c) Consider a market in which the market demand curve is given by P= 18 - X - Y, where X is Firm I's output, and Y is Firm 2's output. Firm 1 has a marginal cost of 3 (MC-3), while Firm 2 has a marginal cost of 6 (MC=6). i. Find the Cournot equilibrium outputs in this market. ii. Also, find the Stackelberg equilibrium in which Firm 1 acts as the leader.
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- 9: Suppose there are two restaurants on an island, Ace's (A) and Betty's (B). They both have to decide how many meals, qa and qB, to sell per day. For Q = qA + ¶B, the market demand function for meals is p = 120 – Q || Both restaurants face a marginal cost per meal of $30. (1) Find the Cournot equilibrium quantities and prices. (2) What if the restaurants decide to form a cartel and split the production and profits evenly. How much will each firm produce and what price do they charge? (3) Suppose they competed with prices instead of quantities. Find the Bertrand equilibrium quantities and prices. (4) Find the deadweight loss of Cournot competition, Bertrand competition, and of the cartel outcome. Then rank each of these from least deadweight loss to most deadweight loss. For the rest of the problem, assume firms compete in quantities (Cournot) and there is no cartel. (5) Suppose Betty's marginal cost per meal increases to $60. Ace's marginal cost remains at $30. What are the new…Question 3 The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has al cost of production of C₁= 15*Q₁ and firm 2 has a cost of production of C₂=20*Q₂. 1) Suppose firm 1 and firm 2 compute simultaneously in quantities. What are the Cournot quantities and prices? What are the profits of firm 1 and 2? 2) Suppose firm 1 and firm 2 compete simultaneously in prices. What are the Bertrand quantities and prices? What are the profits of firm 1 and 2? 3) Suppose that firm play a Stackelberg game. First firm 1 sets the quantity in t=1, then, knowing which quantity firm 1 has set, firm 2 chooses the quantity in t=2. What are the Stackelberg quantities and prices? What are the profits od firm 1 and 2? Compared to part a) which firm benefits and which firm loses?The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has a cost of production of C1= 15*Q1 and firm 2 has a cost of production of C2=20*Q2 a) Suppose firm 1 and firm 2 compute simultaneously in quantities. What are the Cournot quantities and prices?What are the profits of firm 1 and 2?b) Suppose firm 1 and firm 2 compete simultaneously in prices. What are the Bertrand quantities and prices?What are the profits of firm 1 and 2?
- 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?Oligopoly: Quantity Competition 1. Consider two duopolists who each have a constant marginal cost c = c2 = 2 and face inverse demand P = 4 – Q,where Q = Q1+ Q2 is the total output of both firms.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.
- . 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.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?Refer to Figure 14-7. Assume that the market starts in equilibrium at point W in graph (b) and that graph (a) illustrates the cost curves facing individual firms. Suppose that demand increases from D0 to D1. Which of the following statements is not correct? a. Point Z is a long-run equilibrium point. b. Point Y is a long-run equilibrium point. c. Points W, Y, and Z are short-run equilibria points. d. Point W is a long-run equilibrium point. PRICE Graph (a) MC ATC P₂ aa P Q Q QUANTITY PRICE P₂ a a a Graph (b) Q Qy Qx Qz QUANTITY Do D₁
- The daily demand of two firms Firm 1 and Firm 2 producing two products is given by : D1 = 5 - 22P1 + 11P2 D2 = 50 - 22P1 + 11P2 These are the only firms producing the products. MC of Firm 1 is $0.5 per product and MC of Firm 2 is $2 per product. Q1. Calculate the equilibrium quantity and price of both the firms. You may assume that firms want to maximise the profits. Q2.Calculate producer surplus and deadweight loss.Question 3 Assume we have a market with only two companies in it, Company X and Company Y. Now suppose that both companies have to choose one of two potential strategies for pricing their products: setting a low price or setting a high price. The table below shows the expected profits for each company under each pricing scenario. Assume both companies are in competition with each other and seek to maximize their profits. Under these conditions, how much profit should we expect both companies to earn? Company Y Provide your answer below: High Price Low Price High Price Profit for Company Y: $12, 975,000 Profit for Company X: $12, 975,000 Profit for Company Y: $16, 218,000 Profit for Company X: $1,946, 000 Company X Low Price Profit for Company Y: $1,946, 000 Profit for Company X: $16, 218,000 Profit for Company Y: $6,487,000 Profit for Company X: $6,487,000The marginal cost of a product is fixed at MC = 20. The demand for the product is Q = 100 - 2P. (a) Now consider a Cournot model with two firms that are choosing quantities simultaneously. What is the best reply (best response) function for each firm? What is theNash equilibrium? What is the total surplus? (b)What do you expect the total surplus would be with three firms? Why? (You do not need to calculate an exact value. You can say ”total surplus is at least 100”, or ”total surplus is at most 80”)