Two manufacturers, denoted 1 and 2, are competing for 100 identical customers. Each manufacturer chooses both the price and quality of its product, where each variable can take any nonnegative real number. Let pi and xi denote, respectively, the price and quality of manufacturer i’s product. The cost to manufacturer i of producing for one customer is 10 + 5xi. Note in this expression that the cost is higher when the quality is higher. If manufacturer i sells to qi customers, then its total cost is qi(10 + 5xi). Each customer buys from the manufacturer who offers the greatest value, where the value of buying from manufacturer i is 1,000 + xi - pi; higher quality and lower price mean more value. A manufacturer’s payoff is its profit, which equals qi(pi - 10 - 5xi). If one manufacturer offers higher value, then all 100 customers buy from it. If both manufacturers offer the same value, then 50 customers buy from manufacturer 1 and the other 50 from manufacturer 2. Find all symmetric Nash equilibria.

Two manufacturers, denoted 1 and 2, are competing for 100 identical customers. Each manufacturer chooses both the price and quality of its product, where each variable can take any nonnegative real number. Let pi and xi denote, respectively, the price and quality of manufacturer i’s product. The cost to manufacturer i of producing for one customer is 10 + 5xi. Note in this expression that the cost is higher when the quality is higher. If manufacturer i sells to qi customers, then its total cost is qi(10 + 5xi). Each customer buys from the manufacturer who offers the greatest value, where the value of buying from manufacturer i is 1,000 + xi - pi; higher quality and lower price mean more value. A manufacturer’s payoff is its profit, which equals qi(pi - 10 - 5xi). If one manufacturer offers higher value, then all 100 customers buy from it. If both manufacturers offer the same value, then 50 customers buy from manufacturer 1 and the other 50 from manufacturer 2. Find all symmetric Nash equilibria.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.8P

See similar textbooks

Similar questions

Given that If Alfonso's marginal cost is $6, their best-response function is, Pa=(Pb+30)/2 and If Bernice’s marginal cost is $12, their best-response function is, Pb=(Pa+36)/2, Find the equilibrium prices for the case in which Alfonso's marginal cost is $6 and Bernice's marginal cost is $12.
Two 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.
Consider a rent-seeking game with N ≥ 2 contestants. The effort for person i is denoted by xi for i = 1; ... ; N. The cost per unit of effort is C. All contestants are identical. They value the rent at V and each contestant can win the prize with a probability equal to their effort relative to the total effort of all contestants. Thus the payoff function of person i exerting effort xi is given by Exercise 11.10 Three firms have applied for the franchise to operate the cable TV system during the coming year. The annual cost of operating the system is $250 and the demand curve for its services is P = 500 - Q, where P is the price per subscriber per year and Q is the expected number of subscribers. The franchise is assigned for only one year, and it allows the firm with the franchise to charge whatever price it chooses. The government will choose the applicant that spends the most money lobbying the government members. If the applicants cannot collude, how much will each spend on…
The US and Canada have overfished North Atlantic cod stocks nearly to the point of extinction. Both countries wish to preserve the cod industry (and hence the cod stocks), so the two countries sign an agreement to limit fish hauls. Each country has two possible strategies: comply with the agreement (limit fishing) or renege on the agreement (overfish). Each country’s payoffs for different strategy combinations are given in the matrix below. The numbers in the cells represent utilities, and the payoff ordering is (US, Canada). QUESTIONS: 1.If this is a one-shot game (i.e., it is played once), do the players have a dominant strategy? If so, what is it? Briefly explain your answer. 2.What is the equilibrium of this game? Is it Pareto-optimal? How do you know?
The total cost for a product-testing firm is C(q)=70 + 20q2 q= number of products tested Price of a product = average cost Each corporation purchases one product test per year from a product-testing firm in the same city. All other inputs are ubiquitous. Suppose five corporations are initially distributed uniformly, with one corporation in each city (A,B,C,D,E). Is the initial distribution a Nash Equilibrium? Demonstrate it is not by finding how much one corporation would pay if they deviate and move to another city? What is the average price of having two tests conducted? (Which is the price that the corporation would pay if they "live" in a city where two tests are conducted) The average price of moving and thus, having two tests is: $_____
Assume that the effective security level is now determined by the highest (not the lowest) security measures chosen by airlines. Letting max{s1, . . . , sn} denote the highest of the airlines’ strategies, we find that airline i’s payoff is now 50 + 20 x max{s1, . . . , sn} -10 si.Assuming the same strategy sets, find all Nash equilibria.
Considering the actors (i.e., two shipping lines and the port authorities) and the predetermined cost functions described below (i.e., transportation costs and port fees), and determine the equilibrium outcome (price, quantity, and profit) of the game. Let qi for i = 1 and 2 denote the number of containers transported by shipping line i. Assume a standard inverse demand function for a container of the form P = 20 000 − (q1 + q2) , and a total transportation cost function, excluding fixed costs, of the form TC = 200qi + (dt/2)*qi2 for i = 1,2, and t=low, high, representing low and high diseconomies of scale, i.e. dlow < dhigh. When both shipping lines choose the port of Gothenburg, which is characterized by low diseconomies of scale, each vessel incurs a lump sum of €1200 in port fees. In the case when both vessels choose the port of Helsingborg, which is characterized by high diseconomies of scale, each vessel incurs €1000 in port fees. Lastly, when the shipping lines choose…
The Able Manufacturing Company and Better Bettors, Inc. are rival firms in the production of a calculator used by horse racing fans for handicapping (determining betting strategies). Each firm has a fixed cost of $100 and a MC = $10 in producing calculators. The demand for the industry’s product is: Q = 900 – 5P, where P is the market price and Q = Q1 + Q2. If each firm must choose how many calculators to produce and sell without knowing of its rival’s production decision, what will be the Cournot equilibrium price and quantities produced? Calculate the profit for each firm.
Two partners start a business. Each has two possible strategies, spend full time or secretly take a second job and spend only part time on the business. Any profits that the business makes will be split equally between the two partners, regardless of whether they work full time or part time for the business. If a partner takes a second job, he will earn $20,000 from this job plus his share of profits from the business. If he spends full time on the business, his only source of income is his share of profits from this business. If both partners spend full time on the business, total profits will be $200,000. If one partner spends full time on the business and the other takes a second job, the business profits will be $80,000. If both partners take second job, the total business profits are $20,000. a) This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium. b) This game has two Nash equilibria, one in which each partner has an income of $100,000 and one in…
Several 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?
Two employees witness fraud committed in their firm. Each has two pure strategies: to become a whistleblower and report a crime, or not to report a crime. Each employee gets a payoff of 1 if the crime is reported by someone (it does not matter if both or only one employee reports). However, reporting the crime is costly. An employee who reports has to pay the cost of reporting equal to 0.5-0.25*d, where d=1 if the other employee also reports, and d=0 otherwise. Suppose that employees simultaneously decide to report or not. There is a unique mixed strategy Nash equilibrium in this game where each employee reports with the same positive probability less than 1. What is the probability that the crime is reported by at least one employee in such an equilibrium? ________
Q2.1 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.