A homogeneous-good duopoly races an inverse market demand function of p Firm I has a constant marginal cost of MC₁ = 20. Firm 2's constant marginal cost is MC₂ = 30. Calculate the output of each firm, market output, and price for a. A Nash-Cournot equilibrium
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- Two firms with differentiated products are competing in price. Firm A and B face thefollowing demand curves: Q_A = 70 − 2P_A + P_B and Q_B = 120 − 2P_B + P_Arespectively. Assume production is costless.a. Give equations for and graph each firm’s reaction curve.b. If both firms set their prices at the same time, what is the Nash equilibriumprice, quantity, and profit for each firm?c. Suppose A sets its price first and then B responds. What price and quantitydoes each firm set now? Is it advantageous to move first?d. Compare the profits from part b and c. Which firm benefits more from thesequential price choosing? (Please do b-d, thanks :))1. Two firms (A and B) play a competition game (i.e. Cournot) in which they can choose any Qi from 0 to ¥. The firms have the same cost functions C(Qi) = 10Qi + 0.5Qi2, and thus MCi = 10 + Qi. They face a market demand curve of P = 220 – (QA + QB). a. Assume firm A chooses quantity first. Frim B observes this choice and then chooses its own quantity. What is Frim B's profit as a function of QA and QB? b. Firm B has MRB = 220 – 2QB – QA. What is firm B’s best response to an arbitrary QA selected by firm A? c. Given that firm A expects firm B’s best response, what is firm A’s profit as a function of QA? (Hint: the only unknown variable in the profit function should be QA) d. Firm A has MRA = 150 – 4QA/3. What are the equilibrium QA and QB selected in this game? e. What is the equilibrium price, and how much profit does each firm collect?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 1 P(QM) = 780 -Q=780 -0.02222QM 45 QM is total market production (i.e., combined production of firm's A and B. That is: Q(P) = 35, 100- 45P 2M = A +QB As a result, the inverse demand curve for each firm is: P(QA, QB) = 780- -1/32₁-752 45 Unlike the example in class, the two firms have different costs. = 4000A TCA (QA) TCB (QB) = 260QB = 780 -0.022220A -0.02222QB 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 Qg, 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
- Help me please3. Consider a duopoly with a demand curve given by P = a -bQ, where a and b are positive constants and Q is the total production by the two firms. Firms sell identical goods and have an identical constant marginal cost of production c. Fixed costs are equal to zero. We assume firms choose quantities simultaneously (Cournot competition). a. Obtain the first order condition of profit maximization for each firm. Use graphical analysis and economic intuition to explain what they represent. b. Obtain the profit maximizing quantity for each firm. Explain what they represent using game theory concepts c. Demonstrate using relevant graphical analysis and economic intuition that the results obtained in b are not a Pareto Optimum for the firms involved. d. How would the graphical analysis in part a change if Firm A had a fixed cost of productionRefer to the figure at right. Two firms operating in the same market must choose between a collude price and a cheat price. Firm A's profit is listed before the comma, B's outcome after the comma. If each firm tries to choose a price that is best for it, regardless of the other firm's price, which of these statements is correct? O A. Both firms should charge a cheat price. OB. Firm A should charge the collude price; Firm B should charge a cheat price. C. D. Both firms should charge a collude price. Firm A should charge a cheat price; Firm B should charge a collude price. Cheat Price Firm A Firm B Cheat Price Collude Price Collude Price 18, 18 6,30 30,6 24, 24
- 5. Duopolist firms 1 and 2 compete on price with some market differentiation. Demand for firm ie{1, 2} is q, = 2 – 2p, + p, Neither firm has costs. a. Find the best response functions for each firm in the static game. b. Find the unique Nash equilibrium prices in the static game. c. Are prices strategic complements or strategic substitutes? Briefly explain. d. Does Firm 1 want Firm 2 to increase or decrease p,?Problem 1. HHI in the Bertrand Triopoly Equilibrium It's a Bertrand Triopoly - hence we know there are 3 firms in the industry-in-question, who competes in "price". The inverse demand functions for Firm 1, 2, and 3 are as follows: q1 = 40 - 1.5p1 +0.5p2 +p3 q2 = 40 + 1.5p1 - 3p2+p3 q3 = 40 + 2p1 + 1.5p2 - 4p3 For each firm, the marginal cost of production is $2.50/unit produced and sold. Apparently, the firms' products are differentiated. You cannot impose symmetry across firms. Therefore, please solve each firm's profit maximization problem, impose equilibrium, and solve for each firm's "action" in equilibrium. After that, please calculate the Herfindahl- Hirschman Index (HHI) in the industry in equilibrium.The graph below shows a demand curve for a firm operating in an oligopolistic market. Kinked Demand Price 100 90 80 70 60 50 40 30 20 10 0 MR Quantity D 10 20 30 40 50 60 70 80 90 100 MC O relatively more elastic. O relatively more inelastic. O perfectly elastic. O perfectly inelastic. Compared to a price of $75, at a price of $60 demand is O
- Consider the Cournot duopoly with linear demand function ? = 2000 − 2Q, where P is the price and Q = q1 + q2 is the total supply. Firm 1 and firm 2 has constant marginal cost of 600. Just answer the E, F and G, thank you bartleby! a. If firm compete in price, draw in detail the best response of each firm.b. Determine and explain the Bertrand equilibrium.c. What is the equilibrium quantity and how much profit for each firm?d. Explain the Bertrand Paradox in (c)!e. If firm 1 has capacity of production 450 and firm 2 has capacity of 200. Determine the Bertrand equilibrium.f. What is the equilibrium quantity, and how much profit for each firm?g. Is there any paradox in (f)?Please help me ASAP. I will really appriciate it. Thank you Assume a Nash-Cournot equilibrium. How much output does firm 1 produce? Assume a Nash-Cournot equilibrium and no fixed cost. How much profit does firm 2 make? Now assume a collusive equilibrium. What is firm 1's output?Which of the following is an assumption of the theory of oligopoly? O Firms produce and sell either homogeneous or differentiated products. O There are no barriers to entry. O a and c There are many sellers and many buyers.
