Question

Consider an asymmetric Cournot duopoly game, where the two firms have different costs of production. Firm 1 selects quantity q1 and pays the production cost of 2q1 . Firm 2 selects quantity q2 and pays the production cost 4q2 . The market price is given by p = 12 − q1 − q2 . Thus, the payoff functions are u1 (q1,q2) = (12 − q1 − q2 ) q1 − 2q1 and u2 ( q1 , q2 ) = (12 − q1 − q2) q2 − 4q2 .

a.) Calculate the firms’ best-response functions BR1( q2 ) and BR2( q1 )

b.) Find the Nash equilibrium of this game.

Answer #1

a) Pay-off funtion for firm -1,

For maximiing payoff, the partial differential of payoff with
respect to q_{1} has to be 0.

This is the best response function for Firm-1

Payoff for firm-2,

For maximiing payoff, the partial differential of payoff with
respect to q_{2} has to be 0.

This is the best response function for Firm-2

b) For obtaining the Nash Equlibrium, we need to solve the best response functions for both firms simultaneously

That is the Nash equlibrium is (q_{1},q_{2}) =
(4,2)

Two firms in a Cournot duopoly produce quantities Q 1 and Q 2
and the demand equation is given as P = 80 - 2Q 1 - 2Q 2. The
firms' marginal cost are identical and given by MCi(Qi) = 4Qi,
where i is either firm 1 or firm 2.
a. Q1 = 80 - 4Q2 and Q2 = 80 - 4Q1.
b. Q1 = 10 - (1/4)Q2 and Q2 = 10 - (1/4)Q1.
c. Q1 = 80 - 2Q2...

Two Cournot firms produce slightly different products. Product
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Both Firm 1 and Firm 2 have constant marginal cost of $10 and zero
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Q2.
(3pts) Find Firm 1's best response as a function of Firm 2's
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(3pts) Find Firm 2's best response as...

Consider a duopoly with two firms with the cost functions:
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Firm 2: C2(q2)=5q2
The firms compete in a market with inverse demand
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where Q=q1+q2. The firms compete in a
Cournot fashion by choosing output simultaneously.
What is the Nash-Cournot equilibrium output of firm 1? Round to
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There is a Cournot duopoly competition between Firm 1 and Firm
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There is a Cournot game consisting of two different firms that
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Quantity produced by firm one = q
Quantity produced by firm two = q2
The marginal cost for firm one equals average cost, which is
3.
The marginal cost for firm two equals average cost, which is
4.
The formula for the inverse demand curve of the market is P = 70
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Answer the following questions with work:
1. What is the...

A product is produced by two profit-maximizing firms in a
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Consider the infinitely repeated version of the Cournot duopoly
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Answer the following question(s) based on this information: Two
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