PROBLEM (3) Consider the differentiated goods Bertrand price competition model where firms A and B produce similar goods and sell them at på and pв. The demand for each firm's product is given by qA = 400 - 3pA - 2 pв and qв = 400 - 3p³ - 2pA, and MCA(qA) = ATCA(q) = 40 and MCB(qB) = ATCB(qB) = 40. (a) Are the two goods substitutes or complements? Do the firms want to charge higher prices or lower prices, the higher the opponent's price? (Is the best response price increasing (or decreasing, or neither) in the opponent's price?) Calculate the Bertrand equilibrium prices. (b) Now suppose the firms -instead of competing to maximize their own individual profits- decide to "collude" and charge prices to maximize their joint profits (sum of their profits). What would be each firm's optimal price? Are these prices greater/smaller/the same compared to the prices in (a)?

PROBLEM (3) Consider the differentiated goods Bertrand price competition model where firms A and B produce similar goods and sell them at på and pв. The demand for each firm's product is given by qA = 400 - 3pA - 2 pв and qв = 400 - 3p³ - 2pA, and MCA(qA) = ATCA(q) = 40 and MCB(qB) = ATCB(qB) = 40. (a) Are the two goods substitutes or complements? Do the firms want to charge higher prices or lower prices, the higher the opponent's price? (Is the best response price increasing (or decreasing, or neither) in the opponent's price?) Calculate the Bertrand equilibrium prices. (b) Now suppose the firms -instead of competing to maximize their own individual profits- decide to "collude" and charge prices to maximize their joint profits (sum of their profits). What would be each firm's optimal price? Are these prices greater/smaller/the same compared to the prices in (a)?

Survey Of Economics

10th Edition

ISBN:9781337111522

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter9: Monopolistic Competition And Oligoply

Section: Chapter Questions

Problem 18SQ

See similar textbooks

Similar questions

Consider the following Bertrand model setup with differentiated products. There are two firms. q denotes quantity and p denotes price.Firm 1 Demand: q1 = 90-2p1+p2Firm 2 Demand: q2 = 90-2p2+2p1Marginal cost is constant and equal to 1 for each firm. (MC=1)Calculate optimal prices of both firms. Show your calculations.
Please include step by step working and derivation of any methods used in the following questions: 1. a) Consider a homogeneous goods industry where two firms operate and the linear demand is given by p(y1 + y2) = a - b(y1 + y2 ), where p is the market price, and y1 (y2) is the output produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the best responses (reaction curve) for firm 1 and firm 2. Explain the term best response (reaction curve). Illustrate the best responses in a diagram. b) For the case in (a) determine the Cournot equilibrium (Nash equilibrium in quantities) when firm 1 and firm 2 compete simultaneously in quantities. How large are firm 1’s and firm 2’s profits? What is the industry output? c) Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantity demanded and p is the market price. Firm 1 is the leader and has a cost function c1(y1)=cy1 while firm 2 is the follower with a cost function c2(y2 )=. Firm 1 sets its…
PROBLEM (5) (In a market with demand Q = 780 - p, there are 3 identical firms, A, B and C; each with a total cost function TC(Q) = 3(Q)^2. Calculate the market price under each of the 2 scenarios below, (i) B and C jointly form the fringe supply and A is the dominant firm in the dominant firm model. ( ii) They act as perfectly competitive firms -as if trying to maximize total surplus and minimize DWL- that is, their joint MC serves as the “market supply” for the competitive market. Please answer all the parts!
The smartphone market has been dominated by Apple, but recently the Droid has been able to leverage Google's information services into market gains, while Blackberry, known for its secure business-oriented network, has attempted to become more attractive with a “friendlier” interface. At the same time, a number of less capable fringe firms are emerging. Suppose an economist analyzes this industry as follows: ECONOMIST: The market had been a near Apple monopoly. Profits of this monopoly attracted entry by Droid- and Blackberry-based phones, increasing rivalry between firms in the industry. The emergence of smaller fringe firms suggests that entry barriers have fallen substantially, so competition has or will soon become fiercer. True or False: This analysis is consistent with the industrial organization (IO) view.
There are two firms selling differentiated products. Firm A faces the following demand for his product: QA=20-1/2PA+1/4PB Firm B faces the following demand: QB=220-1/2PB+1/4PA PA represents the price set by firm A. PB represents the price set by firm B.Assume that the marginal cost is zero both for firm A and firm B.What are the equilibrium prices of a simultaneous price competition?What would the equilibrium prices be if A is the leader and B is the follower?
Suppose two brothers own identical skydiving companies but have decided to experiment with different pricing structures. The older brother’s company, Air Adventures, charges everyone the same price, while the younger brother’s company, Sky Warriors, sets its prices using a twotiered, price-discrimination model. Assuming that both companies face the same market demand curves, marginal costs, and costs of production, and wield significant market power for their service area, which of the following is most likely to occur? a. Air Adventures will generate a similar net revenue to Sky Warriors. b. Sky Warriors will generate a higher net revenue than Air Adventures. c. Sky Warriors will generate a lower net revenue than Air Adventures. d. Air Adventures will generate a higher net revenue than Sky Warriors. e. Sky Warriors will eventually switch to the Air Adventures model.
Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market demand Q = 400−P, so the inverse demand is P = 400 − Q. Suppose both firms have a constant marginal cost equal to $100 per unit of output and a fixed cost equal to $10,000. Suppose that the firms compete by simultaneously setting price, not simultaneously setting output. That is, suppose we consider the Bertrand model instead of the Cournot. Show that the two firms must earn lower profits. Hint: Create a two-by-two game using two different prices for each firm. One price should be the Cournot price (the Cournot is price of the good when firms produce the Cournot output you found above, which is 100 and 100, so the price is P = 400 − 100 − 100 = 200). The second price should be under 200 and over 150. Then show that the Nash equilibrium of this game is the lower of the two prices. When calculating profits, assume that each firm has equal sales (one half of demand) if they charge…
Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…
Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…
PROBLEM (5) (In a market with demand Q = 780 - p, there are 3 identical firms, A, B and C; each with a total cost function TC(Q) = 3(Q)^2. Calculating the market price under each of the 2 scenarios below, rank/order the Consumer Surplus in each scenario (don’t calculate each CS; just rank them); (i) B and C jointly form the fringe supply and A is the dominant firm in the dominant firm model. (ii) They act as perfectly competitive firms -as if trying to maximize total surplus and minimize DWL- that is, their joint MC serves as the “market supply” for the competitive market. Please answer all the parts!
A homogeneous product duopoly faces a market demand function given by p = 300 - 3Q,where Q = q1 + q2. Both firms have constant marginal cost MC = 100. What is the Bertrand equilibrium price and quantity in this market?
Three firms sell identical products in a market with inverse demand given by P(Q) = 590 - 4Q, where Q = q1 + q2 + q3, i.e., the sum of all quantities produced by all three firms. Each firm has a constant marginal cost of production MC = 18 and no fixed cost. Firm 1 chooses q1 first. Firms 2 and 3 simultaneously choose q2 and q3 after observing q1. Calculate the subgame perfect equilibrium profit of firm 2.