Profit and Price in a Monopoly

(b)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:Q1 = 55 – P1 (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
  MR = 55 -2P1

The next step is to work out profit maximisation.

Profit Maximisation for a Monopolist

• Profit Maximisation occurs where MR=MC

In this example MC = $5 (a constant average cost means the MC=AC)

Therefore, $5 = 55 – 2P1
2P = 50
Therefore, P=25

To find out the Quantity we put 25 into the equation
Q=55-25
Q=30

To Calculate Profit for A Monopoly

Profit = Total revenue – Total Cost

Total Revenue = 25*30 = 750
Total Cost = 5 * 30 = 150

• Therefore, total profit for this section is = 600 (assuming there is no fixed cost)