MGEA02H3 Chap.8 Monopoly and Market Power
Monopoly and Market Power
Restricting output
A monopolist faces market demand, so marginal revenue lies below price: for P = a − bQ, MR = a − 2bQ. It produces where MR = MC and charges the price buyers will pay for that quantity, read from demand.
It always operates on the elastic part of demand, since MR = P(1 − 1/ED) is positive only there.
Welfare and regulation
The course measures welfare as the gain to society, consumer surplus plus profit, and the deadweight loss of monopoly comes from producing too little.
A natural monopoly can be regulated to price at average cost, taking the larger root of the quadratic, or at marginal cost with a subsidy for the fixed cost.
A per-unit tax raises the monopoly price by less than the tax.
What the answer keys reward
The keys write marginal revenue from demand, equate it with marginal cost, read the price from demand, and compute the gain to society as consumer surplus plus profit before and after any change. For regulation they solve the average-cost quadratic and take the larger root.
For taxes they set MR equal to MC plus the tax and measure the excess burden between demand and marginal cost over the lost units.
How this topic connects to later chapters
Chapter 9 places oligopoly between the two extremes studied so far: a cartel behaves like the monopolist of this chapter, and the Nash outcome produces more than a monopoly but less than a competitive industry.
The two-triangles-and-rectangle measurement of a monopoly tax also anticipates the layered surplus areas of the tariff problems at the end of the course.
What this chapter covers
- 01
Marginal revenue below demand
- 02
MR = MC and price from demand
- 03
Monopoly and elasticity
- 04
Gain to society and deadweight loss
- 05
Average-cost and marginal-cost regulation
- 06
A per-unit tax on a monopolist
Worked example · free
Regulating a natural monopoly at average cost
- 2MR = 50 − 0.02Q = 10 gives 2,000 units at $30, with $25,600 profit.
- 2The gain to society is 20,000 + 25,600 = $45,600.
- 2Average-cost pricing solves 0.01Q² − 40Q + 14,400 = 0; take Q = 3,600 at $14.
- 2With zero profit the gain is consumer surplus, $64,800, up $19,200.
Key terms
- Marginal Revenue
- Marginal revenue is the change in total revenue from selling one more unit.
- Gain to Society
- The gain to society is consumer surplus plus producer surplus, the course’s measure of total welfare.
- Natural Monopoly
- A natural monopoly is a market where average cost is still falling at the output demanded, so one firm serves it most cheaply.
- Average-Cost Pricing
- Average-cost pricing is regulation that sets price equal to average cost, leaving the firm zero profit.
- Deadweight Loss
- Deadweight loss is surplus that no one receives because valuable units are not produced.
Monopoly and Market Power FAQ
Why is a monopolist’s marginal revenue below its price?
To sell one more unit the monopolist must lower the price on every unit it sells, not just the last one. The revenue lost on the earlier units is subtracted from the price of the extra unit.
Why would a monopolist never produce where demand is inelastic?
Marginal revenue equals P(1 − 1/ED), which is negative when demand is inelastic. Cutting output there would raise revenue and lower cost, so a profit-maximising firm always moves to the elastic part.
Which root do I take when regulating price at average cost?
Setting demand equal to average cost gives a quadratic with two roots, both with zero profit. Take the larger quantity, because it delivers the bigger gain to society, as the course answers state.
Does a monopolist have a supply curve?
No. A monopolist chooses quantity and price together from its demand and cost curves, so there is no schedule of quantities it would offer at given prices independent of demand. A shift in demand can change price, quantity or both in ways a supply curve could not describe.
Exam move
Solve one linear monopoly by both the profit function and MR = MC, check with the elasticity rule, then compute the gain to society under monopoly, competition and average-cost regulation. Practise one statement set on monopoly behaviour each session, judging each claim against MR = MC and the elasticity rule.
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