Question

Question 5

Demand in a market dominated by two firms (a Cournot duopoly) is determined according to: P = 200 – 2(Q₁ + Q₂), where P is the market price, Q₁ is the quantity demanded by Firm 1, and Q₂ is the quantity demanded by Firm 2. The marginal cost and average cost for each firm is constant; AC=MC = $60.

The cournot-duopoly equilibrium profit for each firm is _____.

Hint: Write your answer to two decimal places.

QUESTION 6

1. The following matrix shows the pricing strategies and resultant profits for two profit-maximizing firms. The profit's are written  (Z,Y) where Z is the profit that Firm A (the firm that chooses which row) receives and Y is the profit Firm B (the firm that chooses the column) receives.

   Strategies	High	Low
   High	X,X	4,11.5
   Low	11.5,4	10,10

   What is the lowest value of X such that High, High is a Nash Equilibrium in this scenario.

   Hint: Write your answer to two decimal places.

   Hint two: X=35 would make High, High a Nash Equilibrium since neither firm would benefit from deviating. However, I want to know the smallest value of X such that High, High is the Nash Equilibrium.

10 points   

QUESTION 7

1. Demand in a market dominated by two firms (a Cournot duopoly) is determined according to: P = 200 – 2(Q₁ + Q₂), where P is the market price, Q₁ is the quantity demanded by Firm 1, and Q₂ is the quantity demanded by Firm 2. The marginal cost and average cost for each firm is constant; AC=MC = $64.

   The cournot-duopoly equilibrium quantity produced by each firm is _____.

   Hint: Write your answer to two decimal places.

Answer 1

Question 5:
Each firm maximizes profit according to the rule: MR = MC.
P = 200 - 2(Q1 + Q2) = 200 - 2Q1 - 2Q2
Firm 1: Total Revenue, TR1 = P*Q1 = (200 - 2Q1 - 2Q2)*Q1 = 200Q1 - 2Q1² - 2Q1Q2
Marginal Revenue, MR1 =
So, MR1 = MC gives,
200 - 4Q1 - 2Q2 = 60
So, 4Q1 = 200 - 60 - 2Q2 = 140 - 2Q2
So, Q1 = (140/4) - (2Q2/4)
So, Q1 = 35 - 0.5Q2
This is the best response function of firm 1, BR1.
As demand function and MC are same for both firms, so best response function of firm 2 is:
Q2 = 35 - 0.5Q1
Now, substituting BR1 in BR2, we get,
Q2 = 35 - 0.5(35 - 0.5Q2) = 35 - 17.5 + 0.25Q2
So, Q2 - 0.25Q2 = 17.5
So, 0.75Q2 = 17.5
So, Q2 = 17.5/0.75 = 23.33
So, Q1 = 35 - 0.5Q2 = 35 - 0.5(23.33) = 35 - 11.67 = 23.33
So, P = 200 – 2(Q₁ + Q₂) = 200 – 2(23.33 + 23.33) = 200 - 93.32 = 106.68

TR 200 200-4Q1-2072

So, equilibrium profit for each firm = Total revenue for each firm - Total cost of each firm = P*Q1 - AC*Q1 = (P - AC)*Q1
= (106.68 - 60)*23.33 = $1,089.04

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