Imagine a Cournot game with two firms (A and B). The demand curve in this market is P=280-Qa-Qb. Each firm has marginal cost equal to $40.

What is the equilibrium market price?

Question

Imagine a Cournot game with two firms (A and B). The demand curve in this market is P=280-Qa-Qb. Each firm has marginal cost equal to $40.

What is the equilibrium market price?

BlackTom AI · Accepted Answer

We start by identifying the Cournot setup with two firms A and B.
The market demand is P = 280 - Qa - Qb, and each firm faces constant marginal cost MC = 40.
Each firm's profit is revenue minus cost: for firm A, πA = (P - MC) * Qa = (280 - Qa - Qb - 40) * Qa = (240 - Qa - Qb) * Qa.
To find the best response, take the derivative with respect to Qa and set to zero: dπA/dQa = 240 - 2Qa - Qb = 0, which yields the reaction function Qa = (240 - Qb)/2.
Similarly for firm B, πB = (P - MC) * Qb = (240 - Qa - Qb) * Qb, and dπB/dQb = 240 - Qa - 2Qb = 0, giving Qb = (240 - Qa)/2.
These two first-order conditions form a system of linear equations.
From A's condition: 2Qa + Qb = 240.
From B's condition: Qa + 2Qb = 240.
Solving the system, subtract the second from the first to get Qa - Qb = 0, so Qa = Qb.
Plugging back into 2Qa + Qb = 240 gives 2Qa + Qa = 240, hence 3Qa = 240 and Qa = 80. By symmetry, Qb = 80 as well.
Now compute the equilibrium price using the demand function: P = 280 - Qa - Qb = 280 - 80 - 80 = 120.
Thus, the equilibrium price in this Cournot duopoly with these parameters is 120.

Imagine a Cournot game with two firms (A and B). The demand curve in this market is P=280-Qa-Qb. Each firm has marginal cost equal to $40. What is the equilibrium market price?数值题

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