3*. Consider the following 2-firm Bertrand pricing model (firm 1 and 2) with differentiated products. Demand for firm i is qi(Pi, Pj) = 3-Pi + bi.Pj Firms have zero cost of production. The sensitivity of firm i's demand to firm j's price is measured by bį. (a) First suppose b₁ = 1 and b₂ = 1/2. Find the equilibrium prices p₁ and p2. (b) Now let b₂ = 3/2 but b₁ remains the same. How does this change the equilibrium prices b- h. - ho

3*. Consider the following 2-firm Bertrand pricing model (firm 1 and 2) with differentiated products. Demand for firm i is qi(Pi, Pj) = 3-Pi + bi.Pj Firms have zero cost of production. The sensitivity of firm i's demand to firm j's price is measured by bį. (a) First suppose b₁ = 1 and b₂ = 1/2. Find the equilibrium prices p₁ and p2. (b) Now let b₂ = 3/2 but b₁ remains the same. How does this change the equilibrium prices b- h. - ho

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter13: best-practice Tactics: Game Theory

Section: Chapter Questions

Problem 1E

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1.7. In Section 1.2.B, we analyzed the Bertrand duopoly model with differentiated products. The case of homogeneous products yields a stark conclusion. Suppose that the quantity that con- sumers demand from firm i is a – p¡ when pi Pj, Pi pi and (a − p¡)/2 when p¡ = pj. Suppose also that there are no fixed costs and that marginal costs are constant at c, where c < a. Show that if the firms choose prices simultaneously, then the unique Nash equilibrium is that both firms charge the price c.
a) A Dutch Brewing company produces Heineken beer, assume further that the marginal cost of producing a six pack of Heineken Beer is $6. Dutch Brewing company sells Heineken in two different Markets namely Africa and Europe whose inverse demand functions are ?? = 24 − ??and ?? = 12 − 0.5?? respectively.Requireda) Calculate the profit maximising Price-Quantity combinations in these two markets Africa and Europe.b) With this Pricing strategy calculate the profit. c) If competitive output (P=MC=6) for Africa is 18 and Europe is 12, Compute the deadweight losses in the two markets. d) Clearly illustrates that the third degree price discrimination is welfare improving over a single price policy. e) Suppose these markets were no longer separated. How would you construct the market demand in this situation? Would the monopolist’s profit-maximizing single price still be 15?
Gary's Gas and Frank's Fuel are the only two providers of gasoline in their town. Below is the demand schedule for the market of gasoline. Assume that the cost of producing gasoline is 3 per gallon (AC=3, FC-D0). Suppose that the two producers collude (split production and profits evenly), what are the joint profits of these two firms? Q demanded (in gallons) 10 12 4 Market price (in dollar) $22 $20 $18 $16 $14 $12 $10 $8 $6 $0 O $27 O None of these options is correct. $55 O $72 O $36 50 00 3)
DuopolyMarket for mechanical pencils can be described by the following demand schedule:Price | Number of pencils demanded$6 | 80$5 | 200$4 | 320$3 | 440$2 | 560$1 | 680$0 | 800The fixed cost is $340, while the variable cost is $0.50.d) If there were two firms on the market and they agreed to cooperate, how much would eachfirm need to produce? Follow the procedure outlined in the lecture and show that the otherfirm would prefer to deviate from the agreement.e) When the firms deviate from the agreement, there is a new optimal level of output. Showwhether the firms have an incentive to deviate from that level?f) If there were two firms on the market, what would be the price and the quantity of pencilstraded if the firms couldn’t cooperate?
Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to$50 and a fixed cost of $22,500. You are asked to advise the CEO as to what prices andquantities BMW should set for sales in Europe and in the United States to maximize its profits.The demand for BMWs in each market is given by:QE = 8,000 – 80PE and QU = 4,000 – 20 PU,where the subscript E denotes Europe, the subscript U denotes the United States. Assume thatBMW can restrict U.S. sales to authorized BMW dealers only. Support your answersgraphically as well.a. If, by an international agreement between Europe and United States, BMW wereforced to charge the same price in each market, what would be the quantity sold in eachmarket, the equilibrium price, and the company’s profit?b. Suppose now that Europe and United States signed a new trade package under whichBMW now can charge different prices across the two markets. What quantity of BMWsshould the firm sell in each market, and what should the price be…
Gary's Gas and Frank's Fuel are the only two providers of gasoline in their town. Below is the demand schedule for the market of gasoline. Assume that the cost of producing gasoline is zero per gallon (AC-D0, FC-0). Suppose that the two producers collude (split production and profits evenly), what are the profits of each firm? Q demanded (in gallons) 4 6 7 8. 10 Market price (in dollar) $22 $20 $18 $16 $14 $12 $10 $8 $6 $0 $70 $72 O $36 O $76 $64 3. 2. 1,
Q5) Distinguish between marginal pricing and cost-plus pricing.
A botanical garden estimates a demand for visits per month as Q = 16 - 2P, where P is the entry fee per visit and Q is monthly visits in 1,000s. There is constant marginal cost of admitting another person to the botanical garden as MC = 2. Mangers currently charge price of P = 5 to enter, resulting in Q = 6 visits (i.e., 6,000 visits per month). The managers are considering a new pricing strategy where they require visitors to pay a flat fee to join a membership to the gardens but then lower the price per visit. a. What price should be charged per visit to the botanical gardens? b. How visits are there at this price? c. What is the maximum amount that visitors would be willing to pay for memberships? Explain.
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 profit of each of the oligopolists? b) 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 remain very close to what they are today and its profits will not increase"
5. Consider a market where there are two mers with inverse demand func- consu tions p(q1) = 10 -91 and p(q2) = 5-92. (a) Suppose there is a single firm with inverse supply function p(q) = }q. Find the competitive equilibrium. (b) Find the elasticity of demand and supply at the equilibrium. (c) Suppose instead that there are three firms with the identical inverse sup- ply function given in part (a). Find the competitive equilibrium.
Microsoft is the market leader in office software with its MSOffice. Its marginal cost of production c is 1 dollar per unit. Home users demand 40 million licenses and are willing to pay 50 dollars, whereas businesses demand 60 million licenses and are willing to pay 100 dollars. Microsoft also produces a home version of MS Office at a marginal cost of c'=2. Home users and businesses are willing to pay 60 and 40 dollars, respectively, for the home version. Which is the best pricing strategy for Microsoft? O Selling MSOffice Professional at 100 Selling MSOffice Home at 40 Selling MSOffice Professional units at 100 and MSOffice Home units at 40 Selling MSOffice Professional at 80 dollars and MSOffice Home at 40 dollars
10. The platypus is a shy and secretive animal that does not breed well in captivity. But two breeders, Sydney and Adelaide, have discovered the secret to platypus fer- tility and have effectively cornered the market. Zoos across the globe come to them to purchase their output; the world inverse demand for baby platypuses is given avby P=1,000-20, where Q is the combined output of blu Sydney (qs) and Adelaide (qA). vide a. Sydney wishes to produce the profit-maximizing quantity of baby platypus. Given Adelaide's choice of output, 9A, write an equation for the residual demand faced by Sydney. 19125 non c. ab. Derive Sydney's residual marginal revenue curve. Assume that the marginal and average total cost of raising a baby platypus to an age at which it can be sold is $200. Derive Sydney's reaction function. d. Repeat steps (a), (b), and (c) to find Adelaide's reac- tion function to Sydney's output choice. 18 e. Substitute Sydney's reaction function into Adelaide's to solve for…