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    Determining Equilibrium output and profits

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    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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    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.

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