Question

Consider a monopolistic firm facing the following market conditions: p = 200 – Q TC = 200 + 40Q Calculate the monopolist's profit maximizing price and output, along with monopoly profits.

Answer 1

Solution

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

P=200-Q

Total revenue= Quantity(Q) * AR

                      =Q* (200-Q)

                      =200Q-Q²

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

200-2Q=40

2Q=160

Q=80

Price(P)= 200-Q

             =200-80

             =$120.

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

           =(200Q-Q²)-(200+40Q)

           = (16000- 6400)- (200 + 3200)

           =9600-3400

           =$6200

Thus, monopoly profit is $6200