Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
expand_more
expand_more
format_list_bulleted
Question
Chapter 15, Problem 15.12P
a
To determine
To find:
The Nash equilibrium.
b)
To determine
To find:
Nash equilibrium of firm 1 and 2.
c)
To determine
To find:
Bayesian Nash equilibrium.
d)
To determine
To find:
Type of firm’s which gain from incomplete information and complete information and whether firm 2 earn more profit on an average.
e)
To determine
To find:
Seperating equilibrium and whether thr loss to the low type from trying to pool in the first period exceeds the second period gain from having convinced firm 2 that it is the high type.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Consider the following Cournot model. • The inverse demand function is given by p = 30 –Q, where Q = q1 + q2. • Firm 1’s marginal cost is $6 (c1 = 6). Firm 2 uses a new technology so that its marginal cost is $3 (c2 = 3). There is no fixed cost. • The two firms choose their quantities simultaneously and compete only once. (So it’s a one-shot simultaneous game.)
d. Suppose there is a market for the technology used by Firm 2. What is the highest price that Firm 1 is willing to pay for this new technology?
e. Now let’s change the setup from Cournot competition to Bertrand competition, while maintaining all other assumptions. What is the equilibrium price?
f. Suppose the two firms engage in Bertrand competition. What is the highest price that Firm 1 is willing to pay for the new technology?
Assuming there are two companies selling personal computers,Company Jackfruit Computers and Company Mangoes Computer. They both have an inventory of personal computers that they would like to sell before a new generation of faster, cheaper machines is introduced. The question facing each competitor is whether or not they should widely advertise a “close out” sale on these discontinued items, or instead let excess inventory work itself off over the next few months. The net revenue to each firm in millions of $, is depicted in the payoff matrixbelow:
Mangoes
Jackfruit
Advertise
Don’t advertise
Advertise
M: $5
J: $5
M: $2
J: $20
Don’t advertise
M: $20
J: $2
M: $10
J: $10
1. Determine the dominant strategy for each firm
2. Would collusion work in this case? Explain.
OLIGOPOLY 1.- Each of two firms, firms 1 and 2, has a cost function C(q) = 30q; the inverse demand function for the firms' output is p = 120-Q, where Q is the total output. Firms simultaneously choose their output and the market price is that at which demand exactly absorbs the total output (Cournot model).(a) Obtain the reaction function of a firm.(b) Map the function obtained in (a), and graphically represent the Cournot equilibrium in this market.(c) Repeat (b), this time analytically.(d) Now suppose that firm 1's cost function is C(q) = 45q instead, but firm 2's cost is unchanged. Analyze the new solution in the market.(e) Obtain the total surplus, consumer surplus, and industry profits in both cases, and compare. What is the effect of the worsening in firm 1's cost?
Knowledge Booster
Similar questions
- Burger Doodle, the incumbent firm, wishes to set a limit price of $8 (rather than the profit-maximizing price of $12) to prevent Designer Burger from entering its profitable market. The game tree above shows the payoffs for various decisions. Burger Doodle makes its pricing decision, then Designer Burger decides whether to enter or stay out of the market. If Designer Burger chooses to enter the market, then Burger Doodle may or may not decide to accommodate Designer’s entry by changing its initial price to the Nash equilibrium price of $10. If Burger Doodle canNOT make a credible commitment to maintain its initial price should Designer Burger decide to enter the market, then Burger Doodle will set price equal to $________ at decision node 1 and the outcome _____________(is, is not) a Nash equilibrium.arrow_forwardWhich of the following is FALSE for the grim trigger strategy and the infinite horizon repeated Prisoner's Dilemma game illustrated above? A. In the grim trigger strategy profile, if a player chooses D in a period, then both players chooses D forever after that period B. The threshold discount factor for sustaining cooperation under grim trigger strategy depends on the utility numbers in the stage game C. If all utility numbers remain the same but 3 is replaced by 5 in the stage game, then cooperation CANNOT be sustained in this game for all possible values of the discount factor.arrow_forwardTwo firms compete in prices in a market for a homogeneous product. In this market there are N > 0 consumers; each buys one unit if the price of the product does not exceed $10, and nothing otherwise. Consumers buy from the firm selling at a lower price. In case both firms charge the same price, assume that N/2 consumers buy from each firm. Assume zero production cost for both firms. Suppose that the firms set prices simultaneously in a game that is repeated infinitely. Let denote the time- discount parameter. Propose trigger price strategies for both firms yielding the collusive prices of ($10, $10) each period. Calculate the minimal value of that would enforce the trigger price strategies you proposed.arrow_forward
- Consider the following Cournot model. The inverse demand function is given by p = 30 –Q, where Q = q1 + q2. Firm 1’s marginal cost is $6 (c1 = 6). Firm 2 uses a new technology so that its marginal cost is $3 (c2 = 3). There is no fixed cost. The two firms choose their quantities simultaneously and compete only once. (So it’s a one-shot simultaneous game.) Answer the following questions. Derive Firm 1 and Firm 2’s reaction functions, respectively. Solve the Nash equilibrium (q1N, q2N). What is the equilibrium price and what is the profitl evel for each firm? Suppose there is a market for the technology used by Firm 2. What is the highest price that Firm 1 is willing to pay for this new technology? Now let’s change the setup from Cournot competition to Bertrand competition, while maintaining all other assumptions. What is the equilibrium price? Suppose the two firms engage in Bertrand competition. What is the highest price that Firm 1 is willing to pay for the new…arrow_forwardSeveral firms collude in an oligopoly where the Industry Supply is given by QS = 6 - 5P and Industry Demand is given by, QD = 5P – 5. If the probability that this collusion will continue is given by (1/P*), what is the minimum number of firms required to break the tacit collusion?arrow_forwardQ2.1 In the second round with two buyers remaining, the probability that a buyer with valuation v wins is vN-1, where N is the number of buyers in the first round. Use the revenue equivalence theorem to derive the symmetric equilibrium bidding function b(v) for the buyers in stage two. Show your work. Q2.2 At the end of the auction what is the value of the actual (not expected) revenue that the seller receives? Round your answer to at least three decimal spaces.arrow_forward
- Consider a duopolistic market in which the two identical firms compete by selecting their quantities. The inverse market demand is P(Q) = 210−Q and each firm has a marginal cost of $15 per unit. Assume that fixed costs are negligible for both firms. Cournot Model Determine the Nash-Cournot equilibrium for this market.(Enter your responses rounded to two decimal places.) Firm 1's quantity: q1= ? units. Firm 2's quantity: q2 = ? units. Market price: P= ? Stackelberg Model Determine the Nash-Stackelberg equilibrium for this market, assuming that Firm 1 is the Stackelberg leader. (Enter your responses rounded to two decimal places.) Firm 1's quantity: q1 = ? units Firm 2s quantity: q2 = ? units. Market price: P = ?arrow_forward10) Consider a repeated game in which the following one-shot game between two players is repeated "infinitely." Denote by "d" the discount factor. (Assume both players have the same discount factor.) Player 2 Cooperate Defect Player 1 Cooperate 5, 4 0, 5 Defect 6, 0 1, 1 The two players try to support cooperation by using "grim trigger strategy" as discussed in class. Answer YES or NO to each of the following three questions. (a) Can they support cooperation if the common discount factor, d, is equal to 0.23? (b) Can they support cooperation if the common discount factor, d, is equal to 0.4? (c) Can they support cooperation if the common discount factor, d, is equal to 0.15?arrow_forwardCournot model: linear demand; identical firms. Q(P)=D-P TC(C)=cQ, where D>c a) Suppose that there are 2 firms. They can either choose to produce the Cournot quantity, or choose to produce one half of the monopoly quantity. Write down the 2X2 “payoff matrix” for this game. b) If D= 6 and c = 2, suppose that the game is repeated infinitely often with a discount factor of beta. For what values of beta will it be possible to sustain collusion? c) Now consider the same game with 3 firms. Compute the profits in the static Cournot- Nash equilibrium, and the profits when the 3 firms each produce one third of the monopoly quantity. For what values of beta will it be possible to sustain collusion in this case?arrow_forward
- Consider the following Cournot model. The inverse demand function is given by p = 30 –Q, where Q = q1 + q2. Firm 1’s marginal cost is $6 (c1 = 6). Firm 2 uses a new technology so that its marginal cost is $3 (c2 = 3). There is no fixed cost. The two firms choose their quantities simultaneously and compete only once. (So it’s a one-shot simultaneous game.) Answer the following questions. (4points)DeriveFirm1andFirm2’sreactionfunctions, respectively. (2 points) Solve the Nash equilibrium (q1N, q2N). (2points)Whatistheequilibriumpriceandwhatistheprofitlevel for each firm? (3 points) Suppose there is a market for the technology used by Firm 2. What is the highest price that Firm 1 is willing to pay for this new technology? (3points)Nowlet’schangethesetupfromCournotcompetitionto Bertrand competition, while maintaining all other assumptions. What is the equilibrium price? (3 points) Suppose the two firms engage in Bertrand competition. What is the highest price that…arrow_forwardConsider a Duopoly model, in which two firms decide a quantity sequentially. For the convenience, let's say Firm 1 is a dominant firm and Firm 2 is a follower. The market demand is given by P=110 - 5Q, where Q is the total output (i.e., Q=Q1+Q2). Each firm has an identical cost function, TCi=7Qi, i=1, 2. Each firm maximizes its profit by choosing the quantity. In this Stackelberg equilibrium, Firm 1 will sell __________ units.arrow_forwardConsider a Duopoly model, in which two firms decide a quantity sequentially. For the convenience, let's say Firm 1 is a dominant firm and Firm 2 is a follower. The market demand is given by P=110 - 5Q, where Q is the total output (i.e., Q=Q1+Q2). Each firm has an identical cost function, TCi=7Qi, i=1, 2. Each firm maximizes its profit by choosing the quantity. In this Stackelberg equilibrium, Firm 1 will sell how many units.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Managerial Economics: Applications, Strategies an...EconomicsISBN:9781305506381Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. HarrisPublisher:Cengage Learning
Managerial Economics: Applications, Strategies an...
Economics
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:Cengage Learning