Consider a duopoly with homogenous goods where Firm 1 has the following production function: Q1 = F1(L,K) = L1/2 K1/2,where Q and K are measured in units and L in hours. Firm 2 uses labour and capital as well but has a different production function, given byQ2 = F2(L,K) = L1/3 K2/3.You may assume that the market for labour and capital is perfectly competitive and the current wage rate is £40 and the rental rate on capital is £10. Both firms sell their products on the same market with inverse demand function P = 52 – (Q1 + Q2),where P is measured in pound sterling.Which production function(s) exhibit(s) decreasing returns to scale? Suppose Firm 1 wishes to produce 6 units. What is the cost minimising input mix for Firm 1? Suppose Firm 2 wishes to produce 4 units. What is the cost minimising input mix for Firm 2? Assume both firms now have the option to produce either 4 units or 6 units. We will consider the situation where both firms simultaneously, but independently, choose their strategies. Both firms are aiming to maximise their profits.For each player (firm), what are their strategies? Write the game in normal form.Find each player’s dominant strategy (if they exists). Find all Nash equilibria.

Given: Q1 = F1(L,K) = L1/2 K1/2, Q2 = F2(L,K) = L1/3 K2/3. P = 52 – (Q1 + Q2), Current wage rate=£40…

Answered: Consider a duopoly with homogenous…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a duopoly with homogenous goods where Firm 1 has the following production function:

Q₁ = F₁(L,K) = L^1/2K^1/2,

where Q and K are measured in units and L in hours. Firm 2 uses labour and capital as well but has a different production function, given by

Q₂ = F₂(L,K) = L^1/3K^2/3.

You may assume that the market for labour and capital is perfectly competitive and the current wage rate is £40 and the rental rate on capital is £10. Both firms sell their products on the same market with inverse demand function

P = 52 – (Q₁ + Q₂),

where P is measured in pound sterling.

Which production function(s) exhibit(s) decreasing returns to scale?
Suppose Firm 1 wishes to produce 6 units. What is the cost minimising input mix for Firm 1?
Suppose Firm 2 wishes to produce 4 units. What is the cost minimising input mix for Firm 2?

Assume both firms now have the option to produce either 4 units or 6 units. We will consider the situation where both firms simultaneously, but independently, choose their strategies. Both firms are aiming to maximise their profits.

For each player (firm), what are their strategies? Write the game in normal form.
Find each player’s dominant strategy (if they exists).
Find all Nash equilibria.

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