Difficulty: Intermediate | Prerequisites: introductory supply and demand, basic calculus (derivatives), understanding of market structures.
Monopoly sits at the opposite end of the market-structure spectrum from perfect competition. Where competitive firms are price takers, a monopolist is the sole seller and therefore a price maker, choosing the point on the market demand curve that maximises profit. Understanding monopoly pricing, the role of demand elasticity, and the welfare losses that result is central to intermediate microeconomics and to policy debates about regulation, antitrust, and patents. You should be comfortable with marginal analysis (MR = MC) and the basics of consumer and producer surplus before working through these notes.
A monopolist maximises profit by producing where MR = MC, then charging the price consumers will pay for that quantity on the demand curve. Because MR < P for a single-price monopolist, output is lower and price is higher than under competition, creating deadweight loss. The firm's ability to mark up price over cost depends on how elastic demand is: less elastic demand means more monopoly power.
Monopoly
A market structure with a single seller facing the entire market demand curve. In simple terms, there is only one firm, so it gets to pick what price to charge.
Average revenue (AR)
Total revenue divided by quantity sold. For any firm, AR equals price, because TR = P x Q, so TR/Q = P.
Marginal revenue (MR)
The additional revenue from selling one more unit. For a monopolist, MR is always less than price because lowering the price to sell an extra unit means accepting a lower price on every unit already being sold.
Monopoly power (market power)
The ability to set price above marginal cost. Think of it as the firm's "pricing room" above its costs. Measured by the Lerner Index: (P - MC) / P.
Price elasticity of demand (Ed)
The percentage change in quantity demanded divided by the percentage change in price. A monopolist always produces in the elastic portion of the demand curve (where |Ed| > 1).
Natural monopoly
An industry where one firm can supply the entire market at lower cost than two or more firms, typically because of very large fixed costs and declining average cost. In simple terms, the technology makes it cheaper to have one big provider than several small ones.
Rent seeking
Spending resources to acquire, maintain, or protect monopoly profits rather than to produce goods. The maximum a monopolist would spend on rent seeking equals the monopoly profit itself.
Perfect (first-degree) price discrimination
Charging each consumer exactly their maximum willingness to pay. Under perfect price discrimination, the firm captures all consumer surplus, which falls to zero.
Deadweight loss (DWL)
The loss in total surplus that occurs because the monopolist restricts output below the competitive level. Even redistributing the monopolist's profit to consumers would not eliminate this inefficiency.
Lerner Index
A measure of monopoly power: L = (P - MC) / P = -1 / Ed. A higher Lerner Index means greater ability to mark up price above cost.
A monopolist maximises profit by choosing the output level where MR = MC, then reading the price off the demand curve at that quantity.
At the profit-maximising output, price does not equal marginal cost. This is a defining difference from perfect competition, where P = MC.
Because the monopolist must lower the price on all units to sell one more, MR lies below the demand curve (below price) at every output level.
Average revenue equals price at every output level (AR = P is always true, for any firm).
Marginal revenue equals price only under perfect competition, not under monopoly.
If a monopolist is currently operating where demand is inelastic (|Ed| < 1), it should cut output. Revenue rises when you sell fewer units in the inelastic range, and costs fall, so profit increases.
Example: if Ed = -0.15, the firm is deep in the inelastic portion and should reduce quantity.
At the profit-maximising point, demand is elastic but not infinitely elastic. The monopolist never voluntarily operates in the inelastic region of the demand curve.
The less elastic a firm's demand curve, the greater its monopoly power. Inelastic demand gives the firm more room to raise price above marginal cost.
The Lerner Index formalises this relationship: L = (P - MC) / P = -1 / Ed.
When |Ed| is close to 1 (barely elastic), the markup is very large.
When |Ed| is very large (highly elastic), the markup shrinks toward zero, approaching the competitive outcome.
As substitutes enter the market, demand facing the original monopolist becomes more elastic and the profit-maximising price declines.
Zinc Communications example: Zinc holds a patent on 3-D phone screens. As competitors introduce similar (non-identical) phones, Zinc's demand becomes more elastic and its optimal price falls.
Calculating price from MR and elasticity uses the inverse-elasticity pricing rule: P = MR / (1 + 1/Ed).
Example: MR = 20, Ed = -2.0. Then P = 20 / (1 + 1/(-2)) = 20 / 0.5 = 40.
Calculating price elasticity from price and marginal cost (assuming MR = MC at the optimum): Ed = -P / (P - MC), or equivalently use the Lerner Index rearranged.
Example: MC = 5, P = 20. Lerner = 15/20 = 0.75, so Ed = -1/0.75 = -1.33.
Example: MC = 5, P = 30. Lerner = 25/30 = 0.833, so Ed = -1/0.833 = -1.2.
A natural monopoly arises when economies of scale are so large that one firm can serve the market at lower average cost than two or more firms.
For a natural monopoly, marginal cost is always below average cost. This is what keeps average cost declining: each additional unit costs less than the average of all units so far.
Even taxing away a monopolist's profits and redistributing them to consumers does not eliminate the inefficiency. Output is still restricted below the competitive level, so deadweight loss remains.
Sirius-XM merger case study:
Two satellite radio providers merged into one, and the government did not challenge the merger.
Plausible reasons the monopoly may have limited impact on consumers:
Very large fixed costs mean the industry may be a natural monopoly, so one seller operates at lower cost than two.
Other forms of radio (terrestrial, internet streaming) are available, making demand for satellite radio relatively elastic, which limits the monopolist's pricing power.
The merged firm may achieve economies of scale and learning-by-doing, reducing costs.
All three reasons are plausible and complement each other.
Under perfect (first-degree) price discrimination, the monopolist charges each consumer their maximum willingness to pay. Consumer surplus falls to zero because the firm captures it all.
Third-degree price discrimination splits consumers into groups with different elasticities and charges each group a different price.
The group with less elastic demand pays a higher price.
Milk coupon example: retail price = $3.00, coupon price = $2.00. Coupon users have Ed = -2. Using the Lerner condition for each group (MC is the same for both), the elasticity for non-coupon users works out to -1.5.
Rent seeking: a monopolist will spend up to the full value of its monopoly profit to maintain its position (lobbying, legal battles, barriers to entry).
Maui Macadamia example: P = 360 - 4Q, MR = 360 - 8Q, MC = 4Q.
Profit-maximising Q: set MR = MC, so 360 - 8Q = 4Q, giving Q = 30 and P = 240.
Monopoly profit = (P - AC) x Q. Total revenue = 240 x 30 = 7,200. Total cost = area under MC from 0 to 30 = 0.5 x 4 x 30 x 30 / 2 = 1,800. Profit = 5,400.
The maximum the firm would spend on rent seeking = 5,400.
Profit-maximisation rule: MR = MC
Average revenue: AR = TR / Q = P (true for all firms)
Marginal revenue for a linear demand curve P = a - bQ: MR = a - 2bQ
Lerner Index: L = (P - MC) / P = -1 / Ed
Inverse-elasticity pricing rule: P = MR / (1 + 1/Ed)
Rearranged: P x (1 + 1/Ed) = MC (at the optimum where MR = MC)
Price elasticity from the Lerner Index: Ed = -1 / L = -(P) / (P - MC)
Monopoly profit = TR - TC. For rent-seeking questions, this is the maximum the firm would spend to maintain its monopoly.
Patent-protected products (pharmaceuticals, novel tech like Zinc's 3-D phone) behave as monopolies until substitutes arrive, at which point demand becomes more elastic and prices fall.
The Sirius-XM satellite radio merger illustrates how natural monopoly conditions and the availability of substitutes (internet radio, AM/FM) shape the real impact of market consolidation on consumers.
Students often think a monopolist can charge any price it wants. It cannot: it is constrained by the demand curve. It chooses the best point on that curve, not a price out of thin air.
Students sometimes confuse AR and MR. AR = P for all firms. MR = P only under perfect competition. For a monopolist, MR < P at every output level.
A common error is thinking that redistributing monopoly profits to consumers fixes the welfare problem. It does not: the deadweight loss from restricted output remains.
Students assume a monopolist always operates where demand is inelastic. The opposite is true: a profit-maximising monopolist always operates in the elastic region of the demand curve.
⚠️ Know the difference between AR and MR for a monopolist. Expect a true/false question testing whether MR = P (it does not).
⚠️ Be ready to use the inverse-elasticity pricing rule, P = MR / (1 + 1/Ed), to calculate the profit-maximising price from MR and elasticity.
⚠️ Understand that "P = MC at the profit-maximising output" is a competitive result, not a monopoly result. This is a common multiple-choice trap.
⚠️ Rent-seeking questions often ask for the maximum a monopolist would spend. The answer is always the monopoly profit itself.
⚠️ Perfect price discrimination eliminates consumer surplus entirely. Expect a direct question on this.
True or false: For a monopolist, average revenue equals price at every output level. (True)
True or false: A profit-maximising monopolist produces where P = MC. (False, it produces where MR = MC)
Fill in the blank: The ________ elastic a firm's demand curve, the greater its monopoly power. (less)
True or false: Under perfect price discrimination, consumer surplus is positive. (False, it equals zero)
True or false: If a monopolist is operating where demand is inelastic, it should increase output. (False, it should cut output)
Q: Which of the following is NOT true for monopoly: (a) MR < P, (b) AR = P, (c) P = MC at profit max, (d) demand is downward sloping?
A: (c). A monopolist produces where MR = MC, not where P = MC. P > MC at the profit-maximising output.
Q: A monopolist's MR is $20 and the price elasticity of demand is -2.0. What is the profit-maximising price?
A: Using P = MR / (1 + 1/Ed) = 20 / (1 + 1/(-2)) = 20 / 0.5 = $40.
Q: At the current output level a monopolist faces Ed = -0.15. Should the firm raise or cut output?
A: Cut output. The firm is in the inelastic region (|Ed| < 1), where reducing quantity raises total revenue and lowers total cost.
Q: A grocery store charges $3.00 for milk (non-coupon) and $2.00 with a coupon. If coupon users have Ed = -2 and the store maximises profit, what is Ed for non-coupon users?
A: -1.5. Use the Lerner condition for each group. With a common MC, the condition implies MC = P(1 + 1/Ed) for each group. Solving: MC = 2(1 + 1/(-2)) = 1. Then 1 = 3(1 + 1/Ed), so 1/Ed = (1/3 - 1) = -2/3, giving Ed = -1.5.
Q: What is the maximum Maui Macadamia would spend on rent seeking given P = 360 - 4Q, MR = 360 - 8Q, MC = 4Q?
A: 5,400. Set MR = MC: 360 - 8Q = 4Q, so Q = 30, P = 240. TR = 7,200. TC (area under MC) = 1,800. Profit = 5,400.
Q: Under perfect price discrimination, what happens to consumer surplus?
A: It equals zero. The monopolist captures the entire surplus by charging each buyer their maximum willingness to pay.
Monopoly pricing connects directly to welfare economics: deadweight loss from monopoly is the starting point for understanding why governments regulate or break up monopolies. The elasticity concepts here carry over to oligopoly and monopolistic competition, where firms also face downward-sloping demand but with more substitutes. Price discrimination links to consumer surplus analysis and is a stepping stone to understanding bundling, two-part tariffs, and other advanced pricing strategies covered later in intermediate micro.
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