The first step here would be to find the Marginal Revenue(MR) and Marginal Cost(MC). Price is maximized where marginal revenue is equal to marginal cost. For a firm which does not undertake price discrimination, the demand curve is the same as the average revenue. Thus, average revenue is
Total revenue= Quantity(Q) * AR
From the total revenue, marginal revenue can be obtained by taking a derivative of the total revenue curve.
Marginal Revenue [dTR/dQ] = 200-2Q1
On the supply side, average cost is calculated by dividing quantity with total cost;
Average cost= TC/Q
=200 + 40Q/Q
=(200/Q) + 40
Marginal cost is the derivative of total cost
Marginal Cost [dTC/dQ]= 40
In order to get, the output, we get marginal revenue equal to marginal cost
Thus, the monopolist will set its price at $120, and its output at 80 units.
The monopoly profit can be calculated by subtracting total cost from total revenue
Profit = TR – TC
= (16000- 6400)- (200 + 3200)
Thus, monopoly profit is $6200