The economics of information and incentives is a relatively new branch of
microeconomics, in which much intriguing work is going on. This chapter
shows you a sample of these problems and the way that economists think
about them.
37.1 (0) There are two types of electric pencil-sharpener producers.
“High-quality” manufacturers produce very good sharpeners that consumers
value at $14. “Low-quality” manufacturers produce less good ones
that are valued at $8. At the time of purchase, customers cannot distinguish
between a high-quality product and a low-quality product; nor can
they identify the manufacturer. However, they can determine the quality
of the product after purchase. The consumers are risk neutral; if they
have probability q of getting a high-quality product and 1 − q of getting
a low-quality product, then they value this prospect at 14q + 8(1 − q).
Each type of manufacturer can manufacture the product at a constant
unit cost of $11.50. All manufacturers behave competitively.
(a) Suppose that the sale of low-quality electric pencil-sharpeners is illegal,
so that the only items allowed to appear on the market are of high
quality. What will be the equilibrium price? .
(b) Suppose that there were no high-quality sellers. How many low-quality
sharpeners would you expect to be sold in equilibrium?
.
(c) Could there be an equilibrium in which equal (positive) quantities of
the two types of pencil sharpeners appear in the market?
.
(d) Now we change our assumptions about the technology. Suppose that
each producer can choose to manufacture either a high-quality or a lowquality
pencil-sharpener, with a unit cost of $11.50 for the former and $11
for the latter, what would we expect to happen in equilibrium?
.
(e) Assuming that each producer is able to make the production choice
described in the last question, what good would it do if the government
banned production of low-quality electric pencil-sharpeners?
.
37.2 (0) In West Bend, Indiana, there are exactly two kinds of workers.
One kind has a (constant) marginal product worth $10 and the other kind
has a (constant) marginal product worth $15. There are equal numbers
of workers of each kind. A firm cannot directly tell the difference between
the two kinds of workers. Even after it has hired them, it won’t be able
to monitor their work closely enough to determine which workers are of
which type.
(a) If the labor market is competitive, workers will be paid the average
value of their marginal product. This amount is .
(b) Suppose that the local community college offers a microeconomics
course in night school, taught by Professor M. De Sade. The highproductivity
workers think that taking this course is just as bad as a
$3 wage cut, and the low-productivity workers think it is just as bad as
a $6 wage cut. The firm can observe whether or not an individual takes
the microeconomics course. Suppose that the high-productivity workers
all choose to take the microeconomics course and the low-productivity
workers all choose not to. The competitive wage for people who take the
microeconomics course will be and the wage for people who don’t
take the microeconomics course will be .
(c) If there is a separating equilibrium, with high-productivity workers
taking the course and low-productivity workers not taking it, then the
net benefits from taking the microeconomics course will be for
the high-productivity workers and for the low-productivity
workers. Therefore there (will be, won’t be) a separating
equilibrium of this type.
(d) Suppose that Professor De Sade is called off to Washington, to lecture
wayward representaatives on the economics of family values. His
replacement is Professor Morton Kremepuff. Kremepuff prides himself on
his ability to make economics “as easy as political science and as fun as
the soaps on TV.” Professor Kremepuff’s claims are exaggerated, but at
least students like him better than De Sade. High-productivity workers
think that taking Kremepuff’s course is as bad as a $1 wage cut, and
low-productivity workers think that taking Kremepuff’s course is as bad
as a $4 wage cut. If the high-productivity workers all choose to take the
microeconomics course and the low-productivity workers all choose not to,
the competitive wage for people who take the microeconomics course will
be and the wage for people who don’t take the microeconomics
course will be .
(e) If there is a separating equilibrium with high-productivity workers
taking the course and low-productivity workers not taking it, then the net
benefits from taking Kremepuff’s microeconomics course will be
for the high-productivity workers and for the low-productivity
workers. Therefore there (will be, won’t be) a separating
equilibrium of this type.
37.3 (1) In Enigma, Ohio, there are two kinds of workers, Klutzes
whose labor is worth $1,000 per month and Kandos, whose labor is worth
$2,500 per month. Enigma has exactly twice as many Klutzes as Kandos.
Klutzes look just like Kandos and are accomplished liars. If you ask,
they will claim to be Kandos. Kandos always tell the truth. Monitoring
individual work accomplishments is too expensive to be worthwhile. In
the old days, there was no way to distinguish the two types of labor, so
everyone was paid the same wage. If labor markets were competitive,
what was this wage? .
(a) A professor who loves to talk offered to give a free monthly lecture
on macroeconomics and personal hygiene to the employees of one small
firm. These lectures had no effect on productivity, but both Klutzes
and Kandos found them to be excruciatingly dull. To a Klutz, each
hour’s lecture was as bad as losing $100. To a Kando, each hour’s
lecture was as bad as losing $50. Suppose that the firm gave each
of its employees a pay raise of $55 a month but insisted that he attend
the professor’s lectures. What would happen to the firm’s labor
force?
What would happen
to the average productivity of the firm’s employees?
.
(b) Other firms noticed that those who had listened to the professor’s
lectures were more productive than those who had not. So they tried to
bid them away from their original employer. Since all those who agreed
to listen to the original lecture series were Kandos, their wage was bid up
to .
(c) After observing the “effect of his lectures on labor productivity,” the
professor decided to expand his efforts. He found a huge auditorium where
he could lecture to all the laborers in Enigma who would listen to him.
If employers believed that listening to the professor’s lectures improved
productivity by the improvement in productivity in the first small firm
and offered bonuses for attending the lectures accordingly, who would
attend the lectures? Having observed this outcome, how
much of a wage premium would firms pay for those who had attended the
professor’s lectures? .
(d) The professor was disappointed by the results of his big lecture
and decided that if he gave more lectures per month, his pupils
might “learn more.” So he decided to give a course of lectures for
20 hours a month. Would there now be an equilibrium in which
the Kandos all took his course and none of the Klutzes took it
and where those who took the course were paid according to their
true productivity?
.
(e) What is the smallest number of hours the professor could lecture and
still maintain a separating equilibrium? .
37.4 (1) Old MacDonald produces hay. He has a single employee, Jack.
If Jack works for x hours he can produce x bales of hay. Each bale of hay
sells for $1. The cost to Jack of working x hours is c(x) = x2
/10.
(a) What is the efficient number of bales of hay for Jack to cut? .
(b) If the most that Jack could earn elsewhere is zero, how much would
MacDonald have to pay him to get him to work the efficient amount?
.
(c) What is MacDonald’s net profit? .
(d) Suppose that Jack would receive $1 for passing out leaflets, an activity
that involves no effort whatsoever. How much would he have to
receive from MacDonald for producing the efficient number of bales of
hay? .
(e) Suppose now that the opportunity for passing out leaflets is no longer
available, but that MacDonald decides to rent his hayfield out to Jack for
a flat fee. How much would he rent it for? .
37.5 (0) In Rustbucket, Michigan, there are 200 people who want to sell
their used cars. Everybody knows that 100 of these cars are “lemons”
and 100 of these cars are “good.” The problem is that nobody except the
original owners know which are which. Owners of lemons will be happy
to get rid of their cars for any price greater than $200. Owners of good
used cars will be willing to sell them for any price greater than $1,500,
but will keep them if they can’t get $1,500. There are a large number of
buyers who would be willing to pay $2,500 for a good used car, but would
pay only $300 for a lemon. When these buyers are not sure of the quality
of the car they buy, they are willing to pay the expected value of the car,
given the knowledge they have.
(a) If all 200 used cars in Rustbucket were for sale, how much would buyers
be willing to pay for a used car? Would owners of good used
cars be willing to sell their used cars at this price? Would there
be an equilibrium in which all used cars are sold? Describe the
equilibrium that would take place in Rustbucket.
.
(b) Suppose that instead of there being 100 cars of each kind, everyone
in town is aware that there are 120 good cars and 80 lemons. How much
would buyers be willing to pay for a used car? Would owners
of good used cars be willing to sell their used cars at this price?
Would there be an equilibrium in which all used cars are sold?
Would there be an equilibrium in which only the lemons were sold?
Describe the possible equilibrium or equilibria that would
take place in Rustbucket.
.
37.6 (1) Each year, 1,000 citizens of New Crankshaft, Pennsylvania, sell
their used cars and buy new cars. The original owners of the old cars
have no place to keep second cars and must sell them. These used cars
vary a great deal in quality. Their original owners know exactly what is
good and what is bad about their cars, but potential buyers can’t tell
them apart by looking at them. Lamentably, though they are in other
respects model citizens, the used-car owners in New Crankshaft have no
scruples about lying about their old jalopies. Each car has a value, V ,
which a buyer who knew all about its qualities would be willing to pay.
There is a very large number of potential buyers, any one of which would
be willing to pay $V for a car of value $V.
The distribution of values of used cars on the market is quite simply
described. In any year, for any V between 0 and $2,000, the number of
used cars available for sale that are worth less than $V is V/2. Potential
used-car buyers are all risk-neutral. That is if they don’t know the value of
a car for certain, they value it at its expected value, given the information
they have.
Rod’s Garage in New Crankshaft will test out any used car and find
its true value V . Rod’s Garage is known to be perfectly accurate and
perfectly honest in its appraisals. The only problem is that getting an
accurate appraisal costs $200. People with terrible cars are not going to
want to pay $200 to have Rod tell the world how bad their cars are. But
people with very good cars will be willing to pay Rod the $200 to get
their cars appraised, so they can sell them for their true values.
Let’s try to figure our exactly how the equilibrium works, which cars
get appraised, and what the unappraised cars sell for.
(a) If nobody had their car appraised, what would the market price for
used cars in North Crankshaft be and what would be the total revenue
received by used-car owners for their cars?
.
(b) If all the cars that are worth more than $X are appraised and all
the cars that are worth less than $X are sold without appraisal, what
will the market price of unappraised used cars be? (Hint: What is the
expected value of a random draw from the set of cars worth less than
$X?) .
(c) If all the cars that are worth more than $X are appraised and all
the cars that are worth less than $X are sold without appraisal, then
if your car is worth $X, how much money would you have left if you
had it appraised and then sold it for its true value? How
much money would you get if you sold it without having it appraised?
.
(d) In equilibrium, there will be a car of marginal quality such that all
cars better than this car will be appraised and all cars worse than this car
will be sold without being appraised. The owner of this car will be just
indifferent between selling his car unappraised and having it appraised.
What will be the value of this marginal car?
.
(e) In equilibrium, how many cars will be sold unappraised and what
will they sell for?
.
(f) In equilibrium, what will be the total net revenue of all owners of used
cars, after Rod’s Garage has been paid for its appraisals?
.
37.7 (2) In Pot Hole, Georgia, 1,000 people want to sell their used cars.
These cars vary in quality. Original owners know exactly what their cars
are worth. All used cars look the same to potential buyers until they have
bought them; then they find out the truth. For any number X between
0 and 2,000, the number of cars of quality lower than X is X/2. If a car
is of quality X, its original owner will be willing to sell it for any price
greater than X. If a buyer knew that a car was of quality X, she would
be willing to pay X + 500 for it. When buyers are not sure of the quality
of a car, they are willing to pay its expected value, given their knowledge
of the distribution of qualities on the market.
(a) Suppose that everybody knows that all the used cars in Pot Hole are
for sale. What would used cars sell for? Would every used
car owner be willing to sell at this price? Which used cars
would appear on the market? .
(b) Let X∗
be some number between 0 and 2,000 and suppose that all
cars of quality lower than X∗
are sold, but original owners keep all cars of
quality higher than X∗
. What would buyers be willing to pay for a used
car? At this price, which used cars would be for sale?
.
(c) Write an equation for the equilibrium value of X∗
, at which the price
that buyers are willing to pay is exactly enough to induce all cars of quality
less than X∗
into the market. Solve this equation for
the equilibrium value of X∗
. .