A6. 2. Consider a duopoly handbag market. The two firms produce identical handbags thatconsumers perceive to be homogeneous products. Consumers derive total benefit fromhandbag consumption of B(x) = 500x-1.5x², where the total quantity of handbags sold inthe market is x = x₁ + x2. The entrant handbag producer has an identical cost function as theincumbent firm, so that c(x₁) = 4x1 + 200 and c(x2)=4x2 + 200.a. Calculate the reaction functions, x1 and x2. Show the equilibrium quantity of handbagsproduced by each firm as the intersection of two reaction functions on a graph.b. Find the equilibrium quantity of handbags produced in a Cournot duopoly. What is themarket price of a handbag in a Cournot duopoly?c. How much profit does each firm make? What is industry profit in the duopoly market?

Total Benefit : B(x) = 500x - 1.5x2 Therefore , Demand function : P = 500 - 3x (Differentiating…

2. Consider a duopoly handbag market. The two firms produce identical handbags that consumers perceive to be homogeneous products. Consumers derive total benefit from handbag consumption of B(x) = 500x-1.5x², where the total quantity of handbags sold in the market is .x = x₁ + x2. The entrant handbag producer has an identical cost function as the incumbent firm, so that c(x₁) = 4x1 + 200 and c(x₂)=4x2 + 200. a. Calculate the reaction functions, x and x2. Show the equilibrium quantity of handbag produced by each firm as the intersection of two reaction functions on a graph. b. Find the equilibrium quantity of handbags produced in a Cournot duopoly. What is th market price of a handbag in a Cournot duopoly?

2. Consider a duopoly handbag market. The two firms produce identical handbags that consumers perceive to be homogeneous products. Consumers derive total benefit from handbag consumption of B(x) = 500x-1.5x², where the total quantity of handbags sold in the market is .x = x₁ + x2. The entrant handbag producer has an identical cost function as the incumbent firm, so that c(x₁) = 4x1 + 200 and c(x₂)=4x2 + 200. a. Calculate the reaction functions, x and x2. Show the equilibrium quantity of handbag produced by each firm as the intersection of two reaction functions on a graph. b. Find the equilibrium quantity of handbags produced in a Cournot duopoly. What is th market price of a handbag in a Cournot duopoly?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

A6.

2. Consider a duopoly handbag market. The two firms produce identical handbags that
consumers perceive to be homogeneous products. Consumers derive total benefit from
handbag consumption of B(x) = 500x-1.5x², where the total quantity of handbags sold in
the market is x = x₁ + x2. The entrant handbag producer has an identical cost function as the
incumbent firm, so that c(x₁) = 4x1 + 200 and c(x2)=4x2 + 200.
a. Calculate the reaction functions, x1 and x2. Show the equilibrium quantity of handbags
produced by each firm as the intersection of two reaction functions on a graph.
b. Find the equilibrium quantity of handbags produced in a Cournot duopoly. What is the
market price of a handbag in a Cournot duopoly?
c. How much profit does each firm make? What is industry profit in the duopoly market?

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