Question

A homogeneous product duopoly faces a market demand function given by p = 300 - 3Q,where Q = q1 + q2. Both firms have constant marginal cost MC = 100. (part 2)

1a. What is the Bertrand equilibrium price and quantity in this market?

1b. Suppose Firm 1 is the Stackelberg leader, what is the equilibrium price in this market if Firm 2 plays the follower in this duopoly market? What is the equilibrium quantity? How much does each firm produce?

1c. In the diagram below, illustrate the Cournot, Bertrand and Stackelberg equilibria in parts (b), (e) and (f). Calculate the consumer surplus in each equilibrium.

Graph:
Price for vertical axis, quantity for horizontal axis. Demand line with a MC horizontal line.

Answer 1

P=300-3Q

MC=100

1a) Equilibrium price and quantity:-

TR=P*Q

=300Q-3Q2

MR=300-6Q

MC=MR

100=300-6Q

6Q=300-100

Q=200/6

=33.33

Pruce :-

P=300-3Q

300-3*33.33

300-100

=200

1c)

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