Question

Messrs Bertrand and Cournot are competitors in the market for gadgets. The demand conditions in this market are given by the equation Q=1000-P, and both Bertrand and Cournot can supply the market with gadgets at a constant marginal cost equal to five crowns (they incur no other costs to run their enterprises).

i. Describe in detail what conditions will give rise to price competition between Bertrand and Cournot. Given that they compete by choosing prices, what is the equilibrium price and quantity in the market for gadgets?

ii. Would the outcome above change if Bertrand (and not Cournot) instead had a constant marginal cost equal to four crowns rather than five? If so, what is the new equilibrium?

iii. Describe in detail what conditions will give rise to quantity competition between Bertrand and Cournot. Given that they compete by choosing quantities, what is the equilibrium price and quantity in the market for gadgets?

iv. Would the outcome in part iii change if Bertrand (not Cournot) had a constant marginal cost equal to four rather than five crowns? If so, what is the new equilibrium?

Answer 1

Qi) This is basically asking for analysis in the framework of Bertrand's model for duopolistic price competition.

The model rests on a few very specific assumptions:

1) There are at least two firms and they do not collude or cooperate in any way.

2) Homogeneous products i.e. no product differentiation.

3) No search and transaction costs.

4) Consumers prefer to buy from the cheapest firm.

5) If firms set the same price, the demand is split between them equally.

The above information in verbal format is sufficient to deduce the equilibrium price in such a situation. Say the price / quantity vector for firms A and B (Cournout and Bertrand) is (Pa, Qa) and (Pb, Qb) respectively.

If Pa > Pb, Qa = 0 and Qb = Q; all consumers buy from B because they sell cheaper

Pa < Pb Qa = Q and Qb = 0; all consumers buy from A for same reason

It is only when Pa = Pb that the demand is satisfied equally by the two: Qa = Qb = Q/2

Thus in this framework there's a strong incentive to undercut in the absence of collusion. Firms undercut each other until P = MC, i.e. until it's no longer possible to undercut given the profit maximizing criteria informing firm's decisions.

Thus in Qi), with both MC's equal to 5, total output = 1000 - 5 = 995; Qa = Qb = 995/2

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Qii) The outcome would change dramatically in that B (Bertrand) captures the entire market as the cheapest producer. Total output Q = Qb = 1000 - 4 = 996 and Qa = 0

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Qiii) This is the case of Cournot competition, with quantity as the firms' decision variable.

Criterial assumptions for Cournot's model:

a) Rival firms produce a homogenous product

b) Each attempts to maximize profits by choosing how much to produce.

c) All firms choose output (quantity) simultaneously.

The basic idea is that firms choose quantity, taking as given the quantity of their rivals. The resulting equilibrium is a Nash equilibrium in quantities, called a Cournot (Nash) equilibrium.