Calculus Version

Profit will be maximized when the derivative of profit with respect to output (dPR/dQ) is equal to zero:

dPR/dQ = dTR/dQ - dTC/dQ = 0

Therefore, at the profit maximizing quantity, dTR/dQ (otherwise known as marginal revenue) must be equal to dTC/dQ (marginal cost). In other words, the monopolist will choose the Q that makes MR=MC.

To solve a monopoly problem you will need to write down equations for TR and TC as functions of Q. Then differentiate the two, set the resulting equations for MR and MC equal to each other, and solve for Q.