Consider a Cournot duopoly. The market demand function is P = 130 – 2(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 = 10.What is the equilibrium price in this market? Round your answer to the nearest integer (e.g. 50)
Question
Consider a Cournot duopoly. The market demand function is P = 130 – 2(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 = 10.What is the equilibrium price in this market? Round your answer to the nearest integer (e.g. 50)
Solution
To find the equilibrium price in this market, we first need to find the reaction functions of the two firms.
The profit function for each firm is given by:
πi = (P - c)qi = (130 - 2(q1 + q2) - 10)qi
Taking the derivative of the profit function with respect to qi (for i = 1, 2) and setting it equal to zero gives us the reaction functions:
q1 = 60 - q2 q2 = 60 - q1
In equilibrium, these two reaction functions must be equal. So, we can set them equal to each other and solve for q1 and q2:
60 - q2 = 60 - q1 q1 = q2
Substituting q1 = q2 into either of the reaction functions gives:
q1 = 60 - q1 2q1 = 60 q1 = 30
Since q1 = q2, we also have q2 = 30.
Finally, we can substitute q1 and q2 into the market demand function to find the equilibrium price:
P = 130 - 2(30 + 30) = 130 - 120 = 10
So, the equilibrium price in this market is 10.
Similar Questions
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 ?
In a Cournot duopoly, we find that Firm 1's reaction function is Q1 = 50 - 0.5Q2, and Firm 2's reaction function is Q2 = 75 - 0.75Q1. What is the Cournot equilibrium outcome in this market?
Consider a Cournot duopoly model we discussed in the lecture where the inverse demand function is P(Q)=5 - Q and the marginal cost for each firm is 8. Which of the following is the Nash equilibrium of this game? A. q1 = q2 = (1,1) B. q1 = q2 = (3,3) C. q1 = q2 = (0,0)
Suppose there are 100 firms each with a short run total cost of STC = q2 + q + 10, so that marginal cost is MC = 2q +1. If market demand is given by QD = 1050 - 50P, what is the equilibrium price?Question 5Select one:a.50.b.10.c.5.d.11.
a monopolist can produce at a average cost of AC rs 5 . it faces market demand curve given by Q=52-P supose second firm enter the market let q1=output market of first firm and q2=output of seond firm , let q=q1+q2 . assume that the second firm has the identical cost as the first firm . calculate equilibrium output of both the form enter the market . what is the resulting market price and profit for each firm ?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.