In a duopoly, suppose that the two firms set prices independently (Bertrand model). For each firm, we have the following information: Firm A demand: QA = 120 - 2PA + PB %3D Firm B demand: QB = 120 - 2PB + PA %3D Firm A Price-Reaction Curve: PA = 30 + 0.25PB %3D Firm B Price-Reaction Curve: PB = 30 + 0.25PA Assume MC = TC = 0 Using this information, report on the value of quantity, price, and profits for each firm in the duopoly. You need not show your work.
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- Consider a duopoly market, where two firms sell differentiated prod- ucts, 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 pi and p2 simultaneously. The derived demand functions for the two firms are: D1 (p1, P2) and D2 (p1, P2) = + 2, where S > 0 and the parameter t > 0 을 + S + P2-P1 2t 2t measures the 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 profits of the two firms.Consider a Cournot Duopoly model. The inverse demand for their products is given byP = 200 − 6Q, where Q is the total quantity supplied in the market (that is, Q = Q1 + Q2). Each firm has an identical cost function, given byT Ci = 2Qi, for i = 1, 2.(a) In the Cournot model, what does each firm choose?(b) What is the timing of each firm’s decision?(c) Find the Nash equilibrium quantities (Q∗1, Q∗2)?(d) What is the equilibrium price? Just help with c and d here pleaseConsider a Duopoly model, in which two firms decide a quantity simultaneously. The market demand is given by P=120 - 3Q, where Q is the total output (i.e., Q=Q1+Q2). Each firm has an identical cost function, TCi=12Qi, i=1, 2. If Firm 1 believes Q2=12, Firm 1 should sell Q1= _____ units in order to maximize its profit.
- 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…Consider the Bertrand model and answer the question below related to the content. Assume that each firm in the Bertrand Duopoly model can only choose non-negative integer quantities: 0, 1, 2, ... . Assume the demand is Q(P)=10-P and the marginal cost is 0 for each firm. Given this information, which of the following is FALSE? [Hint: Check values of profit functions.] A. If firm 2 sets price equal to 1, then the best response of firm 1 to this price is 1 B. If firm 2 sets price equal to 4, then the best response of firm 1 to this price is 4 C. If firm 2 sets price equal to 2, then the best response of firm 1 to this price is 110Two firms produce differentiated products. The demand for each firm’s product is as follows: Demand for Firm 1: q1 = 20 – 2p1 + p2 Demand for Firm 2: q2 = 20 – 2p2 + p1 Both firms have the same cost function: c(q) = 5q. Firms compete by simultaneously and independently choosing their prices and then supplying enough to meet the demand they receive. Please compute the Nash equilibrium prices for these firms.
- What is the homogeneous-good duopoly Cournot equilibrium if the market demand function is Q= 1,800 - 1,000p. and each firm's marginal cost is $0.28 per unit? The Cournot-Nash equilibrium occurs where q, equals and 92 equals (Enter numenic responses using real numbers rounded to two decimai places.) Furthermore, the equilibrium occurs at a price of $ (Round your answer to the nearest penny.)Ugly Dolls Inc. (UD) is a firm in Mytown that sells its products on a market under monopolistic competition. The cost function of UD is represented by TC = 100+10Q. Lately, because of the UD is making a big amount of profit, some firms enter the market to compete. Assume that Mytown engages in free trade in the dolls markets with Yourtown, who also faces a market with monopolistic competition. Because of this we can expect that, (a) The numbers of firms operating in this market will not change. (b) At equilibrium the profit of firms will increase. (c) The quantity of types of dolls available to consumers will increase. (d) All the above answers are correct.Consider a Cournot Duopoly model. The inverse demand for their products is given byP = 200 − 6Q, where Q is the total quantity supplied in the market (that is, Q = Q1 + Q2). Each firm has an identical cost function, given by TCi = 2Qi, for i = 1, 2.(a) In the Cournot model, what does each firm choose?(b) What is the timing of each firm’s decision?
- Consider a "Betrand price competition model" between two profit maximizing widget producers say A and B. The marginal cost of producing a widget is 4 for each producer. Each widget producer has a capacity constraint to produce only 5 widgets. There are 8 identical individuals who demand 1 widget only, and individuals value each widget at 6. If the firms are maximizing profits, then which of the following statement is true: a) Firm A and Firm B will charge 4 b) Firm A and Firm B will charge 6 c) Firm A and Firm B will charge greater than or equal to 5 d) None of the options are correct. Explain clearly.There are two firms in the market (duopoly). These two firms are competingsimultaneously. The first firm chooses its output level (x) by predicting the second firm’soutput (y). Let c denote the total cost function c(x) = x and c(y) = y. Also, let’s assumethat the inverse demand function is p(Y) = 7 - Y where Y = x + y. (1) Obtain the reactionfunction of the first firm. (2) Find the equilibrium (output and profit of each firm) whentwo firms simultaneously compete(5) For each situation, solve for the Bertrand-Nash Equilibrium (differentiated Product). 5a) Suppose Sarah's constant marginal cost is $5 but Joe's is $8 Recall that in a Bertrand model with differentiated product, each supplier faces his/her own demand: Qjoe = 100 – 10 Pjoe + 5 Psarah Qsarah = 100 – 10 Psarah + 5 Pjoe 5b) Suppose Joe and Sarah have the same cost functions as earlier (constant MC of $5) but asymmetric demand functions Qjoe = 100 – 10 Pjoe + 5 Psarah Qsarah = 160 - 10 Psarah + 5 Pjoe