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Barriers to entry, price-making, MR < P, deadweight loss, natural monopoly, and price discrimination
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A monopoly is a market with a SINGLE seller of a product that has no close substitutes, protected by significant barriers to entry. Monopolies arise from:
Unlike a competitive firm, a monopolist faces the entire market demand curve, which is downward-sloping. To sell more, it must lower price.
Because the monopolist must lower price on ALL units (assuming no price discrimination) to sell one more, for every unit beyond the first. For a linear demand , the corresponding โ same intercept, twice the slope.
Why is marginal revenue less than price for a single-price monopolist? Use the words "lower price on all units" in your explanation.
To sell one additional unit, the monopolist must move down its downward-sloping demand curve, which means lowering the price NOT just on the new unit, but on all units sold. So MR equals the price of the new unit MINUS the lost revenue from charging less on the previous units. That subtraction makes for every unit after the first.
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The monopolist still produces where . But it then charges the price consumers are willing to pay for that quantity, read off the demand curve: . Compared to perfect competition, the monopoly produces a lower and charges a higher .
If at , monopoly earns positive economic profit. Because barriers to entry block competitors, monopoly profits can persist in the long run โ unlike perfect competition.
At , . There are units that consumers value above their MC of production but the monopolist won't produce. That gap creates deadweight loss: the triangle between MC, demand, and the vertical line at .
Monopolies are allocatively inefficient () and typically productively inefficient as well (no force pushes them to produce at min ATC).
If the monopolist can identify groups with different willingness to pay AND prevent resale, it can charge different prices to different buyers (e.g., student discounts, airline fares). Perfect price discrimination charges each buyer their maximum willingness to pay; it eliminates DWL but transfers ALL consumer surplus to the firm.
For natural monopolies, regulators may impose:
For other monopolies, antitrust law (breaking up firms, blocking mergers) is the main tool.
Linear demand for a monopoly is . (a) Write the MR function. (b) If MC is constant at $20, find the profit-maximizing quantity and price.
(a) For linear demand , .
(b) Set : . Then 60}60.
For the monopoly in problem 2 (, , , ), suppose ATC at is $30. Compute (a) total profit and (b) deadweight loss versus the perfectly competitive outcome ().
(a) Per-unit profit = P_M - ATC = 60 - 30 = \30$30 \times 20 = \boxed{$600}$.
(b) Competitive outcome: P = MC = \20 \Rightarrow Q_C = 100 - 2P)/220 = 100 - 2Q \Rightarrow Q_C = 40$.
A natural monopoly's ATC declines throughout the relevant output range (continuous economies of scale). (a) Why is this market structure called a "natural" monopoly? (b) Why does setting price at cause the firm to lose money? (c) What price/regulation balances efficiency with the firm's solvency?
(a) Because economies of scale are so large that one firm produces at lower ATC than two or more firms could; competition is unsustainable. The market "naturally" leads to a single producer.
(b) When ATC is continuously falling, MC lies BELOW ATC at every Q. Setting means , so per-unit revenue is less than per-unit cost โ the firm loses money on every unit. Without a subsidy, it cannot survive.
(c) Fair-return regulation: set at the regulated quantity. The firm earns zero economic profit (covers all costs including opportunity cost). is higher and lower than the unregulated monopoly outcome, but DWL is not eliminated entirely. This is the standard "second-best" solution for natural monopoly.
Compare three pricing scenarios for the same monopolist with linear demand and constant MC: (a) single-price monopoly, (b) perfect price discrimination, (c) perfectly competitive equilibrium. Rank them on (i) consumer surplus, (ii) producer surplus, (iii) total surplus, (iv) deadweight loss. Provide a one-sentence justification for each ranking.
Let denote the maximum (efficient) total surplus.
(i) Consumer surplus: Competitive (largest) > Single-price monopoly > Perfect PD (zero). Justification: PD captures every unit of CS for the firm; competitive markets give consumers the largest surplus.
(ii) Producer surplus: Perfect PD (largest, captures full ) > Single-price monopoly > Competitive. Justification: PD turns all of CS into PS; the competitive firm earns zero economic profit in long run.
(iii) Total surplus: Competitive = Perfect PD (, both efficient) > Single-price monopoly. Justification: PD is allocatively efficient because the monopolist serves every buyer whose willingness to pay exceeds MC, eliminating DWL โ but transfers all surplus to the seller.
(iv) Deadweight loss: Single-price monopoly (positive DWL) > Competitive = Perfect PD (both zero). Justification: only the single-price monopoly restricts below .
DWL is the triangle between demand and MC from to :
DWL = \tfrac{1}{2}(20)(40) = \boxed{\400}$.