 # 1. (Stackelberg’s Model of Oligopoly.) The market demand curv...

## Question

1. (Stackelberg’s Model of Oligopoly.) The market demand curve in a commodity chemical industry is given by Q = 600 − 3P, where Q is the quantity demanded per month and P is the market price in dollars. Firm in this industry supply quantities every month, and the resulting market price occurs at the point at which the quantity demanded equals the total quantity supplied. Suppose there are two firms in this industry, Firm 1 and Firm 2. Each firm has an identical constant marginal cost of \$80 per unit.
(a) Find the Cournot equilibrium quantities for each firm. What is the Cournot equilibrium market price?
(b) Assuming that Firm 1 is the Stackelberg leader, find the Stackelberg equilibrium quantities for each firm. What is the Stackelberg equilibrium price?
(c) Calculate and compare the profit of each firm under the Cournot and Stackelberg equilibria. Under which equilibrium is overall industry profit greater?

2. (Dominant Firm Model.) Apple’s iPod has been the portal MP3-player of choice among many gadget enthusiasts. Suppose that Apple has a constant marginal cost of 4 and that market demand is given by Q = 200 − 2P.
(a) If Apple is a monopolist, find its optimal price and output. What is its profits?
(b) Now suppose there is a competitive fringe of 12 price-taking firms, each of which has a total cost function T C(q) = 3q² + 20q. Find the supply function of the fringe.
(c) If Apple operates as the dominant firm facing competition from the fringe in this market, now what is its optimal output? How many units will fringe providers sell? What is the market price, and how much profit does Apple earn?

3. (Extensive Games with Perfect Information.) The only two firms moving crude oil from an oil-producing region to a port in Atlantis are pipelines: Starline and Pipetran. The following table shows the annual profit (in millions of euros) that each firm would earn at different capacities. Starline’s profit is the left number in each cell; Pipetran’s profit is the right number. At the current capacities (with no expansion) Starline is earning 40 million euros, and Pipetran is earning 18 million euros annually. Each company is considering an expansion of its capacity. Sine Pipetran is a fairly small company, it can consider only a small expansion to its capacity. Starline has the ability to consider both a small and a large expansion.

Pipetran
No Expansion      Small
No Expansion               40,18               28,22
Starline       Small                            48,14               32,16
Large                            38,10                24,5

(a) If the two firms make their decisions about expansion simultaneously, is there a unique Nash equilibrium? If so, what is it? If not, why not?
(b) Would Starline have a firs-mover advantage if capacities were chosen sequentially? If so, draw the game tree and briefly explain how it might credibly implement this strategy.
(c) Suppose you were hired to advise Pipetran about its choice of capacity. If Pipetran has the option of moving first, should it do so? Draw the game tree and explain.

## Solution Preview

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Question 1:

The inverse demand curve would become
Q= 600-3P
P=200 – (1/3)Q
Q = (Q1+Q2)
P= 200- (1/3)(Q1+Q2)
The residual demand curve of both the firms is given as
For Firm 1,
P=[200-(1/3)Q2] – (1/3)Q1. The marginal revenue curve is derived as...

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