Question

2. Question 2 (50 marks) Consider two firms (A and B) engaging in Cournot Competition. Both...

2. Question 2

Consider two firms (A and B) engaging in Cournot Competition. Both firms face an inverse market demand curve P(Q)=700-5Q, where Q=qA+qB. The marginal revenue curve for firm A is MRA=700-10qA-5qB and the marginal revenue curve for firm B is MRB=700-10qB-5qA. The firms have identical cost functions, with constant marginal cost MC=20.

A) Determine the profit function for firm A and firm B.

B) Solve for the best-response functions of both firms.

C) Determine the equilibrium quantities both firms will supply, and the corresponding market price.

D) Suppose both firms could collude. Determine the equilibrium price and quantity produced by both firms (assume both firms split the quantity supplied to the market equally).

E) Find the level of dead-weight loss associated with parts C) and D). Which equilibrium has a larger amount of dead-weight loss? Why?

Homework Answers

Answer #1

Q2) answering only first four parts are mandatory

P = 700 - 5Q

A) πA = (P-MC)qA

= (700-5qA- 5qB - 20)qA

= (680-5qB)qA - 5qA2

πB = (680-5qA)qB - 5qB2

B) for BR function

dπA/dqA = 0

(680-5qB) = 10qA

qA= (680-5qB)/10

similarly BR​​​​​B(qA) :

qB = (680-5qA)/10

C) at eqm, two BR curve cuts

qA = 68 -.5(68 - .5qA)

qA = 68- 34 +.25qA

.75qA = 34

qA* = 45.33,

qB* = 45.33

Q= 90.66

P = 700-5*90.66

= 246.667

D) collusion is monopoly outcome

MR = MC

700-10Q = 20

Q* = 68

P* = 700-5*68 = 360

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider a market with 2 identical firms (a and b). The market demand is P =...
Consider a market with 2 identical firms (a and b). The market demand is P = 14 - Q where Q = Qa + Qb. For both firms AC=MC= 2. A. Solve for the Cournot-Nash reaction functions of each firm. B. Solve for the Cournot- Nash equilibrium. Solve for Q, Qa, Qb, Price, and each firms profit. C. Compare the Cournot-Nash equilibrium with perfect competition, and monopoly (you can refer to your results from question 2, if you’ve already done...
Consider a market with 2 identical firms (a and b). The market demand is P =...
Consider a market with 2 identical firms (a and b). The market demand is P = 14 - Q where Q = Qa + Qb. For both firms AC=MC= 2. A. Solve for the Cournot-Nash reaction functions of each firm. B. Solve for the Cournot- Nash equilibrium. Solve for Q, Qa, Qb, Price, and each firms profit. C. Compare the Cournot-Nash equilibrium with perfect competition, and monopoly (you can refer to your results from question 2, if you’ve already done...
Cournot Model: Consider a duopoly where 2 firms produce a homogeneous product. Under the assumption that...
Cournot Model: Consider a duopoly where 2 firms produce a homogeneous product. Under the assumption that one firm’s decision on output would depend on the other firm’s output, a market demand is given as P = 90 - Q where Q = QA + QB (QA is the quantity of a firm A and QB is the quantity of a firm B). Find the quantity and the price in this duopoly when MC of both firms = 0.
Suppose that 2 firms are competing against each other in Cournot (output) competition and that the...
Suppose that 2 firms are competing against each other in Cournot (output) competition and that the market demand curve is given by P = 60 – Q or Q = 60 – P. In addition, assume the marginal cost for each firm is equal to 0 as we did in class. a. Solve for firm 1’s total revenue. Note that this should not require any calculus. b. If you take the derivative of firm 1’s total revenue, you should find...
Two firms, A and B, are Cournot competitors facing the inverse market demand P = 5...
Two firms, A and B, are Cournot competitors facing the inverse market demand P = 5 - 0.001Q, where Q = qA + qB. Each firm has the same total cost function Ci = 2qi , i = A, B. a. (8) Write out the profit function of firm A, then derive the best response functions for A and B. (You only need to derive one best response function because A and B are identical.) Carefully graph the best response...
Consider the following market: Two firms compete in quantities, i.e., they are Cournot competitors. The firms...
Consider the following market: Two firms compete in quantities, i.e., they are Cournot competitors. The firms produce at constant marginal costs equal to 20. The inverse demand curve in the market is given by P(q) = 260 − q. a. Find the equilibrium quantities under Cournot competition as well as the quantity that a monopolist would produce. Calculate the equilibrium profits in Cournot duopoly and the monopoly profits. Suppose that the firms compete in this market for an infinite number...
Consider a market with demand p = a − bq. There are two firms. Both firms...
Consider a market with demand p = a − bq. There are two firms. Both firms produce the same homogeneous product but have different technologies. Firm A has a cost function cA(qA) = cA × qA and firm B has a cost function cB(qB) = cB × qB. If necessary, assume that cA < cB. (a) Find the equilibrium quantities produced by each firm, the total equilibrium quantity, and the equilibrium price as a function of a, b, cA, and...
There is a Cournot game consisting of two different firms that produce the same goods. Quantity...
There is a Cournot game consisting of two different firms that produce the same goods. 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 - (q1 +q2). Answer the following questions with work: 1. What is the...
Consider a Cournot market with two firms that have TC(Q) =5Q. Demand is given by P=...
Consider a Cournot market with two firms that have TC(Q) =5Q. Demand is given by P= 200−2(Q1+Q2). A) Find firm 1’s profit as a function of Q1 and Q2 B) Find the equilibrium price, quantity sold by each firm, and profit for each firm.
Consider two identical firms (no. 1 and no. 2) that face a linear market demand curve....
Consider two identical firms (no. 1 and no. 2) that face a linear market demand curve. Each firm has a marginal cost of zero and the two firms together face demand: P = 50 - 0.5Q, where Q = Q1 + Q2. a. Find the Cournot equilibrium Q and P for each firm. Calculate the results rounded to the second digit after the decimal point b. Find the equilibrium Q and P for each firm assuming that the firms collude...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT