Econ 5700

Econ 5700: Industrial Organization

Problem Set 4 Due: Thursday, February 20, 2020

Instructions:

• I recommend that you use a calculator to complete this assignment.

• Show your work for short answer (SA) questions.

• I strongly recommend that you first work out the problems on scrap paper, then write out a set of neatly-presented answers to turn in to me.

• Staple your pages together if you turn in multiple pages.

• You may work in groups of four students or less. Each group should submit only one copy of their answers. Be sure to include all group members’ names and

dot numbers.

1. [MC] In which of the following scenarios can firms sustain collusion? (I.e., which

of these can prevent cheating?)

(a) An infinitely repeated game with trigger strategies.

(b) A finitely repeated game with trigger strategies.

(c) A one-shot game with a price-matching guarantee.

(d) More than one of the above.

2. [MC] Suppose that there are very few firms operating in a market where it

is difficult to currently observe rivals’ prices. The government is considering

collecting and publishing information on firms’ prices in this market. If produced,

this dataset would be publicly available. Why might an economist recommend

against publishing such a dataset? Which of the following does NOT help firms

in a cartel detect cheating?

(a) Observable prices.

(b) There are many firms.

(c) Firms sell to the same types of consumers.

(d) There are low independent price fluctuations.

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3. [SA] Consider a homogenous good market characterized by monopolistic compe-

tition. The market’s inverse demand function is given by p(Q) = 90 − 1 40 Q and

an individual firm, i, has cost function given by ci(qi) = 30qi + 5760. Notice that

this cost function implies economies of scale. Price and quantity in the market

are determined via Cournot competition. When focusing on firm i, recall this

useful notation from class:

Q = qi +Q−i and Q−i = ∑ k 6=i

qk

We are interested in finding the equilibrium number of firms in the monopolisti-

cally competitive equilibrium.

(a) Find firm i’s best response function, qi = BRi(Q−i).

(b) When there are n firms in the market, they will all produce equal quantities

in the Cournot equilibrium:

q1 = q2 = … = qn = q

Find the value of this individual firm production, q. (It should be a function

of n.)

(c) In the Cournot equilibrium with n firms, what are the aggregate quantity,

Q, market price, p, and individual firm profits, πi? (Again, these should all

depend on n.)

(d) Consider n = 2, 3, 4, 5. For each of these values, compute firm profits. Is any

of these the (Nash) equilibrium number of firms?

(e) Suppose that the government has the policy tools available to reach the first-

best welfare outcome. Describe how the government achieves this goal.

(f) Suppose instead that the government is more limited in its policy tools. All

it can do is levy a lump-sum tax on any firm operating in the industry. Any

firm that enters must pay a lump-sum tax of $3240 to the government. Redo

part (d) with the tax in place. What is the new equilibrium number of firms?

Will implementing the tax most likely increase or decrease total welfare?

(g) [Optional. I would not ask this question on an exam, but you might

find it interesting to work through.] What is the value of total welfare

in the equilibrium without the tax? What about with the tax? (Hint: you

can compute total welfare as consumer surplus minus total industry profits.)

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