### 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

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