Question

Consider a homogeneous-product duopoly where each firm initially produces at a constant marginal cost of \(and there are no fixed costs. Determine what would happen to each firm’s equilibrium output and profits if firm’s marginal cost increased to \)but firm’s marginal cost remained constant at $in each of the following settings:

a. Cournot duopoly.

b. Sweezy oligopoly.

Short answer

The only difference is that firm 2 will have a higher price than firm1.

1. In Cournot duopoly the firm 1 will have higher profits as it can capture greater market share, but the output decreases for firm 2 but firm may or may not increase its output.
2. The equilibrium output of firm 2 will be lower than that of firm 1, and the firm 1 will generate higher profits by capturing greater market share, by increasing output.

Step-by-step solution

 To consider Cournot duopoly

One of the assumptions of the Cournot oligopoly model is that each firm believes rivals firm will hold their output constant if it changes its output, however in the following graph we can see how the output levels change and therefore the profits of both firms before the increase in the marginal cost of firm 2.

Increase in the marginal cost of the firm 2(Cournot Model):

In the following graph we can observe the reaction functions (rl and r2) of firms 1 and 2 respectively, where point A reflects the equilibrium point at which firm 1 producesAt this equilibrium level, the marginal cost of both firms is $200._.

However, by generating an increase in the marginal costs of firm, going fromand having the marginal income constant without changes, the marginal costs will be higher than the marginal income.

Therefore output will need to be reduce of firm 2 at a level of Q1*.

This increase will cause the reaction function of firm 2 to shift to the left, generating a new equilibrium point B where there will be a lower level of This will benefit firm 1 since it has the same marginal costs of $200 and may increase its output level and capture a greater market share due to the lower output of firm .

Sweezy oligopoly 

b.

In this model, the manager of firm2considers that firm1will follow the price reduction decisions so as not to lose its market share but will not follow it in the face of price increases by firm2. The following graph shows the variation in the marginal cost of firm2under the Sweezy Oligopoly model.

Increase in the marginal cost of the firm 2 (Sweezy model):

Therefore, as can be seen in the previous graph, as marginal costs increase from $200 t0 $210, the marginal cost curve will shift to the left However, for firm 2 it will be optimal to continue producing at a QO level (B), since marginal costs will remain equal to marginal revenues and profit will be maximized.

The only difference is that firm 2 will have a higher price than firm 1, but the firm 1 will not increase its output and will remain at the Q0 level, but will obtain higher profits by having a higher market share via lower price.