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.
- OiyLv 51 month ago
PQ=16Q -Q*2, so MR=dPQ=16-2Q.
MR=MC, 16-2Q=4,Q= 12/2=6, P= 16-6=10.