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Determining Equilibrium output and profits

2 companies produce the same item. The companies each determine their own output and the combined output of the two is sold at the market price. Company A has controls its costs better than its competitor, B. The demand curve is P=280-2(Q1+Q2) and the cost function is C1(Q1)=3Q1 and C2(Q2)=2Q2

Find out the followings

1) Marginal revenue for both,
2) Reaction function for both,
3) Equilibrium output,
4) Equilibrium profits.

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Solution:

It is given that Company A has better control over costs,
So, cost function for company A=C2(Q2)=2Q2
cost function for company B=C1(Q1)=3Q2

1) figuring out the marginal revenue for both,
Company B
Total Revenue=Price*Output of company=P*Q1
TR1={280-2(Q1+Q2)}*Q1
TR1=280Q1-2Q1^2-2Q1Q2
To get Marginal Revenue differentiate TR1 w.r.to Q1,
MR1=d(TR1)/dQ1=280-4Q1-2Q2

Company A
Total Revenue=Price*Output of company=P*Q2
TR2={280-2(Q1+Q2)}*Q2
TR2=280Q2-2Q1Q2-2Q2^2
To get Marginal Revenue differentiate TR2 w.r.to ...

Solution Summary

The solution depicts the steps to find reaction functions, equilibrium output and equilibrium profits in a oloigopoly model.

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