Rafael asked in Social ScienceEconomics · 8 months ago

Help with Microeconomics calculus ?

I'm learning about the Cournot game for oligopolies, and I'm having some trouble calculating the Marginal Revenue so I can derive the best response curve for each firm. 

For the problem I'm trying to solve, the inverse demand function is P = 16 - Q. Marginal Cost is equal to 4. I know revenue is price times quantity (R = P.Q). 

When I try to calculate the marginal revenue (MR), I get 16 - q1 - q2. However, the correct answer for the MR is 16 - 2q1 - q2. (q1 is firm 1, and q2 is firm 2).

Could someone please explain why the second MR is the correct one? If possible, please write out the calculus to find the MR. 

1 Answer

  • Oiy
    Lv 6
    8 months ago

    PQ=16Q -Q*2, so MR=dPQ=16-2Q.

    MR=MC, 16-2Q=4,Q= 12/2=6, P= 16-6=10.

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