Two companies produce similar items for the same market. Company 1 produces q₁items and Company 2 produces q2 items. The costs C₁ and C₂ incurred by Company 1and Company 2, respectively, are given by C₁ = 79₁ and C₂ = 1092, and the market priceP is given by P = 100-91-92. Let ₁ and 2 denote the profits made by Company 1and Company 2, respectively. Each company wants to choose its production strategy inorder to maximize its profit.(a) Find expressions for ₁ and ₂ in terms of 9₁ and 92.(b) Find the solution of this problem, using the Cournot model.

Given information Demand function P=100-q1-q2 C1=7q1--- firm 1's cost C2=10q2-- firm 2's cost Firm…

Two companies produce similar items for the same market. Company 1 produces q₁ items and Company 2 produces q2 items. The costs C₁ and C₂ incurred by Company 1 and Company 2, respectively, are given by C₁ = 79₁ and C₂ = 1092, and the market price P is given by P = 100 q1 q2. Let ₁ and 2 den ote the profits made by Company 1 and Company 2, respectively. Each company wants to choose its production strategy in order to maximize its profit. (a) Find expressions for ₁ and ₂ in terms of q₁ and 92. (b) Find the solution of this problem, using the Cournot model.

Two companies produce similar items for the same market. Company 1 produces q₁ items and Company 2 produces q2 items. The costs C₁ and C₂ incurred by Company 1 and Company 2, respectively, are given by C₁ = 79₁ and C₂ = 1092, and the market price P is given by P = 100 q1 q2. Let ₁ and 2 den ote the profits made by Company 1 and Company 2, respectively. Each company wants to choose its production strategy in order to maximize its profit. (a) Find expressions for ₁ and ₂ in terms of q₁ and 92. (b) Find the solution of this problem, using the Cournot model.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter18: Auctions

Section: Chapter Questions

Problem 18.6IP

See similar textbooks

Similar questions

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 construction companies are lobbying to obtain a share of work on repaving city streets. The share of the project going to each firm depends on money contributions to the mayor’s reelection fund. The project has value V in total. The mayor is somewhat biased in favor of firm 1, which is run by his niece. If firm 1 contributes x1 and firm 2 contributes x2, with at least one contribution strictly larger than zero, then the shares of the project going to firms 1 and 2 are s1 and s2, respectively, where (see picture)
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…
You and your partner are choosing how much effort to put towards a group project for a course . You both care about the quality of the project , which increases in both of your effort choices . But you both also pay a cost of effort . You are enjoying the course much more than your partner , so your cost of effort is lower . Where y and p denote the amount of effort put by you and your partner , respectively , • Your payoff is 60yp - y³ . • Your partner's payoff is 60yp - 8p³ . Decisions about effort provision are made simultaneously . Answer the following questions about the set of pure strategy Nash equilibria of this game . Please round to 3 decimal places where rounding is needed . a ) In one pure strategy Nash equilibrium , you put more effort towards the project than your partner . In this Nash equilibrium , what is your effort level ? b ) In one pure strategy Nash equilibrium , you put the same level of effort towards the project as your partner . In this Nash equilibrium ,…
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…
You have created a business-to-business Internet venture directed at an industry with 50 identical firms. Your services allow these firms to do business with each other more efficiently as members of your trading network. You plan to sell access to your service for a price "p" per member firm. Each firm’s benefit from the service is given by "2n", where "n" is the number of other firms joining the network as a member. So, if 21 firms join your service, each places a value of 2 × 20 or 40 on membership in your network. (a) Suppose you set the price, p, and then firms simultaneously and independently decide whether or not to join as members. Show that, for a 0<p<98, there exist exactly two Nash equilibria in the simultaneous-move game played by firms deciding whether or not to join the network as members. Suppose for part (b) that you are able to persuade 10 firms to join your network at an initial stage. At a second stage, you set a price for the remaining 40 firms. These 40 firms…
Two firms compete in a homogeneous product market where the inverse demand function is P = 20 − 5Q (quantity is measured in millions). Firm 1 has been in business for one year, while firm 2 just recently entered the market. Each firm has a legal obligation to pay one year’s rent of $2 million regardless of its production decision. Firm 1’s marginal cost is $2 and firm 2’s marginal cost is $10. The current market price is $15 and was set optimally last year when firm 1 was the only firm in the market. At present, each firm has a 50 percent share of the market. a. Why do you think firm 1’s marginal cost is lower than firm 2’s marginal cost? b. Determine the current profits of the two firms. c. What would happen to each firm’s current profits if firm 1 reduced its price to $10 while firm 2 continued to charge $15? d. Suppose that, by cutting its price to $10, firm 1 is able to drive firm 2 completely out of the market. After firm 2 exits the market, does firm 1 have an incentive to raise…
Two firms compete in a homogeneous product market where the inverse demand function is P = 20 -5Q (quantity is measured in millions). Firm 1 has been in business for one year, while Firm 2 just recently entered the market. Each firm has a legal obligation to pay one year’s rent of $1.4 million regardless of its production decision. Firm 1’s marginal cost is $2, and Firm 2’s marginal cost is $10. The current market price is $15 and was set optimally last year when Firm 1 was the only firm in the market. At present, each firm has a 50 percent share of the market. b. Determine the current profits of the two firms. c. What would each firm’s current profits be if Firm 1 reduced its price to $10 while Firm 2 continued to charge $15?
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: $_____
Exercise 6.8. Two companies with cost functions C1 (q1 )=5q1 and C2 (q2)= 0.5 q2 ² supply the to the same market. If the inverse market demand function is given by P = 100 - 0,5Q , where Q = q₁ + q₂ , find a) The production level of each firm, the price and the profits if the companies compete according to the Cournot model. (b) The level of production of each undertaking, the price and the profits if the undertakings agree to jointly maximise their profits. Show the results with the help of graphs.
Two businesses contribute to maintaining green spaces. Every year the companies 1 and 2 decide how much to contribute, where the joint contribution is x= x1 + x2 The spaces Greens are common so there is no rivalry. The market rents of each company depend on the quality of its infrastructure and green spaces. The utility function of firm 1 is: Z1 = Z1 + ln(x1+x2)-x1 The utility function of firm 2 is: Z2 = Z2 + 2 ln (x1+x2) - x2 Where Z1 and Z2 are constants (a)Find the best response of firm 1 based on the contribution of firm 2, R1(X2) for all x2 [0,oo) (b) Find the best response of firm 2 based on the contribution of firm 1, R2(X1) for all x1 [0,oo) (c) Find the Nash equilibrium (x1, x2) and the total contribution x = x1 + x2. (d) Is there free riding in this equilibrium? From which company? explain. (e) Determine the total Pareto efficient input level. How does it compare to the results? found in (c)? explain Question A
Two businesses contribute to maintaining green spaces. Every year the companies 1 and 2 decide how much to contribute, where the joint contribution is x= x1 + x2 The spaces Greens are common so there is no rivalry. The market rents of each company depend on the quality of its infrastructure and green spaces. The utility function of firm 1 is: Z1 = Z1 + ln(x1+x2)-x1 The utility function of firm 2 is: Z2 = Z2 + 2 ln (x1+x2) - x2 Where Z1 and Z2 are constants (a)Find the best response of firm 1 based on the contribution of firm 2, R1(X2) for all x2 [0,oo) (b) Find the best response of firm 2 based on the contribution of firm 1, R2(X1) for all x1 [0,oo) (c) Find the Nash equilibrium (x1, x2) and the total contribution x = x1 + x2. (d) Is there free riding in this equilibrium? From which company? explain. (e) Determine the total Pareto efficient input level. How does it compare to the results? found in (c)? explain Question e