Q5 Consider the following statements about the Stackelberggame from the slides, assuming both firms are identical:• (1) Denote by q© the Cournot equilibrium quantityproduced by each firm, and by qºCquantity defined by P(qPC) = c (price equals marginal cost).Let s2 denote a strategy where fırm 2 plays q2 = q° if itobserves q 1 = q°, and plays q2 = qPC otherwise. Let s 1the competitive%3Ddenote a strategy where firm 1 plays q1 = q°. Then, (s1,52)is a Nash equilibrium of the Stackelberg game, but it's nota subgame perfect Nash equilibrium.• (II) The first firm is allowed to change its quantity afterobserving firm 2's quantity chosen at the second stage.• (III) Consumers are worse off in the Stackelberg gamecompared with the Cournot outcome given the sameparameters.Only Il is correctAll options are incorrect.O More than one option is correct.O Only IIl is correctO Only I is correct.

Consider the following statements about the Stackelberg game from the slides, assuming both firms are identical: • (1) Denote by qº the Cournot equilibrium quantity produced by each firm, and by q°C the competitive quantity defined by P(qPC) = c (price equals marginal cost). Let s2 denote a strategy where firm 2 plays q2 = q° if it %3D %3D observes g 1 = gC, and plays gɔ = a 1 = gC. and plays gɔ = gPC otherwise, Let s 1

Consider the following statements about the Stackelberg game from the slides, assuming both firms are identical: • (1) Denote by qº the Cournot equilibrium quantity produced by each firm, and by q°C the competitive quantity defined by P(qPC) = c (price equals marginal cost). Let s2 denote a strategy where firm 2 plays q2 = q° if it %3D %3D observes g 1 = gC, and plays gɔ = a 1 = gC. and plays gɔ = gPC otherwise, Let s 1

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.3P

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Consider the following statements about the Stackelberg game from the slides, assuming both firms are identical: (I) Denote by qC the Cournot equilibrium quantity produced by each firm, and by qPC the competitive quantity defined by P(qPC) = c (price equals marginal cost). Let s2 denote a strategy where firm 2 plays q2 = qC if it observes q 1 = qC, and plays q2 = qPC otherwise. Let s 1 denote a strategy where firm 1 plays q1 = qC. Then, (s1,s2) is a Nash equilibrium of the Stackelberg game, but it’s not a subgame perfect Nash equilibrium. (II) The first firm is allowed to change its quantity after observing firm 2’s quantity chosen at the second stage. (III) Consumers are worse off in the Stackelberg game compared with the Cournot outcome given the same parameters. Group of answer choices: a. Only II is correct b. Only I is correct. c. All options are incorrect. d. Only III is correct e. More than one option is correct.
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Consider 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.
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Two firms - firm 1 and firm 2 - share a market for a specific product. Both have zero marginal cost. They compete in the manner of Bertrand and the market demand for the product is given by: q = 20 − min{p1, p2}. 1. What are the equilibrium prices and profits? 2. Suppose the two firms have signed a collusion contract, that is, they agree to set the same price and share the market equally. What is the price they would set and what would be their profits? For the following parts, suppose the Bertrand game is played for infinitely many times with discount factor for both firms δ ∈ [0, 1). 3. Let both players adopt the following strategy: start with collusion; maintain the collusive price as long as no one has ever deviated before; otherwise set the Bertrand price. What is the minimum value of δ for which this is a SPNE. 4. Suppose the policy maker has imposed a price floor p = 4, that is, neither firm is allowed to set a price below $4. How does your answer to part 3 change? Is it now…
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Two firms compete in selling identical widgets. They choose their output levels Q1 and Q2 simultaneously and face the demand curve P = 30 - Q where Q = Q1 + Q2. Until recently, both firms had zero marginal costs. Recent environmental regulations have increased Firm 2’s marginal cost to $15. Firm 1’s marginal cost remains constant at zero. TRUE-FALSE: Is the following statement true of false? ”As a result, the market price will rise to the monopoly level.” Solve for the Cournot equilibrium and write a convincing explanation of your answer.