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**

Thank you!

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it is nice in a glance..but more clarfication is needed.

What is channel pricing?

how is MR twice steep as AR curve?

yawnnnnnnn