Cournot duopolists face a market demand curve given by P = 60 – 1/2Q, where Q is total market demand in units. Each firm can produce output at a constant marginal cost of $15/unit. a) What is the equilibrium price and quantity produced by each firm? b) What if the firm's engaged in Bertrand competition? c) What if one of the firms chose its quantity before its competitor? What is the name for this sort of competition? d) Which of the three forms of competition gives the greatest social surplus?
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- Gamma and Zeta are the only two widget manufacturers in the world. Each firm has a cost function given by: C(q) = 10+20q + q^2, where q is number of widgets produced. The market demand for widgets is represented by the inverse demand equation: P = 200 - 2Q where Q = q1 + q2 is total output. Suppose that each firm maximizes its profits taking its rival's output as given (i.e. the firms behave as Cournot oligopolists). a) What will be the equilibrium quantity selected by each firm? What is the market price? What is the profit level for each firm? Equilibrium quantity for each firm__ price__ profit__ b) It occurs to the managers of Gamma and Zeta that they could do a lot better by colluding. If the two firms were to collude in a symmetric equilibrium, what would be the profit-maximizing choice of output for each firm? What is the industry price? What is the profit for each firm in this case? Equilibrium quantity for each firm__ price__ profit__ c) What minimum discount factor is required…If the inverse demand for bean sprouts were given by P(Y) = 430 − 2Y and the total cost of producing Y units for any firm were TC(Y) = 10Y and if the industry consisted of two Cournot duopolists, then in equilibrium each firm's production would beAssume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function:P = 200 - QA - QBwhere QA and QB are the quantities sold by the respective firms and P is the sellingprice. Total cost functions for the two companies areTCA = 1500 + 55QA + Q2ATCB = 1200 + 20QB + 2Q2BAssume that the firms act independently as in the Cournot model (i.e., each firmassumes that the other firm’s output will not change).a. Determine the long-run equilibrium output and selling price for each firm.b. Determine Firm A, Firm B, and total industry profits at the equilibrium solutionfound in Part (a).
- To examine the effects of a subsidy, consider the large passenger jetliners market with two firms that sell identical products, Firm 1 and Firm 2. Without any subsidy, both firms will have the same cost functions of C(q) = 40q and MC = 40. The market demand is P = 100 – Q. NEED CALCULATION HELP PLEASE!!! Solve for the Cournot equilibrium price, quantities, and profits for each firm given the same MC= 40. Compare the deadweight loss in a monopoly, a Cournot duopoly, and a Bertrand duopoly if both firms have the same marginal cost of 40. How would this market change if Firm 2 receives a subsidy lowering the marginal cost to 25 and Firm 1's marginal cost remains at 40. Calculate new market equilibrium quantity, price, and profits for each firm. Calculate the change in welfare after the subsidy. In this case welfare is defined as the Firm 2’s profit minus the subsidy. Who gains from the subsidy? ExplainThe market demand curve faced by Cournot duopolistsis: Qd = 400 - 8P where Qd is the market quantity demanded and P is the commodity's price in dollars. a. Firm A has a constant marignal cost of $10. What is the equation for Firm A's reaction function with qa expressed as a function of qb? b. Firm B has a constant marginal cost of $7.50. What is the equation for Firm B's reaction function with qb expressed as a function of qa? c. What quantity of output will each firm produce in equilibrium? What price will be established for the commodity?A monopolist can produce at a constant average and marginal cost of ATC = MC = $5. It faces a market demand curve given by Q = 53 - P. Suppose there are N firms in the industry, all with the same constant MC = $5. Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also show that as N becomes large, the market price approaches the price that would prevail under perfect competition. (Hint: your answers will be functions of N)(BONUS)
- Consider two firms, i = 1; 2, producing differentiated products and engaged in Cournot a. Given the market demands, what are the best-response functions of the two firms? b. Draw the best-response functions both for complements (d 0). c. Compute the Cournot equilibrium quantities and prices in this market. d. Compare the outcome between substitutes and complements goods. e. What are the profit-maximizing quantities and prices if firm i is a monopolist in this market? Compare with part c.The market for dark chocolate us characterized by Cournot duopolists - Honeydukes and Wonka industries. The market demand for dark chocolate is: P = 8 - 0.005Qd where P is the price per bar in dollars and Qd is dark chocolate's daily quantity demanded in bars (use qh to represent the quantity of dark chocolate sold by Honeydukes and qw to represent the quantity of dark chocolate sold by Wonka Industries). Honeydukes has a constant marginal cost of $2.50 per bar, while Wonka Industries has a constant marginal cost of $3.00 per bar. The firms move simultaneously in choosing their profit-maximizing quantity of output. a. Given the firms move simultaneously, what is the equation for Honeydukes' reaction function with qh expressed as a function of qw? b. Given the firms move simultaneously, what is the equation for Wonka's reaction function with qw expressed as a function of qh? c. What quantity of dark chocolate will each firm produce in equilibrium and what price will be established for a…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 the inverse demand function for two Cournot dupolists is given by P= 10 – (Q1+Q2) and their cost are zero.a) What is each firm marginal revenue?b) What are the reaction function for the two firmsc) What are the Cournot equilibrium outputd) What is the equilibrium price?Assume that two companies (A and B) are duopolists that produce identical products. Demand for the products is given by the following linear demand functions:P=200-QA-QBwhere QA and QB are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies areTCA = 1500+55 QA +QA2TCB = 1200+20 QB +2QB2Assume that the firms form a cartel and maximize total industry profits,a. Determine the optimal output and selling price for each firm.b. Determine Frim A, Firm B, and total industry profits at the optimal solution foundin part (a).c. Show that the marginal cost of the two firms are equal at the optimal solutionfound in part (a).Cournot’s Model of Duopoly) Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd=5500-25P, where P is the price of a cubic metre of concrete and Qd is the number of cubic metres demanded every year. The marginal cost is $40 per cubic metre. Competition in this market is described by the Cournot model. (a)Given Rebecca’s output is 2000, what is Joe’s residual demand function? What is Joe's output so he maximizes his profit? (b)If Rebecca’s output is qR, what is Joe’s best response function? (c)If Joe’s output is qj, what is Rebecca’s best response function? (d)Plot both Joe and Rebecca’s best response functions on one graph, where the the horizontal axis represents Rebecca’s output qR and the vertical axis represents Joe's output qR. (e)What is the meaning of the interception of the two best response functions?