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The inverse market demand in a homogeneous-product Cournot duopoly is P = 140 – 2(Q1 +...

The inverse market demand in a homogeneous-product Cournot duopoly is P = 140 – 2(Q1 + Q2) and costs are Company 1, C1(Q1) = 18Q1 and Company 2 C2(Q2) = 17Q2. Calculate the equilibrium output for Company 1 Round all calculations to 1 decimal

The inverse market demand in a homogeneous-product Cournot duopoly is P = 133 – 1(Q1 + Q2) and costs are Company 1, C1(Q1) = 10Q1 and Company 2 C2(Q2) = 21Q2. Calculate the equilibrium output for Company 2 Round all calculations to 1 decimal

Solutions

Expert Solution

P = 140 - 2(q1+q2)

Company 1:

Total Revenue TR = P*q1 = 140q1 - 2q12 - 2q1q2

Marginal Revenue = dTR/dq1 = 140 - 4q1 - 2q2

Marginal Cost = 18

The firm equates MR and MC

140-4q1-2q2 = 18

4q1 = 122-2q2

q1 = 30.5 - 0.5q2 ...........1

Company 2:

Total Revenue TR = P*q2 = 140q2 - 2q22 - 2q1q2

Marginal Revenue = dTR/dq1 = 140 - 4q2 - 2q1

Marginal Cost = 17

The firm equates MR and MC

140-4q2-2q1 = 17

4q2 = 123-2q1

q2 = 30.75 - 0.5q1............ Put this value in equation 1 above,

q1 = 30.5 - 0.5q2

q1 = 30.5 - 0.5(30.75 - 0.5q1)

q1 = 30.5 - 15.375 + 0.25q1

0.75q1 = 15.125

q1 = 20.17

Second question:

P = 133 - 1(q1+q2)

Company 1:

Total Revenue TR = P*q1 = 133q1 - q12 - q1q2

Marginal Revenue = dTR/dq1 = 133 - 2q1 - q2

Marginal Cost = 10

The firm equates MR and MC

133 - 2q1 - q2 = 10

2q1 = 123-q2

q1 = 61.5 - 0.5q2 ...........2

Company 2:

Total Revenue TR = P*q2 = 133q2 - q22 - q1q2

Marginal Revenue = dTR/dq1 = 133 - 2q2 - q1

Marginal Cost = 21

The firm equates MR and MC

133 - 2q2 - q1 = 21

2q2 = 112-q1

q2 = 56 - 0.5q1. Put this value in equation 2 above we get,

q1 = 61.5 - 0.5q2

q1 = 61.5 - 0.5(56 - 0.5q1)

q1 = 61.5 - 28 + 0.25q1

0.75q1 = 33.5

q1 = 44.67

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Rahul Sunny answered 2 years ago
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