Suppose two firms engage in simultaneous quantity competition. Both firms have 0 marginal cost. Firm A : P(Q)= 24-Q Firm B: P(Q)= 24-2Q a) Find the Nash Equilibrium quantities q^NE and profits.
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Suppose two firms engage in simultaneous quantity competition. Both firms have 0
marginal cost.
Firm A : P(Q)= 24-Q
Firm B: P(Q)= 24-2Q
a) Find the Nash
(b) Find the
(c) Now suppose the game is repeated infinitely and each firm has a common discount
factor δ. Find the required discount factor to sustain the following grim trigger
strategy as a SPNE: Play Q^M /2 if this has been played in every previous period,
otherwise play q^NE.
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- 1. The market (inverse) demand function for a homogeneous good is P(Q) = 10 - Q. There are two firms: firm 1 has a constant marginal cost of 2 for producing each unit of the good, and firm 2 has a constant marginal cost of 1. The two firms compete by setting their quantities of production, and the price of the good is determined by the market demand function given the total quantity. a. Calculate the Nash equilibrium in this game and the corresponding market price when firms simultaneously choose quantities. b. Now suppose firml moves earlier than firm 2 and firm 2 observes firm 1 quantity choice before choosing its quantity find optimal choices of firm 1 and firm 2.The market price of laptops in a certain city is determined by P = 1,400 – Q where Q represents the total number of laptops produced. The total cost of producing q laptops is TC = 200q +50,000 for any firm in this market. (e) Suppose both firms are able to collude and equally split monopoly production. What is the profit for each firm?Consider two firms that produce the same good and competesetting quantities. The firms face a linear demand curve given by P(Q) =1 − Q, where the Q is the total quantity offered by the firms. The costfunction for each of the firms is c(qi) = cqi, where 0 < c < 1 and qiis the quantity offered by the firm i = 1, 2. Find the Nash equilibriumoutput choices of the firms, as well as the total output and the price, andcalculate the output and the welfare loss compared to the competitiveoutcome. How would the answer change if the firms compete settingprices? What can we conclude about the relationship between competitionand the number of firms?
- = and TCB (QB): PROBLEM (4) Firm A and Firm B with identical total costs TCA (QA) 4 related goods and competing in prices (Bertrand competition), with demands: QA=510-2PA+ pв and Qв=510 - 2pB+ PA, respectively. = are producing (a) Calculate the Bertrand-Nash equilibrium prices. (b) Calculate the prices they charge when A is the leader and sets its price first, anticipating B's best response and taking it into account (like in Stackelberg competition). (c) Calculate the prices they charge when they collude, in order to maximize sum of their profits.Consider the Cournot competition between two firms with different marginal costs. For firm 1, let the cost function be: C1(q1)-3*q1 For firm 2, let the cost function be: C2(q2)-6*q2 The inverse demand function is: P(Q)=12-Q, where Q=q1+q2 In this game, write down the profit functions for firm 1 and firm 2 (as functions of q1 and q2). Then, find the Nash equilibrium quantities for firm 1 and firm 2. In the NE, which firm produces more: the one with the low or the high marginal cost? Note: To get credit, you need to show your calculations and explain your answer.Two firms are engaged in Cournot (simultaneous quantity) competition. Market-level inverse demand is given by P = 160 − 4Q Firm 1 has constant marginal costs of MC1 = 8, while Firm 2 has constant marginal costs of MC2 = 24. 1) Does there exist a low enough positive marginal cost for firm 1 such that firm 1 acts like a monopoly in this market, if so what is the MC if not why?
- Suppose that two firms produce a particular (homogeneous) product. The inverse demand function for the product is P = 100 -Q. The firms have marginal cost equal to 10. (a) Derive the Cournot Nash equilibrium quantities, and the corresponding price and profits. Show all work. (b) Suppose that the current price is the Cournot price you derived in part (a). Using the hypothetical monopolist test and assuming a 5% threshold for the test, does the good in question represent an antitrust market? Show all work and explain your answer. There are different ways to answer this question and any correct approach will be accepted. (c) Suppose more generally that marginal cost is equal to c. For what values of c will this product represent an antitrust market? Show your work and explain your answer. Maximum size for new files: 400MB FilesConsider 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.Cournot model: linear demand; identical firms. Q(P)=D-P TC(C)=cQ, where D>c a) Suppose that there are 2 firms. They can either choose to produce the Cournot quantity, or choose to produce one half of the monopoly quantity. Write down the 2X2 “payoff matrix” for this game. b) If D= 6 and c = 2, suppose that the game is repeated infinitely often with a discount factor of beta. For what values of beta will it be possible to sustain collusion? c) Now consider the same game with 3 firms. Compute the profits in the static Cournot- Nash equilibrium, and the profits when the 3 firms each produce one third of the monopoly quantity. For what values of beta will it be possible to sustain collusion in this case?
- 1. Two firms (A and B) play a competition game (i.e. Cournot) in which they can choose any Qi from 0 to ¥. The firms have the same cost functions C(Qi) = 10Qi + 0.5Qi2, and thus MCi = 10 + Qi. They face a market demand curve of P = 220 – (QA + QB). Now assume firm A chooses quantity first. Firm B observes this choice and then chooses its own quantity. d)Firm A has MRA = 150 – 4QA/3. What are the equilibrium QA and QB selected in this game? e)What is the equilibrium price, and how much profit does each firm collect?Suppose the total demand for specialty coffee per hour in Ruston is Q = 640 - 80P. There are six (n = 6) monopolistically competitive firms currently in the market selling some variety of specialty coffee, each with total cost curves given by: TC₁ = 20+q; +0.0125q²| a. Find the proportional demand faced by one coffee shop, denoted Firm i. That is, suppose the firms have equal market share and determine the demand function for a single firm. b. Calculate the optimal quantity produced by Firm i. c. Calculate Firm i's profits. Will there be entry or exit by other coffee shops over time? d. Provide a generic graph the long-run outcome for Firm i given your prediction from (c). Label curves, axes, and intersection points.An Australian firm and a US firm produce a homogeneous good that is sold only in Japan. The marginal cost of producing the good is constant and equal to 30 in both countries. The demand curve for the good in Japan is: P = 120-Q where Q = QA +QUS represents the sum of the quantities. produced by the Australian and the US firms, respectively. (b) Assume the Australian firm can commit to an output before the US firm. Solve for the Stackelberg Equilibrium price, sales and profits of each firm in Japan. Price profit AUS2 ,output_US2 profit_US2 output_AUS2