1. Best responses in a Cournot OligopolyFirm A and Firm B sell identical goodsTotal market demand for the good is:The inverse demand function is therefore1P(QM) = 780 -Q=780 -0.02222QM45QM is total market production (i.e., combined production of firm's A and B.That is:Q(P) = 35, 100- 45P2M = A +QBAs a result, the inverse demand curve for each firm is:P(QA, QB) = 780--1/32₁-75245Unlike the example in class, the two firms have different costs.=4000ATCA (QA)TCB (QB) = 260QB=780 -0.022220A -0.02222QBa. Using the demand function and the cost functions above, what is firm A's profitfunction.b. Using the profit function above and assuming that firm B produces Qg, calculate whatfirm A's best response is to firm B’s decision to produce QB-Note: Firm A's best response should be a function of B c. Using the demand function and the cost functions above, what is firm B's profitfunctiond. Using the profit function above and assuming that firm A produces A, calculate whatfirm B's best response is to firm A's decision to produce A.Note: Firm B's best response should be a function2. Nash Equilibrium in a Cournot Oligopolya.Using the best response functions you calculated in the previous question, calculatehow much each firm produces at the Nash Equilibrium for this game.b. Using the QA and QB you calculated in part a, calculate the market price.3. Nash Equilibrium in a Cournot Oligopolya.Does firm A or firm B produce more in this case? Does this result make sense to you?Why do you think this is (in words!)? EXPLAIN4. (Nash Equilibrium in a Cournot Oligopolya.Use the profit functions you calculated earlier to calculate profits for both firms in thisexample? Which firm has higher profits? Why do you think this is? EXPLAIN

“Since multiple questions have been asked by you, we will solve the first question. Please specify…

1. Best responses in a Cournot Oligopoly Firm A and Firm B sell identical goods Total market demand for the good is: The inverse demand function is therefore Q(P) = 35, 100 - 45P P(QM) = 780 1 |—— 45 = 780 -0.02222QM QM is total market production (i.e., combined production of firm's A and B. That is: QM = A +QB As a result, the inverse demand curve for each firm is: 1 1 P(Q₁, QB) = 780-5₁528 -QB = 780 -0.022220A-0.02222QB 45 45 Unlike the example in class, the two firms have different costs. TCA (QA) = 400QA TCB (QB) = 260QB a. Using the demand function and the cost functions above, what is firm A's profit function. b. Using the profit function above and assuming that firm B produces QB, calculate what firm A's best response is to firm B's decision to produce QB. Note: Firm A's best response should be a function of B

1. Best responses in a Cournot Oligopoly Firm A and Firm B sell identical goods Total market demand for the good is: The inverse demand function is therefore Q(P) = 35, 100 - 45P P(QM) = 780 1 |—— 45 = 780 -0.02222QM QM is total market production (i.e., combined production of firm's A and B. That is: QM = A +QB As a result, the inverse demand curve for each firm is: 1 1 P(Q₁, QB) = 780-5₁528 -QB = 780 -0.022220A-0.02222QB 45 45 Unlike the example in class, the two firms have different costs. TCA (QA) = 400QA TCB (QB) = 260QB a. Using the demand function and the cost functions above, what is firm A's profit function. b. Using the profit function above and assuming that firm B produces QB, calculate what firm A's best response is to firm B's decision to produce QB. Note: Firm A's best response should be a function of B

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.3P

See similar textbooks

Similar questions

Output is homogenous and the demand curve is P = 448 - Q. There are two firms with identical %3D costs given by C = q2 i where qi is the production of firm i. The marginal cost of firm i is Mci(qi) = 2qi . (a) Find the Cournot equilibrium firm outputs. (b)
4. In 2056, there are two mining firms operating on the moon, extracting Helium 3. Once both firms have entered the market, they compete a la Cournot. The market inverse demand function is given by P(Q) = 8 - Q. Assume that both firms have the total cost functions C(q) =2+2q. Let the star superscript* denote equilibrium quantities/prices/profits. Which of the following statements is true? (a) q₁ =q2 = 4 (b) qt > 92 (c) p* = 6 (d) π₁ < π₂ (e) T₁ = π = 2 the C
5. N - Σ Consider a Cournot model in which N firms compete with each other by setting quantities. The market inverse demand function is P = a i=1 qi, where a > 0 and q; is the quantity of firm i. Firm i's cost function is quadratic: q, where c₂ > 0. (a) Suppose N 2. Find the Nash equilibrium. Show which firm produces more in the equilibrium and explain your result. (b) = Suppose N≥ 2 and ci = c for all i. Find the Nash equilibrium. Show whether the firms produce more or less than the constant marginal cost case where the cost function is cqi, with a>c>0.
1. The market (inverse) demand function for a homogeneous good is P(Q) = 10 - Q. There are two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. a. Calculate the Nash equilibrium in this game and the corresponding market price when firms simultaneously choose quantities. b. Now suppose firml moves earlier than firm 2 and firm 2 observes firm 1 quantity choice before choosing its quantity find optimal choices of firm 1 and firm 2.
4. In 2056, there are two mining firms operating on the moon, extracting Helium 3. Once both firms have entered the market, they compete a la Cournot. The market inverse demand function is given by P(Q) = 8 – Q. Assume that both firms have the total cost functions = 2+ 2q. Let the star superscript* denote equilibrium quantities/prices/profits. Which C(q): of the following statements is true? (a) qi = 4 = 4 (b) qi > qž (c) p* = 6 (d) nj < T (e) Tỉ = = 2 5. Assume the same demand and cost structures as in question 4, but now firm 1 enters the market first and firm 2 follows, as in the Stackelberg model from lecture (both firms are guar- anteed to enter; the only choice is quantities produced). Which of the following statements regarding the equilibrium outcome is FALSE? (a) The first mover produces a greater quantity than the second mover (b) Total market output is Q* = 4.5 (c) The second mover will receive a negative profit (d) The first mover will receive a greater profit than the…
Here is a market with three firms: 1, 2, and 3. The demand curve is P=100-Q. There is no fixed cost but the marginal cost 10 for all firms. Firm 1 is a leader firm so that it decides the quantity Q1 first. Then two firms respectively decide their quantities Q2 and Q3 simultaneously. 1) At an equilibrium (SPE), Q1 is Q2=Q3= 2) At the equilibrium, (the market quantity) Q= and (the market price) P= 3) The profit of firm 1 is while the profit of firm 2 and 3 respectively is
. The market for widgets consists of two firms that produce identical products. Competition in the market is such that each of the firms independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 is known to have a cost advantage over firm 1. A recent study found that the (inverse) market demand curve faced by the two firms is P = 280 – 2(Q1 + Q2), and costs are C1(Q1) = 3Q1 and C2(Q2) = 2Q2. a. Determine the marginal revenue for each firm. b. Determine the reaction function for each firm.
10Two firms produce differentiated products. The demand for each firm’s product is as follows:  Demand for Firm 1: q1 = 20 – 2p1 + p2  Demand for Firm 2: q2 = 20 – 2p2 + p1 Both firms have the same cost function: c(q) = 5q. Firms compete by simultaneously and independently choosing their prices and then supplying enough to meet the demand they receive. Please compute the Nash equilibrium prices for these firms.
An Australian firm and a US firm produce a homogeneous good that is sold only in Japan. The marginal cost of producing the good is constant and equal to 30 in both countries. The demand curve for the good in Japan is: P = 120-Q where Q = QA +QUS represents the sum of the quantities. produced by the Australian and the US firms, respectively. (b) Assume the Australian firm can commit to an output before the US firm. Solve for the Stackelberg Equilibrium price, sales and profits of each firm in Japan. Price profit AUS2 ,output_US2 profit_US2 output_AUS2
Two firms face the same inverse demand curve: P= 370– q, – 92 . Both firms have the same constant marginal cost: MC = 10. (a) %3D if both firms choose their output levels simultaneously, how much profits and consumer surplus will be earned in equilibrium? (b) Firm 1 is offered the following deal: by paying Z it can either (i) acquire a new technology that lowers its marginal cost to zero or (ii) have to opportunity to produce output before firm 2. Which option would it take and what is the maximum Z it would be willing to pay?
2. A homogenous good industry consists of two firms (firm 1 and firm 2). Their cost functions are cq and cq2, respectively, where c<2. The market demand function is p=10-Q, where Q=q₁+q₂. (a) Assume that the two firms play the Bertrand price game. Find the firms' choices in the Bertrand-Nash equilibrium. (b) Assume that the two firms play the Cournot quantity game. Find the firms' choices in the Cournot-Nash equilibrium. (c) Assume the two firms play the Stackelberg game with firm 1 as the leader. Find the firms' equilibrium choices in the Stackelberg equilibrium.
Initially there are six firms producing differentiated products. The demand function for the good produced by firm i, i=1,2..,6, is given by qi = 10-2pi+0.3 summation pj where the sum is taken over the five prices other than firm i. Each firm has the same marginal cost c. The firms choose prices simultaneously; that is, they are differentiated products Bertrand competitors. (a) Solve for the symmetric Nash equilibrium prices. (b) Suppose that you observe each firm to set a price of 4.8. What must c be? (c) Suppose that two of the six firms merge to become a single firm. The firm continues to produce both goods. Using the marginal cost you found in (b), derive the new post-merger Nash equilibrium prices.