In the initial Cournot duopoly equilibrium, both firms have constant marginal costs, m, and no fixed costs, and there is a barrier to entry. Show what happens to thebest-response function of firms if both firms now face a fixed cost of F.

Let market demand be

p=a-−bQ,

where a and b are positive parameters with 2 firms.

Let q1 and q2 be the amount produced by firm 1 and firm 2, respectively. Assuming it is optimal for the firm one to produce, its best-response function is

q1=??

Question

contestada

Respuesta :

ignaciomsarmiento ignaciomsarmiento · Answer 1 · 2019-09-12T00:12:17+02:00

Answer:

[tex]q_1=\frac{a-m}{2b}-\frac{q_2}{2}[/tex]

Explanation:

Note that Total Costs are given by fixed costs (F) and marginal costs (m) that depend on the production level of the firm

[tex]CT_i=F+mq_i[/tex]

for i=1,2. The market demand is given by

[tex]p=a-bQ[/tex]

where [tex]Q=q_1+q_2[/tex] is the total production, so it's the sum of each firms production

Firm 1 will maximize it's own profits

[tex]max\,\Pi_1=p=(a-b(q_1+q_2))q_1-F-mq_1[/tex]

The first order conditions (take derivative of the profit with respect to [tex]q_1[/tex] are given by

[tex]a-2 b q_1-b q_2-m=0[/tex]

Then the best-response function for Firm 1 will be

[tex]q_1=\frac{a-m}{2b}-\frac{q_2}{2}[/tex]

and the solution for Firm 2 would be symmetric.

Note that only marginal costs are relevant for getting the best-response function, so adding fixed costs (F) don't change the results