Consider a Bertrand game between two firms. The demand for firm 1's product is given by q1 = 100-3p1 + 2p2. The demand for firm 2's product is given by q2 = 100 - 3p2 + 2p1. In terms of notation, pi is the price of firm 1's product and pa is the price of firm 2's product. The two firms choose their prices simultaneously. For your calculations below, assume zero costs and that prices are measured in dollars per unit. as Find the equilibrium prices. b Derive the firms' best-response functions and explain whether the prices are strategic substitutes or complements in this game.

Consider a Bertrand game between two firms. The demand for firm 1's product is given by q1 = 100-3p1 + 2p2. The demand for firm 2's product is given by q2 = 100 - 3p2 + 2p1. In terms of notation, pi is the price of firm 1's product and pa is the price of firm 2's product. The two firms choose their prices simultaneously. For your calculations below, assume zero costs and that prices are measured in dollars per unit. as Find the equilibrium prices. b Derive the firms' best-response functions and explain whether the prices are strategic substitutes or complements in this game.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Two countries produce oil. The per unit production cost of Country 1 is C1 = $2 and of country 2 it is C2 = $4. The total demand for oil is Q = 40-p where p is the market price of a unit of oil. Each country can only produce either 5 units, 10 units or 15 units. The total production of the two countries in a Nash equilibrium is 10 15 20 25 30
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 parts
Q3 Consider the following three-player normal form game (Player 3 is the page player): Player 3 A в Player 2 Player 2 A в A B 1,2, 3 в 2,3,1 Player 1 A Player 1 A 2, 1, 3 3, 2, 1 3, 2, 1 1,2, 3 в 1,3, 2 3, 1,2 For each player, strategies are A and B. a) Find the pure strategy Nash equilibrium of the above game. Assume now that the above game is played sequentially, with Player 3 moving first, Player 1 moving second, and Player 2 moving third. b) Write down the game tree. c) For each player, list all the available pure strategies. d) Find the subgame perfect equilibrium outcome and compare it with the equilibrium outcome you found in subquestion a). Comment.
Consider the following static game with two firms as the players. Each firm must decide either to upgrade (U) an existing good to a new version; or not upgrade it (N). The decisions are simultaneous. If a firm chooses to upgrade, they have to pay a fixed cost of 7. If they don’t upgrade, there is no fixed cost. The marginal cost is always equal to 3. The demand side of the market is as follows: If neither firm upgrades, each firm sells 2 units at price 4. If both firms upgrade, each firm sells 3 units at price 5. If only one firm upgrades, the one who upgrades sells 5 units at price 5, and the other firm does not sell anything.
The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has a cost of production of C1= 15*Q1 and firm 2 has a cost of production of C2=20*Q2 a) Suppose that firm play a Stackelberg game. First firm 1 sets the quantity in t=1, then, knowing which quantityfirm 1 has set, firm 2 chooses the quantity in t=2. What are the Stackelberg quantities and prices? What arethe profits od firm 1 and 2? Compared to part a) which firm benefits and which firm loses?
Firm 1 and firm 2 compete with each other by choosing quantities. The market demand is given by P(Q) = ( 300 − Q, if Q < 300) (0, otherwise), where Q = q1 + q2. Firm 1 has a cost function C1(q1) = 40q1, and firm 2 has a cost function C2(q2) = 50q2. Answer the following questions. 1. Assume the game lasts only one period. Compute the equilibrium price, quantities and profits for both firms. 2. If firm 1 becomes the monopolist on this market, what quantities will firm 1 choose to produce? Denote this quantity as QM. 3. One possible strategy is that each firm produces QM 2 . Would the resulting outcome be better for both firms (Pareto improvement)? Explain why this is not the equilibrium in the one period game. 4. Assume this game is infinitely repeated and the interest rate in this economy is r. For what values of r the strategy in (3) is sustainable by using a “Grim Trigger” strategy?
Four firms (A, B, C, and D) play a pricing game (i.e. Bertrand). Each firm (i) may choose any price P; in [0, infinity) with the goal of maximizing its own profit. (Firms do not care directly about their own quantity or others' profits.) Firms A and B have MC = 10, while firms C and D have MC = 20. The firms serve a market with the demand curve Q = 100 - P. All firms produce exactly the same product, so consumers purchase only from the firm with the lowest price. If multiple firms have the same low price, consumers divide their prices evenly among the low-priced firms. If firms choose price simultaneously: A) a price firm A would choose in equilibrium: a price firm B would choose in equilibrium: B) a price firm C would choose in equilibrium: C) a price firm D would choose in equilibrium:
5) Consider the following sequential move game: M 2,1 1,3 1,3 3,0 2,3 4,1 a) If z=0, find any subgame perfect NE. b) For what values of z will M occur in the subgame perfect equilibrium?
Two firms produce and sell differentiated products that are substitutes for each other. Their demand curves are Firm 1: Q₁ = 40-3P₁+ P2 1 Firm 2: Q₂ = 40 -3P 2+P1 Both firms have constant marginal costs of $4.70 per unit. Both firms set their own price and take their competitor's price as fixed. Use the Nash equilibrium concept to determine the equilibrium set of prices. Since the firms are identical, they will set the same prices and produce the same quantities. In equilibrium, each firm will charge a price of $ and produce units of output. (Enter your responses rounded to two decimal places.) Each firm will earn a profit of $ (Enter your response rounded to two decimal places.)
Suppose that there are two firms operating in the market of laptops, the first firm supplies quantity qi and the second firm supplies q2. The inverse demand function for laptops is P(q1 +q2)=2,000-2(q₁ +q2). The marginal costs are constant and equal to $400. a. b. c. Find the Cournot equilibrium outputs and price. Find the Bertrand equilibrium outputs and price. Suppose that the first firm is the leader choosing the output first, and the second firm is the follower choosing the output after observing the firm firm's choice. Find the new equilibrium output and price and compare them with those in parts a and b. Which of the equilibria is socially preferable?
You work for a marketing firm that has just landed a contract with Run-of-the-Mills to help them promote three of their products: splishy splashers, raskels, and kipples. All of these products have been on the market for some time, but, to entice better sales, Run-of-the-Mills wants to try a new advertisement that will market two of the products that consumers will likely consume together. As a former economics student, you know that complements are typically consumed together while substitutes can take the place of other goods. Run-of-the-Mills provides your marketing firm with the following data: When the price of splishy splashers decreases by 8%, the quantity of raskels sold increases by 6% and the quantity of kipples sold decreases by 8%. Your job is to use the cross-price elasticity between splishy splashers and the other goods to determine which goods your marketing firm should advertise together. Complete the first column of the following table by computing the cross-price…
Consider the Bertrand pricing game from class. If both firms have identical marginal cost of $10 and consumers will purchase from whichever firm is cheapest as long as the price is under $50, what will be the Nash equilibrium?. a 50, 50 b 50, 10 c 10, 10 d 10, 50