3. Suppose there is a duopoly of two identical firms, A and B, facing the inverse demand P = 310-Q, and cost functions are CA = 10QA and CB = 10QB respectively. a) Find the Cournot - Nash equilibrium quantities, price, and profits for each firm. b) Suppose that A acts as the leader in a Stackelberg model and B responds. What are the respective prices, quantities, and profits of each firm now? c) What are the prices, quantities, and profits for the firms if they decide to collude and share profits equally? d) Show that

3. Suppose there is a duopoly of two identical firms, A and B, facing the inverse demand P = 310-Q, and cost functions are CA = 10QA and CB = 10QB respectively. a) Find the Cournot - Nash equilibrium quantities, price, and profits for each firm. b) Suppose that A acts as the leader in a Stackelberg model and B responds. What are the respective prices, quantities, and profits of each firm now? c) What are the prices, quantities, and profits for the firms if they decide to collude and share profits equally? d) Show that

Survey Of Economics

10th Edition

ISBN:9781337111522

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter9: Monopolistic Competition And Oligoply

Section: Chapter Questions

Problem 11SQP

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Suppose there is a duopoly of two identical firms, A and B, facing a market inversedemand of P = 110 − Q/4 , and cost functions of C_A = 10Q_A and C_B = 10Q_Brespectively.a. Plot the best response functions and find the Cournot-Nash equilibriumquantities, equilibrium price, and profits for each firm.b. Suppose that A acts as the leader in a Stackelberg model and B responds.What are the respective quantities and profits of each firm now? Is itadvantageous to move first?c. If the firms were able to collude, how much additional profit could they earnif they switch from simple monopoly pricing to perfect price discrimination?d. Graph and label the cartel outcome, the Cournot outcome and theStackelberg outcome on the inverse demand. Calculate the consumersurplus and deadweight loss in each case.
1. In class, we showed that in a Cournot duopoly with demand p: ab(91 +92) and marginal costs of c₁ for firm 1 and c2 for firm two, the firms' best response functions were as follows: a C1 92 2b 91 a-c2 92 - 2b 91 822 and (a) Find equilibrium expressions for q₁ and q in terms of a, b, C1, and C2 only. (b) Show that the equilibrium price will be p": = a + c1 + €2 3
Duopoly: 1. Consider a duopoly game with 2 firms. The market inverse demand curve is given by P(Q) = 120-Q, where Q = 9₁ +9₂ and q; is the quantity produced by firm i. The firm's long run total costs are given by C₁(9₁)=2q₁ and C₂(92)=92, respectively. a. Determine the Nash Equilibrium for Cournot competition, in which firms compete based on quantity. What is each firm's best response as a function of the other firm's output? Graph these best response functions in on the same graph. Compute the associated payoffs for each firm. b. Determine the Nash Equilibrium for Bertrand competition, in which firms compete based on price and stand ready to meet market demand at that price. What is each firm's best response as a function of the other firm's price? Graph these best response functions in on the same graph. Compute the associated payoffs for each firm. Game Th
1.6. Consider the Cournot duopoly model where inverse demand is P(Q) = a - Q but firms have asymmetric marginal costs: c₁ for firm 1 and c2 for firm 2. What is the Nash equilibrium if 0 a+c₁?
11. Suppose there is a duopoly of two identical firms, A and B, facing a market inverse demand of P = 140 – 0.5Q, and cost functions of CA = 20QA and Cg = 20QB respectively. a. Find the Cournot-Nash equilibrium and profit for each firm. b. Suppose that A acts as the leader in a Stackelberg model and B responds. What are the respective quantities and profits of each firm now? Is it advantageous to move first? c. If the firms were able to collude, how much additional profit could they earn if they switch from simple single pricing to perfect price discrimination? d. Graph and label equilibria on the inverse demand.
Consider a Cournot oligopoly with three firms i = 1,2, 3. All firms have the same constant marginal cost c = 1. The inverse demand function of the market is given by P = 9-Q, where P is the market price, and Q = E1 9i is the aggregate output. 3 (a) Solve for the Nash equilibrium of the game including firm out- puts, market price, aggregate output, and firm profits (Hint: the NE is symmetric). (b) Now suppose these three firms play a 2-stage game. In stage 1, they produce capacities q1, 72 and 73, which are equal to the Nash equilibrium quantities of the Cournot game characterised by part (a). In stage 2, they simultaneously decide on their prices p1, p2 and p3. The marginal cost for each firm to sell up to capacity is 0. It is impossible to sell more than capacity. The residual demand for firm i is 9 – Pi - Eiti āj if pi > P; for all j # i if p; = Pj for all j # i if p; < P; for all j #i | 9-pi D; (pi, p-i) = 3 9 – p; (Note, here we assume that the efficient/parallel rationing ap-…
Consider two oligopolistic firms (Firm 1 and Firm 2) in a price-setting duopoly. Both firms have no marginal costs (MC = 0) but do have fixed costs F = 10, i = 1,2. The demand functions for Firm 1 and Firm 2 are given by q, = 13 – 2p, + p, and q, = 13 - 2p, + P,, respectively. A. Calculate the values of profit-maximizing quantities and prices for Firm 1 and Firm 2, and their respective profits. B. If the two firms are working together and collude on price (p, = p, = p), find the new collusion price,
Consider a Cournot oligopoly with three firms i = 1; 2; 3. All firms have the same constant marginal cost c = 1. The inverse demand function of the mParket is given by P = 9Q, where P is the market price, and Q = (q1 + q2+q3) is the aggregate output. Solve for the Nash equilibrium of the game including firm outputs, market price, aggregate output, and firm profts
Consider a market in which there are two firms: A and B. Each firm produces a differentiated product and chooses its price. Assume that each firm can set price equal to $60 or $70. The payoffs associated with each set of prices are shown. If the firms choose price simultaneously, then the Nash equilibrium price for firm A is chooses price first and can commit to that price, then firm A will set its price equal to If firm A ○ A. $70; $60 B. $70; $70 ○ C. $60; $70 ○ D. $60; $60 Q Firm B's Price ✓ $60 $70 $1800 $1650 $60 $1800 $2250 Firm A's Price $2250 $2200 $70 $1650 $2200
In the Cournot duopoly model, the analogous statement is that the quantity pair (q₁,q) is a Nash equilibrium if, for each firm i, q solves max Ti(9₁,9₁) 0<9;<∞0 and = * Assuming q
Assume that two firms, Wilson and Spalding, can manufacture basketballs for the entire Norfolk market, and that the market is oligopolistic in structure. Market Demand: Q-120-P Total Costs: TC-200 Q the quantity of basketballs P the price of a basketball in $ US TC the total cost of producing a given quantity of basketballs (in $ US) Show all of your work in solving the problems below. 1) The Cournot Model: Now assume that the two firms are Cournot competitors, and that all the assumptions of the Cournot model are met: no firm entry, homogeneous goods, a single period, and that the firms choose the quantities of basketballs to supply. Now, how many basketballs will be sold by each firm and at what price? What will be the total revenues, total costs, and the profits for each of the two firms? Demonstrate the model using graphs. (See Figs. 9-3 to 9-10) 2) The Stackelberg Model: Assume that the two firms are Stackelberg competitors, and that Wilson is the Stackelberg leader and Spalding…
If firm 1 and firm 2 are the oligopolistic firms in bottled spring water production in Nomansland. The market demand is given by ? = 5000 −20?, Qd is the number of kilolitres demanded per month while P is the price of kilolitres of bottled water. The marginal cost of a kilolitre of bottled water is R10.How do I Find the Cournot equilibrium quantities and price? and how do I Find the Cournot profits and the monopolist profits?