Imagine that firm X chooses their quantity first, then firm Y observes the quantity of firm X and chooses their own quantity. What is the subgame perfect Nash Equilibrium? Is there a first or second-mover advantage here? You don't need to draw the whole game tree but you should give some kind of explanation for how you came to this equilibrium. (You may assume that firm X can only choose quantities that are multiples of 200. This prevents you from having to deal with prices that are not on the schedule and makes firm Y's strategy easier to write. ) ### Cournot Nash Equilibrium Graph Analysis#### Data Table| Y | X ||-----|-----|| 0 | 600 || 200 | 500 || 400 | 400 || 600 | 300 |#### Graph ExplanationThe graph demonstrates the Cournot Nash Equilibrium between two firms, Firm X and Firm Y. The x-axis (labeled as Qx) denotes the quantity produced by Firm X, ranging from 0 to 1200 in increments of 100. The y-axis (labeled as Qy) indicates the quantity produced by Firm Y, ranging from 0 to 1200, also in increments of 100.- The solid line labeled "Firm X" starts from (Qx=1200, Qy=0) and declines to (Qx=0, Qy=600).- The solid line labeled "Firm Y" starts from (Qx=0, Qy=0) and inclines to (Qx=1200, Qy=600).These lines represent the reaction functions for Firm X and Firm Y, respectively. The point where the two lines intersect, labeled as E (400, 400), signifies the Cournot Nash Equilibrium, where both firms produce 400 units.#### ExplanationAt the intersection of the two reaction functions (denoted by point E), the quantities for both firms are equal at 400 gallons each. This point of intersection represents the Cournot Nash Equilibrium. To arrive at this intersection point, the two reaction functions were solved, showing that \( Qx = Qy = 400 \). This equilibrium point indicates that both firms' production behaviors are optimal given the output of the other firm.

To determine the Nash equilibria which is subgame perfect, we will use the extensive form…

Answered: Imagine that firm X chooses their…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Imagine that firm X chooses their quantity first, then firm Y observes the quantity of firm X and chooses their own quantity. What is the subgame perfect Nash Equilibrium? Is there a first or second-mover advantage here? You don't need to draw the whole game tree but you should give some kind of explanation for how you came to this equilibrium.

(You may assume that firm X can only choose quantities that are multiples of 200. This prevents you from having to deal with prices that are not on the schedule and makes firm Y's strategy easier to write. )

### Cournot Nash Equilibrium Graph Analysis

#### Data Table

| Y | X |
|-----|-----|
| 0 | 600 |
| 200 | 500 |
| 400 | 400 |
| 600 | 300 |

#### Graph Explanation

The graph demonstrates the Cournot Nash Equilibrium between two firms, Firm X and Firm Y. The x-axis (labeled as Qx) denotes the quantity produced by Firm X, ranging from 0 to 1200 in increments of 100. The y-axis (labeled as Qy) indicates the quantity produced by Firm Y, ranging from 0 to 1200, also in increments of 100.

- The solid line labeled "Firm X" starts from (Qx=1200, Qy=0) and declines to (Qx=0, Qy=600).
- The solid line labeled "Firm Y" starts from (Qx=0, Qy=0) and inclines to (Qx=1200, Qy=600).

These lines represent the reaction functions for Firm X and Firm Y, respectively. The point where the two lines intersect, labeled as E (400, 400), signifies the Cournot Nash Equilibrium, where both firms produce 400 units.

#### Explanation

At the intersection of the two reaction functions (denoted by point E), the quantities for both firms are equal at 400 gallons each. This point of intersection represents the Cournot Nash Equilibrium. To arrive at this intersection point, the two reaction functions were solved, showing that \( Qx = Qy = 400 \). This equilibrium point indicates that both firms' production behaviors are optimal given the output of the other firm.

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