3. Reuben and Simeon are duopolists producing jeans in a differentiated goods market. Themarket demand for Reuben's jeans is y₁ = 75 − P₁ + P2, while the market demand for11Simeon's jeans is y₂ = 75 − P2 + ₂P₁. Reuben's cost function is C₁(y₁) = 75y₁ whileSimeon's cost function is C₂ (y₂) = 75y2.a) Calculate the Bertrand equilibrium in this market. Indicate each firm's price, outputlevel, and profits. (Answer: p₁ = 100 USD, y₁ = 25 units)b) Find prices and output levels that would maximize joint profits, and calculate themaximum joint profits.c) Draw a payoff matrix using the results from a) and b) and determine the Nashequilibrium.

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c) Draw a payoff matrix using the results from a) and b) and determine the Nash equilibrium.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

3. Reuben and Simeon are duopolists producing jeans in a differentiated goods market. The
market demand for Reuben's jeans is y₁ = 75 − P₁ + P2, while the market demand for
1
1
Simeon's jeans is y₂ = 75 − P2 + ₂P₁. Reuben's cost function is C₁(y₁) = 75y₁ while
Simeon's cost function is C₂ (y₂) = 75y2.
a) Calculate the Bertrand equilibrium in this market. Indicate each firm's price, output
level, and profits. (Answer: p₁ = 100 USD, y₁ = 25 units)
b) Find prices and output levels that would maximize joint profits, and calculate the
maximum joint profits.
c) Draw a payoff matrix using the results from a) and b) and determine the Nash
equilibrium.

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