Question

1. Fuji and Kodak produce identical film. The market demand for film is given by P = 8 - Q, where P is the price (in dollars per roll of film) and Q is the quantity (in hundreds of rolls). Each firm has the option of producing 150, 200, or 300 rolls of film at a constant marginal cost of $2 per roll with no fixed costs. The firms' possible profits for various outcomes are summarized in the accompanying table.

		150 rolls	Kodak's Strategies 200 rolls	300 rolls
	150 rolls	Fuji gets $450	Fuji gets $375	Fuji gets $225
		Kodak gets $450	Kodak gets $500	Kodak gets $450
Fuji's	200 rolls	Fuji gets $500	Fuji gets $400	Fuji gets $200
Strategies		Kodak gets $375	Kodak gets $400	Kodak gets $300
	300 rolls	Fuji gets $450	Fuji gets $300	Fuji gets $0
		Kodak gets $225	Kodak gets $200	Kodak gets $0

(i)	If the two firms behave competitively (Bertrand price competition), what will be the outcome of this game? Is this outcome Pareto optimal for the firms?
(ii)	If the two firms merge and form a monopoly, what will be the outcome of this game? Is this outcome Pareto optimal for the firms?
(iii)	What is the Nash equilibrium for this game? Is it Pareto optimal for the firms? How does it compare with the competitive and monopoly outcomes?
(iv)	Suppose this game is played sequentially, with Fuji as the first player. What will be the Stackelberg equilibrium? Is it Pareto optimal?

Answer 1

Payoff table

	150	200	300
150	(450,450)	(375,500•)	(225*,450)
200	(500*,375)	(400*,400•)	(200,300)
300	(450,225•)	(300,200)	(0,0)

I) betrand Game

At eqm, P1= P2 = MC = 2

Then from demand curve , P= 8-Q

Q = 600

So each produce Q = 300,

Each gets (0,0)

its not pareto optimal, bcoz other strategies result in increasing payoff of both individuals

ii) monopoly, at eqm,

MR = MC, 8-2Q = 2

Q = 300, each produce = Q/2 = 150

Each gets payoff = 450

Yes its Pareto optimal, no other strategy pair exist, where both could be made better off, without making one worse off

iii) NE : ( both produce Q = 200)

its not pareto optimal, if both could Cooperate & produce Monopoly output, then both will be better off

Compared to MONOPOLY, Price is Lower , Q is higher

compared to perfect Competition, price is higher & Q is Lower

iv) sequential game

Fuji will Produce = (8-2)/2 = 300

Kodak produce = (8-2)/4 = 150

So Eqm ( 300,150)

Payoff ( fuji gets 450) & kodak gets 225

No it's not Pareto optimal

Both could be made better off, if strategy pair is (200,150)