ppose two firms face market demand of P=150-Q, where Q = q1+ q2. Both ns have the same unit cost of C, C=28. Assume the firms compete a la ackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. a) What is the follower's total revenue function? b) Determine the equilibrium output level for both the leader and the follower. c) Determine the equilibrium market price, the profits of the leader and the follower. te: The writing is clear and abbreviations are not allowed.
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- Inverse elasticity rule Use the first-order condition (Equation 15.2 ) for a Cournot firm to show that the usual inverse elasticity rule from Chapter 11 holds under Cournot competition (where the elasticity is associated with an individual firm's residual demand, the demand left after all rivals sell their output on the market). Manipulate Equation 15.2 in a different way to obtain an equivalent version of the inverse elasticity rule: pMCp=sieQ,p , where si=qi/Q is firm i's market share and eQp is the elasticity of market demand. Compare this version of the inverse elasticity rule with that for a monopolist from the previous chapter.Suppose two firms face market demand of P=150-Q, where Q=q1+q2 . Both firms have the same unit cost of 26. Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. (a)What is the follower’s total revenue function? (b)Determine the equilibrium output level for both the leader and the follower. (c)Determine the equilibrium market price. (d)Determine the profits of the leader and the follower (Please write clearly, thank you)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.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. What is the follower’s total revenue function? Determine the equilibrium output level for both the leader and the follower. Determine the equilibrium market price. Determine the profits of the leader and the follower.Suppose two firms face market demand of P=150-Q, where . Both firms have the same unit cost of C, C= 22. Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. What is the follower’s total revenue function? Determine the equilibrium output level for both the leader and the follower. Determine the equilibrium market price. Determine the profits of the leader and the follower.
- Two firms, 1 and 2, compete in price Market demand in period t is given by D(t) = AtD(p) with A > 0 The common discount factor is ? ? (0, 1) Suppose the firms use trigger strategies to collude at the monopoly price pm = arg max(p ? c)(A)tD(p) ? (A)t?m (note that pm does not depend on A and t due to the function form) Suppose the punishment after deviation is returning to marginal cost pricing forever If the firms collude, they set the same prices and evenly split the profits What are firms’ collusive profits in period t? If a firm undercuts below pm in period t, what are the (optimal) deviating price and deviating profit Write down the no-deviating condition in period t? Simplify the no-deviating condition and derive the critical discount factor ? Compared to when the market is shrinking (A 1) make collusion easier? Explain in words your finding in [e]Suppose that there are two firms producing a homogenous product and let the market demand besiven by Q(P) = 120 -P/2 . For simplicity assume that each fir operates with zero total cost. a) Assuming that firms compete over quantities, find the price best-response functions of firms 1 and2. Draw a diagram that shows the BRFs and the equilibrium, Are outputs strategic substitutes orcomplements? Find each firm's Cournot equilibrium output, price, profit, and total surplus. DefineNash equilibrium and argue that it is indeed a Nash equilibrium. b) Show that the duopolists have incentives to collude, Find their joint profit-maximizing price, output,and profit: find each firm's output and profit. Is collusion a Nash equilibrium? If not, what is theoptimal defection for each firm? Show this game in a 2X2 matrix form. What does this imply aboutthe Nash equilibrium or the stability of their collusive agreement? Is it a Prisoner's Dilemma Type? c) Suppose now that fims play the above game in…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?
- Suppose two firms face market demand of P=150-Q, where Q=q1+q2. Both firms have the same unit cost of 22. Assume the firms compete a la 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 profits of the leader and the follower.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 duopoly market with 2 firms. Aggregate demand in this market is given by Q = 500 – P, where P is the price on the market. Q is total market output, i.e., Q = QA + QB, where QA is the output by Firm A and QB is the output by Firm B. For both firms, marginal cost is given by MCi = 20, i=A,B. Assume the firms compete a la Cournot. What are the equilibrium quantities? What is the total quantity supplied on this market? What is the equilibrium price in this market?