To solve this problem, we need to find the reaction function of Firm 1. The reaction function shows the optimal quantity a firm will produce given the quantity produced by the other firm.

Step 1: Firm 1's profit function is given by:

π1 = P*q1 - c*q1
= (131 - 1*(q1 + q2))*q1 - 18*q1
= 131*q1 - q1^2 - q1*q2 - 18*q1

Step 2: To maximize its profit, Firm 1 will set its marginal profit equal to zero. The marginal profit is the derivative of the profit function with respect to q1.

dπ1/dq1 = 131 - 2*q1 - q2 - 18 = 0

Step 3: Solve the above equation for q1 to get Firm 1's reaction function:

q1 = (131 - q2 - 18)/2
= (113 - q2)/2

This equation tells us that Firm 1's optimal quantity depends on the quantity produced by Firm 2. However, since we don't know q2, we can't find a specific value for q1.

In a Cournot duopoly, both firms simultaneously choose quantities, so the equilibrium is found where the reaction functions intersect. If Firm 2's reaction function was also given, we could solve the two equations simultaneously to find the equilibrium quantities.

Question

To solve this problem, we need to find the reaction function of Firm 1. The reaction function shows the optimal quantity a firm will produce given the quantity produced by the other firm.

Step 1: Firm 1's profit function is given by:

π1 = P*q1 - c*q1
   = (131 - 1*(q1 + q2))*q1 - 18*q1
   = 131*q1 - q1^2 - q1*q2 - 18*q1

Step 2: To maximize its profit, Firm 1 will set its marginal profit equal to zero. The marginal profit is the derivative of the profit function with respect to q1.

dπ1/dq1 = 131 - 2*q1 - q2 - 18 = 0

Step 3: Solve the above equation for q1 to get Firm 1's reaction function:

q1 = (131 - q2 - 18)/2
   = (113 - q2)/2

This equation tells us that Firm 1's optimal quantity depends on the quantity produced by Firm 2. However, since we don't know q2, we can't find a specific value for q1.

In a Cournot duopoly, both firms simultaneously choose quantities, so the equilibrium is found where the reaction functions intersect. If Firm 2's reaction function was also given, we could solve the two equations simultaneously to find the equilibrium quantities.

Knowee AI · Accepted Answer

To solve this problem, we need to find the reaction function of Firm 1. The reaction function shows the optimal quantity a firm will produce given the quantity produced by the other firm.

Step 1: Firm 1's profit function is given by:

π1 = P*q1 - c*q1
   = (131 - 1*(q1 + q2))*q1 - 18*q1
   = 131*q1 - q1^2 - q1*q2 - 18*q1

Step 2: To maximize its profit, Firm 1 will set its marginal profit equal to zero. The marginal profit is the derivative of the profit function with respect to q1.

dπ1/dq1 = 131 - 2*q1 - q2 - 18 = 0

Step 3: Solve the above equation for q1 to get Firm 1's reaction function:

q1 = (131 - q2 - 18)/2
   = (113 - q2)/2

This equation tells us that Firm 1's optimal quantity depends on the quantity produced by Firm 2. However, since we don't know q2, we can't find a specific value for q1.

In a Cournot duopoly, both firms simultaneously choose quantities, so the equilibrium is found where the reaction functions intersect. If Firm 2's reaction function was also given, we could solve the two equations simultaneously to find the equilibrium quantities.

Consider a Cournot duopoly. The market demand function is P = 131 – 1(q1 + q2), where P is the market price, q1 is the output produced by Firm 1 and q2 is the output produced by Firm 2. The two firms have a constant marginal cost c = 18.What quantity does Firm 1 produce ?

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