Question

A duopoly faces a market demand of p=120minus−Q.

Firm 1 has a constant marginal cost of MC1equals=​$4040.

Firm​ 2's constant marginal cost is MC2=​$80.

Calculate the output of each​ firm, market​ output, and price if there is​ (a) a collusive equilibrium or​ (b) a Cournot equilibrium.

The collusive equilibrium occurs where

q1 equals _____

and

q2 equals ________

  ​(Enter numeric responses using real numbers rounded to two decimal​ places)

Answer 1

In collusion, the outcome will be monopoly equilibrium

Market Demand: P = 120 - Q

Q = 120 - P

Total Revenue = P * Q = (120 - Q) * Q = 120Q - Q2

Marginal Revenue (MR) = Derivative of TR wrt Q

= 120 - 2Q

MC1 = 4040

MC2 = 80

At collusive equilibrium,

MR = MC2 (Here we take the lowest marginal cost out of the two MCs given)

120 - 2Q = 80

2Q = 40

Q* = 20

This industry output will be divided into two firms equally.

So, q1 = 10

q2 = 10

For the firm 1 I believe that the MC1 is not 4040 as given in the question. Is it a typo. If yes, do let me know in the comments.

If it is only $40, then following will be the answer:

120 - 2Q = 40

2Q = 80

Q* = 40

q1 = 20

and q2 = 20