Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
expand_more
expand_more
format_list_bulleted
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Q8
Consider the following normal form representation of the standard competition between firm A and
firm B. Each firm can choose either standard A or standard B. Their payoffs are given as follows:
Firm B
A
В
A
Firm A
В
1
1
3
1
(1) (10 points) What's Nash equilibrium (NE) in this game? If there are more than one, find them
all. But there is no NE, state that there is no NE.
(2) (10 points) If you find a NE (or multiple Nash equilibria), is it (or are they) Pareto efficient?
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.
Knowledge Booster
Similar questions
- QUESTION 13 Consider a market where two firms (1 and 2) produce differentiated goods and compete in prices. The demand for firm 1 is given by D₁(P₁, P2) = 140 - 2p1 + P2 and demand for firm 2's product is D2 (P1, P2) 140 - 2p2 + P1 Both firms have a constant marginal cost of 20. What is the Nash equilibrium price of firm 1? (Only give a full number; if necessary, round to the lower integer; no dollar sign.)arrow_forwardPart 2: First Long Question There are two French bakeries in a small town: Le Meilleur Croissant (C), owned by Camille, and Le Meilleur Pain Au Chocolat (P), owned by Paul. In each period of an infinitely repeated game, they compete a la Bertrand, with market demand given by Q(pmin) = 10 - Pmin- Even though they sell identical goods, they have different marginal costs: cc = 2 and %3D Cp = 4 (Paul bakes just as well but is bad at business decisions). There are no fixed costs. Question 6 Turns out that Camille and Paul are married, and so they choose prices to maximize the joint profits of the two firms. Because both love baking and love each other, they also jointly decide that both firms should be selling positive amounts in their optimal plan. What prices do they choose? Pc = 6, pp = 11 Pc = 6.5, pp = 6.5 Pc = 6, pp = 6 Pc = 7, pp = 7 %3D O pc = 6, pp = 7arrow_forward. Using a payoff matrix to determine the equilibrium outcome Suppose there are only two firms that sell tablets: Padmania and Capturesque. The following payoff matrix shows the profit (in millions of dollars) each company will earn, depending on whether it sets a high or low price for its tablets. Capturesque Pricing High Low Padmania Pricing High 9, 9 3, 15 Low 15, 3 7, 7 For example, the lower-left cell shows that if Padmania prices low and Capturesque prices high, Padmania will earn a profit of $15 million, and Capturesque will earn a profit of $3 million. Assume this is a simultaneous game and that Padmania and Capturesque are both profit-maximizing firms. If Padmania prices high, Capturesque will make more profit if it chooses a price, and if Padmania prices low, Capturesque will make more profit if it chooses a price. If Capturesque prices high, Padmania will make more profit if it chooses a price, and if Capturesque prices low, Padmania…arrow_forward
- 2. Consider a Cournot competition environment with one good and two firms, Firm 1 and Firm 2. The (pure) strategy space of Firm 1 is S₁ = [0, 1], and the strategy s₁ of Firm 1 corresponds to the amount of the good they produce. Similarly, the (pure) strategy space of Firm 2 is S2 = [0, 1], and the strategy s2 of Firm 2 corresponds to the amount of the good they produce. If Firm 1 were to produce quantity s₁ and Firm 2 were to produce quantity s2, the prevailing price in the good market would be 1 — 81 — 82, the utility of Firm 1 would be their profit, u₁ (81, 82) = (1-81-82 - c)81, and the utility of Firm 2 would be their profit, u2($1, $2) = (1-81-82-c)s2, where 0 ≤ c< 1 is the marginal cost of production for both firms. (a) Find the pure-strategy Nash equilibria of this game. (b) Are there other Nash equilibria in this game.arrow_forwardIn a given market the demand for a homogenous product is given by p(q) = 120 – 5Q. The market has two firms, firm 1 has a marginal cost cı 5 and firm 2 has a marginal cost c2 = : 10. (i) Assume that the firms compete in a Cournot game. Compute the price in equilibrium, quantity produced by each firm and deadweight loss generated in this market.arrow_forwardAt a busy intersection on Route 309 in Quakertown, Pennsylvania, the convenience store and gasoline station, Wawa, competes with the service and gasoline station, Fred's Sunoco. In the Nash-Bertrand equilibrium with product differentiation competition for gasoline sales, the demand for Wawa's gas is qw=740-400pw + 400ps and the demand for Fred's gas is as = 740-400ps + 400pw. Assume that the marginal cost of each gallon of gasoline is m = $6. The gasoline retailers simultaneously set their prices. What is the Bertrand-Nash equilibrium? The Bertrand-Nash equilibrium is where pw = $ 7.85 and Ps =$7.85. (Enter your responses rounded to two decimal places.) Suppose that for each gallon of gasoline sold, Wawa earns a profit of $1.00 from its sale of salty snacks to its gasoline customers. Fred sells no products that are related to the consumption of his gasoline. What is the Nash equilibrium? The Bertrand-Nash equilibrium is where Pw = $ and Ps = $ (Enter your responses rounded to…arrow_forward
- 1. Two firms (A and B) play a competition game (i.e. Cournot) in which they can choose any Qi from 0 to ¥. The firms have the same cost functions C(Qi) = 10Qi + 0.5Qi2, and thus MCi = 10 + Qi. They face a market demand curve of P = 220 – (QA + QB). Now assume firm A chooses quantity first. Firm B observes this choice and then chooses its own quantity. d)Firm A has MRA = 150 – 4QA/3. What are the equilibrium QA and QB selected in this game? e)What is the equilibrium price, and how much profit does each firm collect?arrow_forward5arrow_forward2. An industry contains two firms that have identical cost functions C(q)=10+2q. The inverse demand function for the market is P=50-2Q where Q is the total industry output. Assuming the firms compete in quantities: Find the firms' best response functions. b. Solve for the Cournot Nash Equilibrium of the game. What is the total industry output in equilibrium? What is the equilibrium price? с. i. If both firms could collude, what would the industry output and price be? Suppose they decide that each firm produces half of the industry output found in part (i). Is this agreement self-enforcing? Explain. ii. a.arrow_forward
- Suppose that Fizzo and Pop Hop are the only two firms that sell orange soda. The following payoff matrix shows the profit (in millions of dollars) each company will earn depending on whether or not it advertises: Рop Hop Advertise Doesn't Advertise Advertise 8, 8 15, 2 Fizzo Doesn't Advertise 2, 15 11, 11 For example, the upper right cell shows that if Fizzo advertises and Pop Hop doesn't advertise, Fizzo will make a profit of $15 million, and Pop Hop will make a profit of $2 million. Assume this is a simultaneous game and that Fizzo and Pop Hop are both profit-maximizing firms. If Fizzo decides to advertise, it will earn a profit of $ million if Pop Hop advertises and a profit of $ million if Pop Hop does not advertise. If Fizzo decides not to advertise, it will earn a profit of $ million if Pop Hop advertises and a profit of $ million if Pop Hop does not advertise. If Pop Hop advertises, Fizzo makes a higher profit if it chooses If Pop Hop doesn't advertise, Fizzo makes a higher…arrow_forwardConsider a Stackelberg duopoly:There are two firms in an industry with demand Q = 1 − Pd.The “leader” chooses a quantity qL to produce. The “follower” observes qL and chooses a quantity qF.Suppose now that the cost function is Ci(qi) = qi2 for i = L, F. (a) Find the subgame perfect equilibrium. (b) Compare the equilibrium you found with the Nash equilibrium if the game was simultaneous (i.e., Cournot competition). Is the Nash equilibrium of the Cournot game also a Nash equilibrium of the sequential game? Why or why not?arrow_forward6arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
