of the relevant quantities required to determine the optimal length of the contract are:
Age
Years
on the
Job VMP
Accumulated
VMP
Contract
Wage
Accumulated
Contract
Wage
21 1 \$18 \$18 \$10.00 \$10.00
22 2 \$18 \$36 \$10.40 \$20.40
23 3 \$18 \$54 \$10.80 \$31.20
24 4 \$18 \$72 \$11.20 \$42.40
40 20 \$18 \$360 \$17.60 \$276.00
41 21 \$18 \$378 \$18.00 \$294.00
42 22 \$18 \$396 \$18.40 \$312.40
43 23 \$18 \$414 \$18.80 \$331.20
60 40 \$18 \$720 \$25.60 \$712.00
61 41 \$18 \$738 \$26.00 \$738.00
62 42 \$18 \$756 \$26.40 \$764.40
The VMP is constant at \$18 per year. The accumulated VMP gives the total product the worker has
contributed to the firm up to that point in the contract. The wage in the contract follows from the
equation, and the accumulated wage is the total wage payments received by the worker up to that point.
Until the 20th year in the firm, the worker receives a wage lower than her VMP; after the 21st year the
worker’s wage exceeds the VMP. The contract will be terminated when the total accumulated VMP
equals the total accumulated wage under the delayed compensation contract, which occurs on the
worker’s 41st year on the job. So the optimal retirement age is age 61.
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12-5. Suppose a firm’s technology requires it to hire 100 workers regardless of the wage level. The
firm, however, has found that worker productivity is greatly affected by its wage. The historical
relationship between the wage level and the firm’s output is given by:
Wage Rate
Units of
Output
\$8.00 65
\$10.00 80
\$11.25 90
\$12.00 97
\$12.50 102
What wage level should a profit-maximizing firm choose? What happens to the efficiency wage if
there is an increase in the demand for the firm’s output?
The data in the problem can be used to calculate the elasticity of the change in output with respect to the
change in the wage. The efficiency wage is determined by the condition that this elasticity must equal 1.
This elasticity is 1 when the firm raises the wage from \$10 to \$11.25 an hour: (90-80)/80 ÷ (11.25-10)/10
= 1. The efficiency wage, therefore, is \$11.25. Note that this efficiency wage is independent of any labor
market conditions, and particularly does not depend on the demand for the firm’s output.
12-6. Consider three firms identical in all aspects except their monitoring efficiency, which cannot
be changed. Even though the cost of monitoring is the same across the three firms, shirkers at Firm
A are identified almost for certain; shirkers at Firm B have a slightly greater chance of not being
found out; and shirkers at Firm C have the greatest chance of not being identified as a shirker. If
all three firms pay efficiency wages to keep their workers from shirking, which firm will pay the
greatest efficiency wage? Which firm will pay the smallest efficiency wage?
In this example, there is no connection between the cost of monitoring and the efficiency of monitoring.
Moreover, the value of unemployment is the same for workers regardless of their employer. Focusing just
on the probability of being caught shirking, therefore, workers in Firm A have the least incentive to shirk
(as they are most likely to get caught) while workers in Firm C have the greatest incentive to shirk (as
they are least likely to get caught). The idea of efficiency wages is to use wages to buy-off the incentive
to shirk. Therefore, Firm A will pay the lowest efficiency wage, while Firm C will pay the greatest
efficiency wage.
12-7. Consider three firms identical in all aspects (including the probability with which they
discover a shirker), except that monitoring costs vary across the firms. Monitoring workers is very
expensive at Firm A, less expensive at Firm B, and cheapest at Firm C. If all three firms pay
efficiency wages to keep their workers from shirking, which firm will pay the greatest efficiency
wage? Which firm will pay the smallest efficiency wage?
In this example, there is no connection between the cost of monitoring and the efficiency of monitoring.
The efficiency wage, therefore, is determined by the incentives of the workers, not the costs of the firms.
(The decision of whether to monitor workers, of course, will depend on the cost of monitoring.) Thus, all
three firms will offer the same efficiency wage.

## Document Summary

Suppose there are 100 workers in an economy with two firms. All workers are worth per hour to firm a but differ in their productivity at firm b. Worker 1 has a value of marginal product of per hour at firm b; worker 2 has a value of marginal product of per hour at firm b, and so on. Firm a pays its workers a time-rate of per hour, while firm b pays its workers a piece rate. Suppose a decrease in demand for both firms" output reduces the value of every worker to either firm by half. Workers 1 to 34 work for firm a as a time rate of is more than their value to firm b, while workers. More productive workers, therefore, flock to the piece rate firm. After the price of output falls, firm a values all workers at . 50 per hour, while worker.