Econ

ECON 175 Problem Set 1

Instructor: Yang Xie∗

Due in hard copy at lectures or office hours by May 1, 2017. Late, electronic, or

not-at-lecture-or-office-hour submission will not be accepted.

1 Market for lemons

Assume that a good second-hand car worths $10 to the seller and $12 to the buyer,

an ordinary second-hand car worths $7 to the seller and $9 to the buyer, and a bad

second-hand car worths $5 to the seller and $3 to the buyer. Assume that one third of

the cars are good, one third are ordinary, and one third are bad.

a. If the buyer can tell good or ordinary or bad, will the good cars sell? Will the

ordinary cars sell? Will the bad cars sell?

b. Now assume that the buyer cannot tell good or ordinary or bad but knows that the

probabilities of a good, ordinary, and bad car are 1/3, respectively. How much will

a risk neutral buyer be ready to pay?

c. Will the seller keep the good cars in the market?

d. Understanding this, now the buyer sees a car in the market. What are the probabil-

ities that this car is good, ordinary, and bad, respectively?

e. How much will the buyer be ready to pay now?

f. Will the seller now keep the ordinary cars in the market?

g. Understanding this, now the buyer sees a car in the market. What is the probability

that this car is good, or ordinary, or bad?

∗Affiliation: Department of Economics, University of California, Riverside.

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h. How much will the buyer be ready to pay now?

i. Will the seller now keep the bad cars in the market?

j. Will any car be sold?

2 Hold-up problem

Assume that an Indian firm is contacted by a multinational car company to produce

brake systems. This requires an initial specific investment of I from the Indian sub-

contractor and a variable cost c per braking system. The car company plans to buy n

braking systems from the subcontractor at price p per braking system.

a. Looking from now, at what price, p = p0, the Indian subcontractor would break

even?

b. Once the specific investment is made, at what price, p1, that the Indian subcontractor

will be willing to produce the braking systems?

c. Which price is higher, p0 or p1? What is their difference?

d. Understanding this potential situation, will the Indian subcontractor make the initial

investment?

e. The difference between p0 and p1 is a measure of the severity of the hold-up problem.

If the initial investment increases, will the problem become more severe?

f. Consider an extreme case in which I = 0. Will there still be a hold-up problem?

g. Given some I > 0, will the variable cost, c, affect the severity of the hold-up problem?

h. What can you conclude from this exercise?

3 Cooperation problem and coordination problem

Consider Table 1, a payoff matrix for Player A and Player B.

a. Under what condition will Option 1 be a dominant strategy for Player A?

b. Under what condition will Option 1 be a dominant strategy for Player B?

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Table 1

B chooses Option 1 B chooses Option 2

A chooses Option 1 (a11, b11) (a12, b12) A chooses Option 2 (a21, b21) (a22, b22)

c. Under what conditions will “both players choosing Option 1” be a Nash equilibrium?

d. Under what conditions will “both players choosing Option 1” not be a Nash equi-

librium?

e. Under what conditions will “A choosing Option 2 while B choosing Option 1” be a

Nash equilibrium?

f. Now consider Table 2, another payoff matrix for Player A and Player B. Which

situation will Player A like the best?

Table 2

B chooses Option 1 B chooses Option 2

A chooses Option 1 (4, 3) (2, −1) A chooses Option 2 (−1, 2) (100, 200)

g. Which situation will Player B like the best?

h. Is “both players choosing Option 2” a Nash equilibrium? Why?

i. Is “both players choosing Option 1” a Nash equilibrium? Why?

j. Which problem do we see now, a coordination problem or a cooperation problem?

k. Now consider Table 3, another payoff matrix for Player A and Player B. Which

problem do we see now, a coordination problem or a cooperation problem?

Table 3

B chooses Option 1 B chooses Option 2

A chooses Option 1 (4, 3) (500, −1) A chooses Option 2 (−1, 500) (400, 400)

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4 Price vs. quantity

Assume that the estimated marginal cost of a technology to purify water is EMC =

2 + 2q. Assume that the estimated marginal benefit of one unit of cleaner water is

MB = 14 − 2q.

a. What is the estimated optimal quantity of cleaner water?

b. What is the estimated optimal price, pe, to pay for one unit of cleaner water?

c. Now assume the true marginal cost is MC = 6 + 2q. What is the true optimal

quantity of cleaner water?

d. If we use the former optimal estimated quantity to coordinate, how many units of

cleaner water will be generated? Do we over-generate or under-generate cleaner

water? Draw a graph and show the welfare loss.

e. If we use the former optimal estimated price to coordinate, how many units of cleaner

water will be generated? Do we over-generate or under-generate cleaner water? On

the same graph, show the welfare loss.

f. Is the price signal better, or is the quantity signal better in this case, in terms of

having smaller welfare loss? Why?

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