Assume firms' marginal and average costs are constant and equal to c and that inverse market demand is given by P = a-bQ where a, b>0. Suppose now the market is served by 2 firms (one leader, and one follower) that choose quantities for their identical products. Calculate: i. ii. iii. iv. The Nash equilibrium quantities for the Stackelberg duopolists Market output Market price Firm profit
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- Assume firms' marginal and average costs are constant and equal to c and that inverse market demand is given by P = a - bQ where a, b > 0. Suppose now the market is served by k firms that choose quantities for their identical products simultaneously. Calculate: i. ii. iii. iv. The Nash equilibrium quantities for the Cournot firms as functions of k. 2 Market output and price as a function of k Firm profit as a function of k Using your answers in i, ii, iii and iv, describe what happen to firm output, market output, market price and firm profit as the number of firms increases.Assume firms' marginal and average costs are constant and equal to c and that inverse market demand is given by P = a - bQ where a, b > 0. Suppose now the market is served by 2 firms that choose quantities for their identical products simultaneously. Calculate: i. ii. iii. iv. The Nash equilibrium prices for Cournot duopolists Firm output Market out Firm profit1. Consider two duopolists who each have a constant marginal cost c = e2 = 3 and face inverse demand P = 15 – Q,where Q = Q1 + Q2 is the total output of both firms. 1. Find the Cournot equilibrium quantity for each firm, the resulting market price, and the profits for each firm. 2. Find the Stackelberg equilibrium quantities for each firm, and the price, and the profits for each firm supposing that Firm 1 is the industry leader. 3. Suppose that Firm 2 figures out a way to lower its marginal cost to ez = 0 while firm 1 still has a marginal cost equal to 1: c = 3. How does this affect the Cournot equilibrium quantities, price, and profits? 4. How does this affect the Stackelberg equilibrium (with Firm 1 still as the leader) quantities, price, and profits?
- What is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q= 1,800 - 1,000p. and each firm's marginal cost is $0.28 per unit? The Cournot-Nash equilibrium occurs where q, equals and 92 equals (Enter numenic responses using real numbers rounded to two decimai places.) Furthermore, the equilibrium occurs at a price of $ (Round your answer to the nearest penny.)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. 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
- 8. Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by 92. Each firm faces a constant marginal cost of 3. Let Q denote total output, 1.e. Qq1 +42. The inverse demand curve in the market is given by P-15-Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. (b) If the firms could collude, what would be the total output in the mar- ket? Assuming each firm produces half of the collusive output, what is the profit of each firm?Suppose that in the market for cell phone service the number of competitors has dwindled until D & C Romer Net and Spa T. Wireless have become the only providers left in the nation. Seeking to boost their profits, the two companies secretly agree to a coordinated increase in their prices for cell phone minutes. This practice is known as a Nash equilibrium. O tying. collusion. antitrust. predatory pricing.6. Two firms, Firm 1 and Firm 2 and are competing in quantities. The demand they are facing is given by p=1-91-92, with p being the price of the good, and 9₁ and 92 the quantities produced by firm 1 and 2 respectively. The total cost of firm 1 is TC1 (91) = 9₁ and the one of firm 2 is TC₂ (92) = 292. (a) Find the Cournot equilibrium. (b) The government decides that it wants to make the market more competitive. As such it decides to offer to Firm 1 a license to become the leader in the market. The licence costs F, and if Firm 1 buys it, it will be allowed to choose its quantity before Firm 2. What is the maximum Firm 1 would be willing to pay for this license?
- 8. Suppose there are two identical firms in an industry who compete by setting quantities. The output of firm 1 is denoted by q1 and that of firm 2 is denoted by 92. Each firm faces a constant marginal cost of 3. Let Q denote total output, 1.e. Q-91 +42. The inverse demand curve in the market is given by P-15-Q (a) Find the Cournot-Nash equilibrium quantity produced by each firm and the market price. "// (b) If the firms could collude, what would be the total output in ket? Assuming each firm produces half of the collusive output, the profit of each firm? the mar- what is (c) Suppose each firm produces half of the collusive output identified in part (b). Firm 1 considers a deviation from this arrangement. What would be the best deviating output of firm 1 and its deviation profit? (d) Suppose firms interact repeatedly over an infinite horizon, and firms have a common discount factor & € (0,1). Specify a trigger strategy for each firm to sustain the collusive arrangement as an…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.Suppose that there are two firms producing a homogenous product and competing in Cournot fashion and let the market demand be given by Q = 120- Assume for simplicity that each firm operates with zero %3D total cost. Find Cournot Nash equilibrium total surplus. 12800 O 6400 O 13600 19200