# 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.

https://brainmass.com/economics/general-equilibrium/determining-equilibrium-output-profits-277883

#### Solution Preview

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.