Monopoly: sources of power and equilibrium – Market Structures (Senior 5 Economics) | Ganzaa

Market Structures

Lessons

Senior 5 · Economics

Market Structures

5 lessons

Lesson 3 of 5

Monopoly: sources of power and equilibrium

45 min

One grid, one supplier

Every home in Rwanda that is connected to the national electricity grid buys its power from the same supplier, Rwanda Energy Group (REG), through its utility company. No rival company has built a second set of poles and wires down the same streets, and none is likely to. In most towns, piped water also comes from a single supplier, the Water and Sanitation Corporation (WASAC). The prices both charge are not set freely by the companies: they are approved by the Rwanda Utilities Regulatory Authority (RURA). This lesson asks why such markets end up with one seller, how a single seller chooses its price and output, and why governments rarely leave it alone.

Definition

Monopoly: a market structure with a single seller of a product that has no close substitute, protected by barriers that stop other firms entering. The firm is the industry, so its demand curve is the market demand curve, which slopes downward.

Price maker: a firm that can choose its price, accepting that a higher price means it sells less. A monopolist is a price maker: it can choose the price or the quantity, but not both, because the demand curve links them.

Forms of monopoly

Form	Meaning	Illustration
Natural monopoly	Economies of scale are so large that one firm can supply the whole market at a lower average cost than two or more could	Electricity transmission lines, water mains, a railway track
Statutory (legal) monopoly	A monopoly created by law or by an exclusive government licence	A national postal service's sole right to carry certain letters
Public monopoly	A monopoly owned by the state	A state-owned utility company
Private monopoly	A monopoly owned by private shareholders	A private firm holding the only patent on a medicine
Spatial (local) monopoly	The only seller within a distance that buyers find too costly to travel beyond	The only fuel station or pharmacy for many kilometres on a rural road
Simple and discriminating monopoly	A simple monopolist charges every buyer the same price; a discriminating one charges different prices for the same product (Lesson 4)	One fare for all, versus cheaper student tickets
Collusive monopoly (cartel)	Several firms agree to act as if they were one seller	Producers jointly fixing output and price, as OPEC tries to for crude oil

Sources of monopoly power: the barriers to entry

A monopoly lasts only as long as something keeps rivals out. The main barriers are:

Economies of scale. If average cost keeps falling over the whole range of output the market wants, the established firm can always undercut a smaller newcomer (the natural monopoly case, drawn below).
Legal barriers. Exclusive licences, franchises and government decrees give one firm the sole right to supply.
Patents, copyrights and trademarks. The law gives an inventor the sole right to make and sell a new product for a period, usually about 20 years for a patent, to reward the cost of research.
Control of an essential raw material or of the only suitable site.
Very large start-up capital, such as the cost of building a national network, which few investors can raise.
Strategic barriers: heavy advertising and brand loyalty, exclusive deals with distributors, or cutting prices sharply whenever a rival appears (predatory pricing).
Mergers and takeovers, which can absorb rivals until one firm remains.

Definition

Natural monopoly: an industry in which the long-run average cost curve is still falling where it meets market demand, so a single firm supplies the market at a lower cost than any number of competing firms could. In the diagram one firm produces Q1 at average cost A1; two firms splitting the market would each produce half as much at the higher cost A2.

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Revenue under monopoly: why MR lies below AR

To sell one more unit, a monopolist must lower its price, and (if it is a simple monopolist) it must lower it on all the units it sells, not just the extra one. So the extra revenue from the extra unit is less than its price: $\text{MR} < \text{AR}$ at every output after the first.

Worked example 1: the revenue schedule for P = 100 − 2Q

Q	P = AR (Frw)	TR = P × Q	MR = ΔTR
10	80	800	–
11	78	858	58
20	60	1,200	–
21	58	1,218	18
25	50	1,250	–
26	48	1,248	−2

Selling the 11th unit raises revenue by only 58, although its price is 78: the firm gains 78 on the new unit but loses 2 Frw on each of the 10 units it was already selling, $78 - 10 \times 2 = 58$ . For a straight-line demand curve $P = a - b Q$ , the MR curve is

\text{MR} = a - 2bQ

It starts at the same point on the price axis and is twice as steep, cutting the quantity axis halfway along. Here $\text{MR} = 100 - 4Q$ , which is zero at $Q = 25$ , where TR is at its maximum of 1,250.

Important

A monopolist never produces where demand is inelastic. Where demand is inelastic, MR is negative, so cutting output would raise revenue and lower costs at the same time. Any profit-maximising monopolist with positive marginal cost therefore produces on the elastic, upper part of its demand curve, where MR is positive.

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Equilibrium of the monopolist

Like every firm, a monopolist maximises profit where $\text{MC} = \text{MR}$ . The difference is in the next step: it reads the price off the demand (AR) curve, which lies above MR.

Find the output where MC cuts MR from below: $Q_{m}$ .
Go up from $Q_{m}$ to the demand curve to find the price $P_{m}$ .
Find average cost at $Q_{m}$ on the ATC curve: $C_{m}$ .
Profit $= (P_m - C_m) \times Q_m$ , the shaded rectangle.

Because barriers stop new firms entering, this abnormal profit can last in the long run, unlike under perfect competition. A monopolist can make a loss in the short run if demand is weak (AR below ATC at every output), but it will not stay in the industry in the long run unless it earns at least normal profit. Note also that a monopolist has no supply curve: the quantity it offers at a given price depends on the shape of demand, not on price alone.

Worked example 2: monopoly against competition, in numbers

A firm protected by a patent faces demand $P = 100 - 2 Q$ . Its marginal and average cost are constant at 20 (illustrative units).

Monopoly. $\text{MR} = 100 - 4Q$ . Set $\text{MR} = \text{MC}$ :

100 - 4Q = 20 \;\Rightarrow\; Q_m = 20, \qquad P_m = 100 - 2(20) = 60

\text{Profit} = (60 - 20) \times 20 = 800

Perfect competition. Price is driven to marginal cost: $100 - 2Q = 20 \Rightarrow Q_c = 40,\; P_c = 20$ .

The cost of monopoly. Consumer surplus falls from $\frac{1}{2} \times 40 \times 80 = 1\,600$ to $\frac{1}{2} \times 20 \times 40 = 400$ . Of the 1,200 lost, 800 goes to the monopolist as profit, and

\text{Deadweight loss} = \frac{1}{2} \times (40 - 20) \times (60 - 20) = 400

is gained by nobody: units that consumers valued at more than they cost to make are simply not produced.

Monopoly judged: advantages and disadvantages

Possible advantages	Disadvantages
Economies of scale can give lower costs than many small firms (the natural monopoly case)	Higher price and lower output than under competition, with a deadweight loss
Abnormal profits can fund research and new products (the reason patents exist)	Allocative inefficiency: $P > \text{MC}$
Avoids wasteful duplication of networks such as pipes and power lines	Productive inefficiency: no pressure to produce at minimum ATC, so costs may drift up (X-inefficiency)
A public monopoly can cross-subsidise poorer users or remote areas	Less choice for consumers and less pressure to improve quality
Stable supply and planning in industries of national importance	Transfers income from consumers to owners; may use its power against suppliers

Warning

Three slips to avoid. (1) Reading the price off the MR curve: the price is always read up from $Q_{m}$ to the demand curve. (2) Drawing MR meeting the quantity axis at the same point as demand: for a straight-line demand, MR cuts it halfway. (3) Saying "a monopolist charges the highest price it can": it charges the price that maximises profit, and a higher price would lose more in sales than it gains.

Marginal Revolution University, "Maximizing Profit Under Monopoly" (about 11 minutes). Watch how the profit-maximising quantity is found where MR = MC and the price then read from the demand curve, the same three steps as in the diagram above.

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Practice

Define monopoly and explain why a monopolist's demand curve is the market demand curve.
Distinguish between a natural monopoly and a statutory monopoly, with an example of each.
Explain four barriers to entry that create and protect monopoly power.
For the demand curve $P = 60 - 3 Q$ : (a) write the MR equation; (b) find the output at which TR is greatest and the value of TR there.
A monopolist faces $P = 80 - Q$ and has constant MC = AC = 20. Find its output, price and profit, and the deadweight loss compared with perfect competition.
Explain why a profit-maximising monopolist never produces on the inelastic part of its demand curve.
With the help of a diagram, explain how a monopolist can earn abnormal profit in the long run.
"Monopolies are always against the public interest." Discuss, with reference to utilities in Rwanda.

Show answersHide answers

A single seller of a product with no close substitute, protected by barriers to entry. Because it is the only firm, the whole market's demand is its demand, which slopes down.
A natural monopoly arises from economies of scale so large that one firm supplies the market most cheaply (electricity or water networks). A statutory monopoly is created by law or exclusive licence (a postal service's sole right to carry letters).
Any four: economies of scale; legal licences; patents and copyrights; control of raw materials; large capital needs; brand loyalty and advertising; predatory pricing; mergers.
(a) MR = 60 − 6Q. (b) MR = 0 at Q = 10; P = 60 − 30 = 30; TR = 300.
MR = 80 − 2Q = 20 gives Q = 30, P = 50, profit = (50 − 20) × 30 = 900. Competition: 80 − Q = 20 gives Q = 60. DWL = ½ × (60 − 30) × (50 − 20) = 450.
Where demand is inelastic, MR is negative. Cutting output would raise TR and also save costs, so profit rises; the firm keeps cutting until it is on the elastic part, where MR is positive and can equal MC.
Diagram as in the lesson: MC = MR gives Qm; price Pm from AR; ATC at Qm below Pm; shaded profit. Barriers to entry stop new firms entering, so the profit is not competed away.
Against the public interest: higher prices, restricted output, deadweight loss, less pressure to cut costs. In its favour: one electricity grid or water network avoids wasteful duplication and gives economies of scale; profits can fund investment; a public or regulated monopoly can extend service to poor or remote areas. In Rwanda, RURA approves utility tariffs, which limits the abuse. Conclusion: not always; it depends on the source of the monopoly and on regulation.

Sources and credits

Roles of REG, WASAC and RURA: Rwanda Utilities Regulatory Authority, the regulator of energy, water and other utilities; stated as general facts.
Video: Maximizing Profit Under Monopoly, Marginal Revolution University, embedded from YouTube.

Written by Ganzaa: the text, the four diagrams (values computed from the stated demand and cost functions), the tables, the worked examples and the practice items. All prices, costs and quantities in the examples are illustrative.

1One grid, one supplier

2Forms of monopoly

3Sources of monopoly power: the barriers to entry

4Revenue under monopoly: why MR lies below AR

5Equilibrium of the monopolist

6Monopoly judged: advantages and disadvantages