### Cournot and Stackelberg Competition Analysis#### OverviewConsider two firms that are Cournot competitors. The industry demand curve is defined by the equation $ P = 200 - Q $, where $ Q $ represents the combined output of the two firms. Assume that both Firm 1 and Firm 2 have constant marginal and average total costs of $20.#### Questions for Analysis1. **Solving the Cournot Equilibrium** - Determine the Cournot equilibrium in terms of price, quantity, and profit for each firm. 2. **Impact of Technology Investment by Firm 1** - Analyze how the equilibrium changes if Firm 1 reduces its costs to $14 per unit through new technology. - Calculate the maximum amount Firm 1 should be willing to spend to ensure exclusive access to this technology if it guarantees Firm 2 will not acquire it. 3. **Stackelberg Competition Scenario** - If Firm 2 decides to move first in response to Firm 1's new technology, turning the competition into a Stackelberg model where Firm 2 is the leader, determine the new equilibrium for price, quantity, and profit. - Assess if this strategy benefits Firm 2 in the long run.#### Detailed Breakdown1. **Cournot Equilibrium Calculation** - The firms simultaneously choose quantities to maximize their respective profits. - The market price $ P $ is determined by the total output, $ Q $, of both firms. - Each firm’s revenue is $ PQ $, and costs are constant at $20 per unit.2. **Investing in Cost-Reducing Technology** - Firm 1's new cost is $14 per unit. - Calculate the new equilibrium with Firm 1's reduced costs. - Determine the investment value by calculating the change in Firm 1's profit and considering the strategic advantage.3. **Changing to Stackelberg Competition** - Firm 2 moves first (leader) and Firm 1 responds (follower). - Determine the new equilibrium outcomes in terms of price and quantity. - Evaluate the effect on Firm 2’s profit compared to the Cournot equilibrium.By analyzing the questions and calculations in this framework, students will understand the strategic interactions between firms in different competitive scenarios and how cost structures influence market outcomes. The application of Cournot and Stackelberg models offers practical insights into strategic decision-making in economics.

An oligopoly market is one that has very few firms that are interdependent. Firms can homogenous as…

Suppose that two firms are Cournot competitors. Industry demand is given by: P = 200 – Q, where Q is the combined output of the two firms. If both Firm 1 and Firm 2 face constant marginal and average total costs of $20: a. Solve for the Cournot price, quantity, and firm profits. b. Suppose that Firm 1 is considering investing in costly technology that will enable it to reduce its costs to $14 per unit. How would this change the equilibrium values you found in part a? How much should Firm 1 be willing to pay if such an investment can guarantee that Firm 2 will not be able to acquire it? c. If Firm 2 tries to counteract Firm 1's new technology by changing this game to Stackelberg Competition in which they (Firm 2) moves first (after Firm 1 adopts their new technology), what will be the new equilibrium values of price, quantity and firm profits? Will this strategy work for Firm 2?

Suppose that two firms are Cournot competitors. Industry demand is given by: P = 200 – Q, where Q is the combined output of the two firms. If both Firm 1 and Firm 2 face constant marginal and average total costs of $20: a. Solve for the Cournot price, quantity, and firm profits. b. Suppose that Firm 1 is considering investing in costly technology that will enable it to reduce its costs to $14 per unit. How would this change the equilibrium values you found in part a? How much should Firm 1 be willing to pay if such an investment can guarantee that Firm 2 will not be able to acquire it? c. If Firm 2 tries to counteract Firm 1's new technology by changing this game to Stackelberg Competition in which they (Firm 2) moves first (after Firm 1 adopts their new technology), what will be the new equilibrium values of price, quantity and firm profits? Will this strategy work for Firm 2?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Consider two Cournot oligopolists, firm 1 and firm 2, in a homogenous product market. The market demand is P = 100 - 3Q and each firm has a constant marginal cost MC=10. The market price of equilibrium and total quantity in the market is: Select one: a. P* 30 and Q* = 20 O b. P* 40 and Q* = 20 ○ c. P* = 40 and Q* = 30 O d. P*20 and Q* = 30
Consider two cigarette companies, PM Inc. and Brown Inc. If neither company advertises, the two companies split the market and earn $60 million each. If they both advertise, they again split the market, but profits are lower by $20 million since each company must bear the cost of advertising. Yet, if one company advertises while the other does not, the one that advertises attracts customers from the other. In this case, the company that advertises earns $70 million while the company that does not advertise earns only $30 million. What will these two companies do if they behave as individual profit maximizers? One company will advertise, and the other will not. Brown Inc. earns $70. Both companies will advertise. PM Inc. earns $60. Neither company will advertise. Brown Inc. earns $60. Both companies will advertise. Brown Inc. earns $40.
**Practice** Consider a market with three firms. Each firm has a different cost function. We assume C1(q1) = 7q1, C2(q2) = q2 + 1, and C3(q3) = 3q3.
QUESTION 1A) Two cournot competitors face inverse demand P = 50 - Q. Where, Q = q1+q2, is the total output of firms 1 and 2. What are the equilibrium output levels for q1 and q2, If firm 1 marginal cost is 1, and firm 2's marginal cost is 12? QUESTION 1B. Continuing with the inverse demand, P = 50 - Q, if each firm has a marginal cost of 0, what is the difference between the equilibrium price under Cournot competition and under Bertrand competition? b. C. d. a. The Cournot price is higher than the Bertrand price by 50. The Cournot price is lower than the Bertrand price by 25. The Cournot price is higher than the Bertrand price by 50/3. Equilibrium prices under Cournot and Bertrand are the same, so the difference is zero.
Q3. There are two firms selling differentiated products. Firm A faces the following demand for his product: e, = 20 – -P, + -P, 2. Firm B faces the following demand: 1 P. +-P, 2. 0, = 220- Assume that the marginal cost is zero both for firm A and firm B. What are the equilibrium prices of a simultaneous price competition? What would the equilibrium prices be if A is the leader and B is the follower?
The diagram illustrate an industry under oligopoly consisting of 10 equal-sized firms, and a particular firm in that industry. Each of the firms produces an identical product. To what output will an individual firm be restricted if the price is to be maintained?Assume that all firms are permitted to produce the same level of output. If the other firms stick to this output, how much would an individual firm be tempted to produce if it wished to maximize its own profit at the agreed price? If it undercut the cartel price, what and output would maximize its profit (assuming the other members did not retaliate)?
In the mobile phone market, Samsung and Apple constitute a duopoly in the production of devices.The American firm has the following demand q(a) = 10 - p(a )+ 0.25p(s), and the Korean firm, q(s) = 20 -p(s)+ 0.5p(a). Because both firms assembly their devices in China, their cost structure is the same andequal to ?(q) = 10q, answer the following questions.a) What would be the equilibrium (quantity, price, and profit) in this market, and interpret youranswer.b) If they decide to form a cartel, what are the new quantities, prices, and profits? NB.a=apple and s=Samsung
Two firms engage in Cournot competition in the Everlasting Gobstopper industry. The price elasticity of demand is-2. Firm 1 has aconstant marginal cost of $110.00 per unit, and firm 2 has a constant marginal cost of $181.50 per unit. If the two firms are currently inequilibrium, what is firm 2's share of the market? Enter your answer as a decimal, rounded to two places if necessary.______ Please show all steps
Economics: Industrial Economics Question: In a market that operates under quantity competition there are 2 firms (Cournot duopoly). The inverse demand function is P = A - B Q. The cost structure of firm 1 is given by C1(q1) = F1 + c1 q1 and that of firm 2 is given by C2(q2) = F2 + c2 q2. Prior to competing, the two firms can engage in research at levels (x1, x2) respectively in order to lower their marginal costs. As a result, marginal costs are c1 = c - x1 - β2x2 and c2= C - x2 - β1 X1. where β1 = β2 > ½. Finally, the research costs are F1 = a1 (x1)^2 /2 and F2 = a2 (x2)^2 /2, where a1 > 0 and a2> 0. 1. The Nash Equilibrium research levels are Choices: A. Higher than the cooperative research levels for both firms. B. Higher than cooperative research levels for firm 1 but lower for... C. Lower than the cooperative research levels for both firms. D. Higher than cooperative research levels for firm 2 but lower for... 2. An increase in the value of a2 would Choices: A.…
2
Duopolists following the Bertrand pricing strategy face a market demand curve given by P = 90 - 2Q where Q is total market demand. Each firm can produce output at a constant marginal cost of 40 per unit. How much profit will each firm make? Duopolists following the Cournot strategy face a market demand curve given by P = 90 - 2Q where Q is total market demand. Each firm can produce output at a constant marginal cost of 40 per unit. If firm 1 moves first, how much profit will firm 1 make? Duopolists following the Cournot strategy face a market demand curve given by P = 90 - 2Q where Q is total market demand. Each firm can produce output at a constant marginal cost of 40 per unit. If firm 1 moves first, how much profit will firm 2 make? Round to the nearest whole number.
Suppose two firms compete as Bertrand duopolists for an identical product, where demand is given by Q = 5000 – 50P and both firms have marginal cost of 10 per unit of output. If firm 1 has capacity of 1500 and firm 2 has capacity of 2000, what will the equilibrium price be in this market?