How to work out output, price and profit from monopoly equations.

How to work out output, price and profit from monopoly equations.

Readers Question: A monopolist operates under a production technology which allows the production of any output level at a constant average cost of $5 per unit. This monopolist sells into two distinct markets the demand curves for which are: P1=55-Q1  (for market one) and Q2 = 70 – 2P2 (for market 2). If this monopolist operates so as to maximize total profit then calculate:

(i) Total output;
(ii) The quantity sold in each market;
(iii) The price charged in each market;
(iv) The monopolist’s total profit.

The Demand Curve equals the average revenue curve.
We need to find out the Marginal revenue Curve

The Marginal Revenue curve is twice as steep.

• If Q.D = 55 – P1(AR).
• P = 55 – Q
• MR = 55 -2Q1

The next step is to work out profit maximisation.

Profit Maximisation for a Monopolist

• Profit Maximisation occurs where MR=MC
• MC = $5 (a constant average cost means the MC=AC)
• MR = 55 -2Q

Therefore,

• 5 = 55 – 2Q
• 2Q = 50
• Q = 25
• P = 55 – Q
• P = 30

Example using diagram

Profit maximisation at Q = 25. Price = 30

To Calculate Profit for A Monopoly

Profit = Total revenue – Total Cost

Total Revenue = 25*30 = 750
Total Cost = 5 * 25 = 125

• Therefore, total profit for this section is = 625 (assuming there is no fixed cost)

Related

• Monopoly Diagram
• Supply and demand equations