1. 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.

1. 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.

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

Evaluate the following statement: “Predatory pricing in a market is a Nashequilibrium strategy whether or not the incumbent has an advantage; hence, it canwork in practice”. Include diagrams to aid you in your analysis when appropriate.
The following is a static game: Convert this game into dynamic form game. Find the Nash equilibrium and subgame perfect Nash equilibrium of this game. If you consider this game as dynamic then what kind of dynamic game is this.
Define a dominant strategy and Nash equilibrium. Can two firms interacting with each other have no Nash equilibria if both have a dominant strategy?
Question 2. Entry Game. Consider the following entry game: There are two periods: Firm I is in the market for both periods, and Firm E decides to enter or not in the second period. Market demand is P 140 - Q. Each firm has fixed costs of $1200 and marginal cost MC $20. Suppose in period 1, I has two strategies: set the price at Pm $80 (monopoly price), or at P₁ $40 (limit price). After seeing the price set by I in the first period, E decides to enter the market or not (In or Out). If E chooses Out, then I selects Pm in the second period. If E chooses In, then I as a price leader can decide whether the market price is P₁ or Pc 60 (Cournot price), and demand is shared equally between the two firms. Draw a game tree and find the SPNE of the game. = = = = =
Part 3,4, and 5
**Practice** Consider a market with three firms. Each firm has a different cost function. We assume C1(q1) = 7q1, C2(q2) = q2 + 1, and C3(q3) = 3q3.
Assume a simultaneous-move game. Firm B Low Price High Price Firm A Low Price 10,10 100,2 High Price 2,100 90, 90 What is the Nash equilibrium of the game?
Two firms with differentiated products are competing in price. Firm A and B face thefollowing demand curves: Q_A = 70 − 2P_A + P_B and Q_B = 120 − 2P_B + P_Arespectively. Assume production is costless.a. Give equations for and graph each firm’s reaction curve.b. If both firms set their prices at the same time, what is the Nash equilibriumprice, quantity, and profit for each firm?c. Suppose A sets its price first and then B responds. What price and quantitydoes each firm set now? Is it advantageous to move first?d. Compare the profits from part b and c. Which firm benefits more from thesequential price choosing? (Please do b-d, thanks :))
Suppose that Toyota and GM are considering entering a market for electric cars and that their profits from entering or not entering the market are given in the table below. (a) Does GM have a dominant strategy? If so, what is it? (b) Does Toyota have a dominant strategy? If so, what is it? (c) What is the Nash Equilibrium? (d) Is there any incentive for the two firms to have a collusive outcome different from the Nash equilibrium? Please explain.
Question 1 An industry consists of two firms. The demand function for the product of firm i is q = 24 - 5p; + 2pj. The marginal cost of production for each firm is zero. Find the Nash equilibrium in prices if the game is non-repeated and firms choose their prices simultaneously.
2 firms are engaged in Cournot competition; firm A faces the cost curveCA(yA)=40yAand firm Bfaces the cost curveCB(yB)=40yB. The inverse market demand curve isP(y)=100y, whereyrepresents market level of output. a)Define the Cournot game. b)In 1 or 2 sentences explain why a firm has no incentive to deviate from the Cournot Nash equilibrium(holding their opponent’s strategy constant). c)Find the Cournot Nash Equilibrium. d)Now suppose instead of playing their strategies at the same time, firm A moves first and then firm B moves second(sequentialgame).Does firm A earn higher profits in this game or the game in part c)?
X Y (ZERO-SUM GAME) Consider the game x [1 aj. What are the values of a that will make: Y a. (X,X) a Nash equilibrium (NE)? b. (X,Y) a Nash equilibrium (NE)? c. If a=-1, set-up the linear programming models that will solve the mixed Nash equilibria of the given game.