(1) Let us assume that in Region X, there are only 2 hospitals available and that they act as Cournot duopolists. MC₁ MC₂ = 10 Market demand Q = 100-0.5p (a) Compute for the best response functions of each hospital. (b) Compute for the best output level for each. (c) Suppose the 2 hospitals decide to collude, what will be the new output level? Show.
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- Consider any market that has a demand curve given by: Qd = 240 - 2P. Where Qd is the total quantity demanded in the market, given in millions of units and P is the market price, calculated in monetary units. Imagine that there are 2 Cournot oligopolists operating in this market with Cmg = CVme = 15 and fixed monthly costs equal to 1,400. About this market, ask yourself: a) What is the reaction curve of oligopolists? b) What will be the production of each of the companies? c) What is the selling price practiced by oligopolists? d) What is the profit of each of the oligopolists? e) Imagine that one of the companies managed to implement a process innovation capable of halving its Cmg and CVme, so that they would go from 15 to 7.5. This investment implies an additional monthly expense of $1,800. Discuss the statement: "If this situation occurs, the innovative company will not implement variable cost reduction, as the quantity supplied in the market will increase very little; prices will…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.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?
- The Able Manufacturing Company and Better Bettors, Inc. are rival firms in the production of a calculator used by horse racing fans for handicapping (determining betting strategies). Each firm has a fixed cost of $100 and a MC = $10 in producing calculators. The demand for the industry’s product is: Q = 900 – 5P, where P is the market price and Q = Q1 + Q2. If each firm must choose how many calculators to produce and sell without knowing of its rival’s production decision, what will be the Cournot equilibrium price and quantities produced? Calculate the profit for each firm.Exercise 6.6. Consider a duopoly in which companies compete according to Cournot's model. The inverse market demand curve is: P(Q)=100-Q , where Q=Q1+Q2 and the average and marginal costs of firms are constant and equal to 40 Calculate profits would each company make? How much would company 1 be willing to invest to reduce its CM from 40 to 25, assuming company 2 does not support it? Graphically show and comment on all results.The marginal cost of a product is fixed at MC = 20. The demand for the product is Q = 100 - 2P. (a) Now consider a Cournot model with two firms that are choosing quantities simultaneously. What is the best reply (best response) function for each firm? What is theNash equilibrium? What is the total surplus? (b)What do you expect the total surplus would be with three firms? Why? (You do not need to calculate an exact value. You can say ”total surplus is at least 100”, or ”total surplus is at most 80”)
- 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?Exercise 6.5 Suppose there are only two companies (1 and 2) that fix flat tyres in the local market and compete in a duopoly of Cournot. The two companies repair punctures identically, so consumers will not care about repairing the puncture in company 1 or 2. The inverse demand curve for this market is: P=100-2Q, where Q is the total number of punctures repaired per day by the two companies, that is: Q=q1+q2. The marginal cost of repairing a flat tyre for company 1 is 12 euros, while for company 2 it is 20 euros. We will assume that neither company has fixed costs. a) Suppose that this market is a Stackelberg oligopoly and that company 1 is the first to decide how many punctures to repair each day. How many punctures a day will each company repair? What will be the market price of repairing a puncture? How much profit will each company make per day? b) Suppose now that the two firms, instead of competing in quantities, compete on prices according to Bertrand's model. Determine what the…Suppose that two Japanese companies, Hitachi and Toshiba, are the sole producers (i.e., duopolists) of a microprocessor chip used in a number of different brands of personal computers. Assume that total demand for the chips is fixed and that each firm charges the same price for the chips. Each firm’s market share and profits are a function of the magnitude of the promotional campaign used to promote its version of the chip. Also assume that only two strategies are available to each firm: a limited promotional campaign (budget) and an extensive promotional campaign (budget). If the two firms engage in a limited promotional campaign, each firm will earn a quarterly profit of $14 million. If the two firms undertake an extensive promotional campaign, each firm will earn a quarterly profit of $11 million. With this strategy combination, market share and total sales will be the same as for a limited promotional campaign, but promotional costs will be higher and hence profits will be lower.…
- Consider the optimal pricing policy of a monopolist selling information goods. There are three types of consumers, and there is one consumer of each type. The monopolist knows that there arethree types of consumers and the valuations of each type (i.e. the tables below), but cannot tell to which type a consumer belongs (so that personalised pricing is impossible). As the products are information goods, marginal costs are zero, and fixed costs are already sunk. Assume throughout that, when a player is indifferent, she will choose the higher-priced version.The monopolist can offer up to three versions (versions X, Y and Z) of the information good. The three types of consumers have valuations for the different versions as given in the following table: Version x Version Y Version z 1 consumer: 70 120 130 2 consumer: 140 140 200 3 consumer: 170 180 250 (I.e.: If the type 1 consumer is charged a price of 60 for version X and a price of 100 for version Y, the consumer will…Consider the optimal pricing policy of a monopolist selling information goods. There are three types of consumers, and there is one consumer of each type. The monopolist knows that there arethree types of consumers and the valuations of each type (i.e. the tables below), but cannot tell to which type a consumer belongs (so that personalised pricing is impossible). As the products are information goods, marginal costs are zero, and fixed costs are already sunk. Assume throughout that, when a player is indifferent, she will choose the higher-priced bundle. There are three basic goods (products A, B and C), and the monopolist can choose which bundles of goods they want to offer, and the price of these bundles. The three types of consumers have valuations for the different products as given in the following table: (I.e.: If consumers are charged a price of 5 for product A, the type 1 consumer would buy this product as she achieves a surplus of 10 – 5 = 5. If, in addition, the consumers…A decorator, who is a monopolist, makes two types of specialty picture frames. From experience, the decorator has determined that if x frames of the first type and y frames of the second type are made and put on sale in a showroom, they can be sold for (100 - 2x) dollars and (120 - 3y) dollars each, respectively. The total cost of constructing these frames is (12x + 12y + 4xy) dollars. How many frames of each type should be produced to realize the maximum profit. and what is the maximum profit? Make sure to verify that this is indeed a maximum.