Question

Market demand for two sellers of homogeneous products is Q = 10 - 2P. Each has marginal cost c = 1. Suppose they compete as capacity-constrained Bertrand duopolists.

A) Calculate the equilibrium capacities, prices, and profits.

B) Now suppose they compete as Cournot duopolists. Calculate the equilibrium quantities, price, and profits.

C) Compare the two equilibria.

Answer 1

a)

Q = 10 - 2P

P = 5- 0.5Q

MC = 1

P = MC

5 - 0.5Q = 1

4 = 0.5Q

Q = 4/0.5

= 8

Each firm produces 4 units.

Since P = MC, hence each firm earns only normal profit or zero economic profit.

B)

Cournot output = ( N/N+1) * Competitive output

= (2/3) *8

= 5.33

Each firm produces 2.66 units

P = 5-0.5*2.66

=3.66

Profit = 2.66*3.66 - 1*2.66

= 7.07

each firm profit $ 7.07

C)

Bertrand model maximizes the social welfare by producing equivalent to a perfectly competitive market. While the cournot model does not produce socially optimal output.