Source: Lecture Notes of Prof. Guoqiang Tian, Texas A&M University
Tags: monopoly, monopolist, price maker, MR less than P, deadweight loss, welfare cost, price discrimination, monopolistic competition, product differentiation, oligopoly, barriers to entry, limit pricing, market structure spectrum
Monopoly is the polar opposite of perfect competition: a single firm, downward-sloping demand, and the ability to set price above marginal cost. Monopolists produce less and charge more than a competitive industry would, creating a welfare (deadweight) loss. In between these extremes sit monopolistic competition (many firms, differentiated products, free entry driving long-run profit to zero) and oligopoly (few large firms, mutual interdependence, barriers to entry). Price discrimination allows monopolists to capture more surplus.
Monopoly
A market structure in which there is only one producer of a product that has no close substitutes. The firm is the industry.
Natural monopoly
A monopoly arising from large economies of scale: the first firm in the market achieves such low per-unit costs that no rival can profitably enter.
Price maker
A monopolist can choose its price (subject to the demand curve), unlike a competitive firm which takes the market price as given.
Marginal revenue for a monopolist
Always less than price (except for the first unit) because reducing price to sell one more unit means accepting a lower price on all units. For a linear demand p = a + bq, MR = a + 2bq (the slope of MR is twice the slope of the demand curve).
Relationship between MR, price, and elasticity
MR = P(1 - 1/|Ed|). When demand is elastic (|Ed| > 1), MR > 0. When unit elastic (|Ed| = 1), MR = 0. When inelastic (|Ed| < 1), MR < 0. A profit-maximising monopolist always operates on the elastic portion of its demand curve.
Monopoly profit-maximising rule
Produce where MR = MC (provided AR >= AVC), then read the price from the demand curve at that quantity.
Welfare cost of monopoly (deadweight loss)
The net loss in social welfare because the monopolist restricts output below the competitive level. Consumers and the economy lose more than the monopolist gains.
Price discrimination
Selling the same good at different prices to different buyers. Conditions needed: resale not possible, ability to segment the market into identifiable groups, monopoly power, different demand elasticities across groups.
Perfect (first-degree) price discrimination
The monopolist charges each buyer the maximum they are willing to pay for each unit. The demand curve becomes the MR curve. The monopolist captures the entire consumer surplus.
Monopolistic competition
A market structure with many firms, slightly differentiated products, freedom of entry and exit, and significant non-price competition (e.g. advertising). Each firm faces a downward-sloping demand curve.
Oligopoly
A market structure characterised by a few large firms producing most or all of the industry's output. Key features: economies of scale, mutual interdependence, non-price competition, price rigidity, temptation to collude, incentive to merge, and substantial barriers to entry.
Limit pricing
An oligopolist sets a price low enough to make entry unprofitable for potential competitors, thereby protecting its market position.
Exclusive ownership of a unique resource (e.g. DeBeers and diamond mines).
Economies of scale (natural monopoly): large-scale production has much lower unit costs, so a single firm can underprice any new entrant.
Government-granted monopoly: patents (17 years in the US), copyrights, licences, exclusive franchises (e.g. public utilities, where the government regulates the price in exchange for the franchise).
The monopolist faces the market demand curve, which slopes downward. Key relationships:
TR = P * q
AR = TR / q = P (average revenue equals price)
MR = delta TR / delta q, which is less than P for all units after the first
For a linear inverse demand P = a + bq (where b < 0), MR = a + 2bq. The MR curve has the same intercept as the demand curve but twice the slope.
The link to elasticity: MR = P(1 - 1/|Ed|).
When |Ed| > 1 (elastic): MR > 0
When |Ed| = 1 (unit elastic): MR = 0
When |Ed| < 1 (inelastic): MR < 0
A monopolist would never produce on the inelastic portion of demand because MR would be negative there, and reducing output would increase both revenue and lower costs.
Set MR = MC to find q*.
Read p* from the demand curve at q*.
TR = p* q.
TC = ATC q.
Profit = TR - TC.
If AR < AVC at all output levels, the firm shuts down (q* = 0).
If AR is between AVC and ATC, the monopolist operates at a loss but smaller than TFC.
Unlike perfect competition, a monopolist can earn positive economic profits in the long run because barriers to entry prevent new firms from entering.
In perfect competition, each price maps to a unique quantity (the MC curve is the supply curve). For a monopolist, different demand curves can lead to different prices for the same output level. Therefore, there is no unique price-quantity relationship, and hence no supply curve.
If a competitive industry is taken over by a single monopolist (using the industry supply curve as its MC):
The monopolist produces less output (qm < qc).
The monopolist charges a higher price (pm > pc).
Income is redistributed from consumers to the monopolist.
A deadweight welfare loss arises from the output restriction.
The monopolist can increase profits by charging different prices to different groups.
Under perfect price discrimination, the monopolist charges each buyer's maximum willingness to pay. The demand curve becomes the marginal revenue curve, output expands to the competitive level, and the monopolist captures the entire area under the demand curve above MC. While output is efficient, all surplus goes to the producer.
Short run: same as a monopolist. Set MR = MC, earn economic profit or loss.
Long run: free entry and exit drive economic profit to zero. Entry shifts each firm's demand curve left (demand is shared among more firms) until P = ATC. The firm still faces a downward-sloping demand curve, so P > MC at equilibrium. This means some allocative inefficiency compared to perfect competition.
Key result: in long-run equilibrium, the monopolistically competitive firm produces on the downward-sloping portion of its ATC, meaning it operates with excess capacity.
A few large firms dominate the market. Key features:
Economies of scale make it efficient for a small number of firms to supply the market.
Mutual interdependence: each firm's actions affect rivals, so strategic behaviour matters.
Non-price competition (advertising, product differentiation) and price rigidity (fear of price wars).
Temptation to collude (illegal in the US) to maximise collective profits.
Incentive to merge (the ultimate collusion is monopoly).
Barriers to entry:
Economies of scale: an incumbent can undercut a new entrant by operating at lower unit cost.
Cost structure: if the incumbent has lower costs (e.g. from learning-by-doing), it can set a limit price between its own ATC and the entrant's ATC, making entry unprofitable.
For linear inverse demand P = a + bq: MR = a + 2bq
MR = P(1 - 1/|Ed|)
Monopoly profit max: MR = MC, then read P from demand curve
Profit = (P - ATC) * q
Deadweight loss = area between demand curve and MC curve, from qm to qc
Perfect price discrimination: D curve = MR curve, profit = area under D above MC
⚠️ The MR curve has twice the slope of a linear demand curve. This is a standard derivation question.
⚠️ A profit-maximising monopolist always operates on the elastic portion of demand. If demand is inelastic, MR < 0, and the firm could increase profit by reducing output.
⚠️ There is no supply curve for a monopolist. Be prepared to explain why (the same quantity can correspond to different prices depending on the demand curve).
⚠️ In monopolistic competition, long-run economic profit is zero (like competition) but price exceeds MC (like monopoly). The firm has excess capacity.
⚠️ Understand the welfare comparison: monopoly vs. competition. The key losses are higher price, lower output, and deadweight loss.
⚠️ Know the conditions for price discrimination: no resale, market segmentation, monopoly control, different elasticities.
Q: Why is marginal revenue less than price for a monopolist?
A: To sell one more unit, the monopolist must lower the price on all units (not just the marginal one). The revenue gain from the extra unit is offset by the revenue loss from the price reduction on all previous units. So MR < P.
Q: A monopolist faces demand P = 100 - 2q and has MC = 20. What is the profit-maximising price and quantity?
A: MR = 100 - 4q. Set MR = MC: 100 - 4q = 20, so q* = 20. P* = 100 - 2(20) = 60.
Q: Why does a monopolist have no supply curve?
A: Because the profit-maximising output depends on the position and shape of the demand curve. Different demand curves can lead to different prices for the same quantity. There is no unique price-quantity mapping.
Q: What happens in the long run under monopolistic competition if firms are earning economic profits?
A: New firms enter the industry, attracted by the profits. Each existing firm's demand curve shifts left as market demand is divided among more sellers. Entry continues until economic profit falls to zero, and each firm's demand curve is tangent to its ATC curve.
Q: Under what conditions can a monopolist practise price discrimination?
A: The good cannot be resold between buyers. The monopolist must be able to segment the market into identifiable groups with different demand elasticities. And the firm must have monopoly control over the product.
Q: How does the welfare cost (deadweight loss) of monopoly arise?
A: The monopolist restricts output below the competitive level. Units between qm and qc have a marginal value to consumers (read from the demand curve) that exceeds the marginal cost of producing them. Because these units are not produced, the potential gains from trade are lost. This lost surplus is the deadweight loss.
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