978-0393123982 Chapter 38 Solution Manual

Unlock access to all the studying documents.

View Full Document

Chapter 38 NAME

Asymmetric Information

Introduction. The economics of information and incentives is a rela-

tively 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.

38.1 (0) There are two types of electric pencil-sharpener producers.

“High-quality” manufacturers produce very good sharpeners that con-

sumers value at $14. “Low-quality” manufacturers produce less good ones

that are valued at $8. At the time of purchase, customers cannot distin-

guish 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 qof getting a high-quality product and 1 −qof 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 ille-

gal, so that the only items allowed to appear on the market are of high

(b) Suppose that there were no high-quality sellers. How many low-quality

sharpeners would you expect to be sold in equilibrium? Sellers

of the two types of pencil sharpeners appear in the market? No.

470 ASYMMETRIC INFORMATION (Ch. 38)

(d) Now we change our assumptions about the technology. Suppose

that each producer can choose to manufacture either a high-quality or

a low-quality pencil-sharpener, with a unit cost of $11.50 for the for-

mer and $11 for the latter, what would we expect to happen in equilib-

rium? No trade. Producers would produce the

(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? If

there is no ban, there will be no output

38.2 (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

(b) Suppose that the local community college offers a microeconomics

course in night school, taught by Professor M. De Sade. The high-

productivity 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

NAME 471

workers all choose not to. The competitive wage for people who take the

taking the course and low-productivity workers not taking it, then the

net benefits from taking the microeconomics course will be $2

(d) Suppose that Professor De Sade is called off to Washington, to lec-

ture 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

(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 $4

equilibrium of this type.

38.3 (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,

472 ASYMMETRIC INFORMATION (Ch. 38)

(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? All Klutzes

(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

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

(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? Yes. If

NAME 473

(e) What is the smallest number of hours the professor could lecture and

38.4 (1) Old MacDonald produces hay. He has a single employee, Jack.

If Jack works for xhours he can produce xbales of hay. Each bale of hay

sells for $1. The cost to Jack of working xhours is c(x)=x2/10.

(a) What is the efficient number of bales of hay for Jack to cut? 5.

(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?

(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

38.5 (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.

474 ASYMMETRIC INFORMATION (Ch. 38)

(a) If all 200 used cars in Rustbucket were for sale, how much would

buyers be willing to pay for a used car? $1,400. Would owners

of good used cars be willing to sell their used cars at this price? No.

(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

owners of good used cars be willing to sell their used cars at this price?

Yes. Would there be an equilibrium in which all used cars are sold?

Yes. Would there be an equilibrium in which only the lemons were

sold? Yes. Describe the possible equilibrium or equilibria that would

38.6 (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 $Vfor a car of value $V.

The distribution of values of used cars on the market is quite simply

described. In any year, for any Vbetween 0 and $2,000, the number of

used cars available for sale that are worth less than $Vis 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.

NAME 475

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? They’d

(b) If all the cars that are worth more than $Xare appraised and all

the cars that are worth less than $Xare 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

the cars that are worth less than $Xare sold without appraisal, then if

your car is worth $X, how much money would you have left if you had

(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.

(e) In equilibrium, how many cars will be sold unappraised and what

476 ASYMMETRIC INFORMATION (Ch. 38)

(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?

38.7 (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 Xbetween

0 and 2,000, the number of cars of quality lower than Xis 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

(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

that buyers are willing to pay is exactly enough to induce all cars of