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Let the market demand for carbonated water be given by Q = 100 - 5P. Let there be two
firms producing carbonated water, each with a constant marginal cost of 2. If both firms
choose their prices simultaneously, what price would each of them charge in the Nash
equilibrium?
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- 1.7. In Section 1.2.B, we analyzed the Bertrand duopoly model with differentiated products. The case of homogeneous productsConsider 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.What is the homogeneous-good dupopoly's Nash-Cournot equilibrium if the market demand function is Q = 300 - 1200p, and each firm's marginal cost is $0.22 per unit?
- 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 compete10Two 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.)
- Two firms Intel and AMD in the CPU market have combined demand given by Q = 100 - P. Their total costs are given by TC Intel = 4 Q Intel + 2 Q Intel^2 and TC AMD = 4 Q AMD + 2 Q AMD^2. If they successfully collude, the market price will be??Jane and Sara are competing orange juice salespersons in Amherst. Their stands are next to each other on a street and consumers regard them as identical. The marginal cost of an orange juice is $1. The demand for orange juice every hour is Q = 20 − P where P is the lowest price between the two salespersons. If their prices are equal they split demand equally. a. If they set prices simultaneously (prices can be any real number), what is the Nash equilibrium price? b. If, against what we have assumed in class, orange juice salespersons have to charge prices in whole dollars ($1, $2, $3, etc), what are the Nash equilibrium prices? c. Assuming whole dollar pricing, if Jane sets her price before Sara, what price would she charge? Answer all 3 partsSuppose a town only has two petrol stations, United and BP. Each could choose to charge a high price or low price, as shown in the matrix below. ВР BP charges a low price: BP has low profit; United BP charges a high price: BP has no profit; United has high profit United charges a United low price: has low profit ВР United charges a high price: has BP has average profit; United high profit; United has no has average profit profit (a) What is the dominant strategy for the above matrix (i.e., a Nash equilibrium)? Explain briefly (b) If the two petrol stations could collude, what would be the likely strategy? Explain briefly. (c) Briefly explain the principles of the 'kinked' demand curve by using an example such as pricing a product by the two supermarket giants.
- Suppose we have two identical fırms A and B, selling identical products. They are the only firms in the market and compete by choosing quantities at the same time. The Market demand curve is given by P=390-Q. The only cost is a constant marginal cost of $14. Suppose Firm A produces a quantity of 57 and Firm B produces a quantity of 44. If Firm A decides to increase its quantity by 1 unit while Firm B continues to produce the same 44 units, what is the Marginal Revenue for Firm A from this extra unit? Enter a number only, no $ sign. Don't forget to include the negative sign if revenue decreases. 2311. 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.(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