1) Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 – 2pi + P2 and 92 = 12 + P1 – 2p2. So this is like Bertrand competition, except that when pi > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, Pi the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. BR1 (P2) is || (1) N
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- Two firms are engaged in Cournot (simultaneous quantity) competition. Market-level inverse demand is given by P = 160 − 4Q Firm 1 has constant marginal costs of MC1 = 8, while Firm 2 has constant marginal costs of MC2 = 24. 1) Does there exist a low enough positive marginal cost for firm 1 such that firm 1 acts like a monopoly in this market, if so what is the MC if not why?A large firm has two divisions: an upstream division that is a monopoly supplier of an input whose only market is the downstream division that produces the final output. To produce one unit of the final output, the downstream division requires one unit of the input. If the inverse demand for the final output is P = 1,000 − 80Q, would the company’s value be maximized by paying upstream and downstream divisional managers a percentage of their divisional profits?Suppose two firms face market demand of P=150-Q, where . Both firms have the same unit cost of C, which consist of your student number a plus 20 (i.e. if your student number a=3, then cost C=20+3=23). Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. 1.What is the follower’s total revenue function? 2.Determine the equilibrium output level for both the leader and the follower. 3.Determine the equilibrium market price. 4.Determine the profits of the leader and the follower.
- Suppose two Bertrand competitors, F1 and F2, make identical products for a market with inverse demand P = 600 – 0.5Q. Both firms have the same costs Ci = 20qi, and each firm has sufficient capacity to supply the entire market. a. What prices will the firms choose? How much might each produce and what profit would they make? Is the result a Nash equilibrium? Explain. b. Suppose F1 improves its efficiency, reducing its cost to C1 = 16q1. What will happen in this market? Explain. c. Assume now that the firms have their original identical costs, but that F1 has only 100 units of capacity and F2 has only 200 units of capacity. What prices will the firms choose now? Explain why neither firm will want to decrease its price at the equilibrium you identify. Why would neither firm want to increase its price? Prove this for F1.Assume that annual inverse demand for a particular product is P=150-Q. The product is offered by a pair of Bertrand competitors, each with marginal costs of $75. The discount factor is 0.9. What is the current equilibrium price and total surplus? Now, assume though that if R&D is conducted at rate x, it incurs one-off costs of r(x)=10x^2 and reduces the marginal costs to (75-x). Suppose that one firm decides to conduct R&D at rate x=10. This research will be protected by a patent of T years. a) What profit(ignoring the one-off costs of R&D) does the innovating firm make each year during the period of patent protection? b) What is the new equilibrium price and total surplus once patent protection expires? c) Use your answer above to write the total surplus from the innovationConsider a single country and a single good. The demand curve for this good is given by QD = 144 - 4P. Thereare two firms serving the market: Firm A and Firm B, where Firm A has a marginal cost of $20 and Firm B hasa marginal cost of $16. There are no fixed costs incurred by either firm. Assume that these firms compete in Bertrand fashion. Part V. What is the equilibrium price in the market now? Explain your reasoning. Part VI. How many units of output each firm produces? Show your work. Part VII. How much profit each firm makes now? Show your work. Part VIII. What is the consumer surplus? Show your work. Part IX. Under which competition, Cournot vs. Bertrand, social welfare is higher? Show your work.
- Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…Two firms produce a homogeneous good and compete in price. Prices can only take integer values. The demand curve is Q = 6 p, where p denotes the lower of the two prices. The lower - priced firm meets all the market demand. If the two firms post the same price p, each one gets half the market demand at that price, i. e., each gets (6p)/2. Production cost is zero.a) Show that the best response to your rival posting a price of 6 is to post the monopoly price of 3. What is the best response against a rival's price of 4? of 5?
- There are two firms A and B. Firms compete in a Cournot Duopoly in Karhide. They set quantities qA and qB. Inverse demand isP(qA +qB) = 18−qA −qB and costs are C(q) = 3∗q for both firms. Firm B is a domestic firm (in Karhide,) and firm A is a foreign firm (from Orgoreyn.) The government of Karhide engages in a strategic trade intervention by giving firm B a per unit subsidy of s. (That is, when firm B produces and sells qB units, firm B receives a payment of s ∗ qB from the government.) We begin by examining the model with an unspecified s ≥ 0. A)Find profit functions for both firms. B)Use first order conditions to find each firm’s best response function.Consider a single country and a single good. The demand curve for this good is given by QD = 144 - 4P. Thereare two firms serving the market: Firm A and Firm B, where Firm A has a marginal cost of $20 and Firm B hasa marginal cost of $16. There are no fixed costs incurred by either firm. Firm A produces 16 units and firm B produces 32 units. The equilibrium price is $24. Total Profit for Firm A = $64 Total Profit for Firm B = $256 Assume that these firms compete in Cournot fashion. What is the consumer surplus? Show your work.Indicate whether the statement is TRUE, FALSE, or UNCERTAIN and explain why. Answer 1 & 2 1. If a monopsonist faces a perfectly elastic supply curve, there will be no deadweightloss relative to the competitive outcome 2. In a Cournot duopoly market, the two firms agree to produce half of the monopolyoutput level for that market and split the resulting profit. Since the monopoly profit is the highest profit that can be obtained, the two firms will always stick to that agreement even if it’s not legally (or in any other way) binding.