Profit and Price in a Monopoly

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.

 monopoly-diagram

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

monopoly-price

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

monopoly prices

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)

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By on December 18th, 2016

6 thoughts on “Profit and Price in a Monopoly

  1. Thank you!

    I had a similar question due tomorrow, and you’ve been a lifesaver. I was completely lost before 🙂

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