There are two firms A and B. Firms compete in a Cournot Duopoly in Karhide. They set quantities qA and qB. Inverse demand is P(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.) (d) Solve for the equilibrium outputs (q∗A, q∗b). (e) Solve for the equilibrium price. (f) Solve for firm B profits.

Two identical firms compete as a Cournot duopoly. The demand they face is P = 100-2Q. The cost function for each firm is C(Q)= 40. In equilibrium, the deadweight loss is Multiple Choice $256. $512 $128 5394

Problem 3 Consider the infinitely repeated game with the discount factor & € (0, 1) of the following Cournot duopoly model with inverse demand function P(Q) = a Q if Q≤ a 0 if Q > a where Q = 91 +92 and cost functions Ci(qi) = cqi, i = 1,2. The profit function of firm i is given by Ti (91, 92) = qiP(9₁ +92) - cqi. Consider the following grim-trigger strategy. Produce half the monopoly output in the first period and as long as everybody has produced that amount so far. Otherwise produce the Cournot output. Verify that this is a subgame perfect equilibrium.

All question are with regards to the following set up. There are two firms A and B. Firms compete in a Cournot Duopoly in Karhide. They set quantities qa and qB. Inverse demand is P(qA + qB) = 18 – qA – qB and costs are C(q) (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.) You must show your work at each step, unless the questions is followed by "No work required." 3 * q for both firms. Firm B is a domestic firm   (4) We now consider the government’s choice of s≥0. We can see from above thatprofits and outputs depend upon s. With that in mind, let πB(s) and qB(s) denote firm B’s profit and output as a function of the subsidy s. Let qA(s) denote firm A’s equilibrium output as a function of s. Let G(s) = πB(s) − s*qB(s) denote the government’s objective…

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?

Consider a duopoly market, where two firms sell differentiated products, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices p, and p2 simultaneously. The derived demand functions for the two firms are: D1 (P1, P2) = SG+P1)and D2 (P1, P2)= S(;+-P2), where S > 0 and the parameter t > 0 measures the 2t 2t degree of product differentiation. Both firms have constant marginal cost c> 0 for production. (a) Derive the Nash equilibrium of this game, including the prices, outputs and profit of the two firms. (b) From the demand functions, qi= D¡ (p; , p¡ )= SG+P), derive the residual inverse demand functions: p; = P; (qi , p¡) (work out: P; (qi , P;)). Show that for t > 0, P;(qi , P;) is downward 2t aPi (qi ,Pj) . sloping, i.e., c, i.e., firm į has market power. %3D (c) Calculate the limits of the equilibrium prices and profit as t → 0 ? What is P; (qi , p;) as t → 0? Is it downward sloping?…

Consider a Cournot oligopoly with two firms, where the demand curves are given by P, = 100-Q,-2Q2 P2= 100-2Q,-Q2 and that costs are given by TC(Q,) = Q'1. MC, = 2Q1, TC(Q2) = Q²2, and MC2 = 2Q2. Also, marginal revenues can be written as MR, = 100-2Q,-2Q2. MR2= 100- 2Q, - 2Q2. Solve for each firm's profit. Profit for firm 1= 600, Profit for firm 2= 300 Profit for firm 1= 300, Profit for firm 2= 600 Profit for firm 1= 555.55, Profit for firm 2= 555.55 O Profit for firm 1= 0, Profit for firm 2= 0

The firms in a duopoly produce differentiated products. The inverse demand for Firm 1 is The inverse demand for Firm 2 is and P₁ = 52-9₁-0.592. Each firm has a marginal cost of m= $1 per unit. Solve for the Nash-Cournot equilibrium quantities. The Cournot equilibrium quantities are (Enter your responses rounded to two decimal places.) P₂ = 100-92-0.5q1₁. 91 = units 92 units. =

Consider a Bertrand oligopoly where two firms (Firms 1 and 2) sell goods that are imperfectsubstitutes and compete by choosing prices simultaneously. Their market demands areq!= 1,200 − 3/2p!+ 3/2p", q"= 800 − 2p"+ 1/2p!For simplicity, assume the marginal cost is zero for both firms (MC!= MC"= 0). Find the bestresponse curve of each firm. Which of the following alternatives is correct?(a) Firm 1’s best response curve is p!= 400 + 0.5p"(b) Firm 2’s best response curve is p"= 400 + 0.5p!(c) Firm 1’s best response curve is q!= 45 − 0.5q"(d) Firm 2’s best response curve is q"= 200 + 0.8p!  Then, find the optimal price and quantity of each firm.Hint: Start by finding the Nash equilibrium, that is, the combination of mutual best responses.Which of the following alternatives is correct?(a) For firm 1, p!= $1,600/3 and q!= 800/3(b) For firm 1, p!= $800 and q!= 1,600/3(c) For firm 2, p"= $800 3⁄ and q"= 1,600/3(d) For firm 2, p"= $1,600 and q"= 800  key: !=1 "=2

Two firms are engaged in duopoly competition in a market with demand Q = 120 - p and zero costs.   The reaction function for firm i given firm j's output q i = 60 - 1 2 q j .   What is the payoff to firm i if the two firms engaged in collusion to maintain monopoly output and prices. Assume that each firm gets half the monopoly profit.