profit is maximized when
The marginal cost function is: MC = 10 + 2Q. The marginal revenue is: MR = 25 - 2Q. The monopolist's profit is found by subtracting total cost from its total revenue. In terms of calculus, the profit is maximized by taking the derivative of this function, Ï = TR - TC, and equating it to zero. Therefore, the quantity supplied that maximizes the monopolist's profit is found by equating MC to MR: 10 + 2Q = 30 - 2Q. The quantity it must produce to satisfy the equality above is five.