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Lecture # 16 Monopoly Lecturer: Martin Paredes

Lecture # 16 Monopoly Lecturer: Martin Paredes. Outline. The Monopolist's Profit Maximization Problem The Profit Maximization Condition Equilibrium The Inverse Elasticity Pricing Rule The Welfare Economics of Monopoly. Monopoly Market.

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Lecture # 16 Monopoly Lecturer: Martin Paredes

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  1. Lecture # 16 Monopoly Lecturer: Martin Paredes

  2. Outline • The Monopolist's Profit Maximization Problem • The Profit Maximization Condition • Equilibrium • The Inverse Elasticity Pricing Rule • The Welfare Economics of Monopoly

  3. Monopoly Market Definition: A monopoly market consists of a single seller facing many buyers. Assumption: There are barriers to entry.

  4. Profit Maximisation • The monopolist's objective is to maximise profits: Max (Q) = TR(Q) – TC(Q) = P(Q)· Q – C(Q) Q where P(Q) is the (inverse) market demand curve.

  5. Profit Maximisation • Profit maximizing condition for a monopolist: dTR(Q) = dTC(Q) …or… MR(Q) = MC(Q) dQ dQ • In other words, the monopolist sets output so that the marginal profit of additional production is just zero.

  6. Profit Maximisation • Recall that a perfect competitor sets P = MC, because MR = P. • This is not true for the monopolist because the demand it faces is NOT flat. • As a result, MR < P

  7. Profit Maximisation • Since TR(Q) = P(Q) · Q, then: dTR(Q) = MR(Q) = P(Q) + dP(Q) · Q dQ dQ • In perfect competition, demand is flat, meaning dP(Q)/dQ = 0, so MR = P. • For a monopoly, demand is downward-sloping, meaning dP(Q)/dQ < 0, so MR < P.

  8. Example: Marginal Revenue Price Price Competitive firm Monopolist Demand facing firm Demand facing firm P0 P0 C P1 B A B A q q+1 Firm output Q0 Q0+1 Firm output

  9. Price Example: Marginal Revenue Curve and Demand The MR curvelies below the demand curve. P(Q0) P(Q), the (inverse) demand curve Quantity Q0

  10. Price Example: Marginal Revenue Curve and Demand The MR curvelies below the demand curve. P(Q0) P(Q), the (inverse) demand curve MR(Q0) MR(Q), the marginal revenue curve Quantity Q0

  11. Example: Marginal revenue for linear demands • Suppose demand is linear: P(Q) = a – bQ • Total revenue is TR = Q*P(Q) = aQ – bQ2 • Marginal revenue is: MR = dTR = a – 2bQ dQ • So, for linear demands, marginal revenue has twice the slope of demand.

  12. Market Power Definition: An agent has market power if she can affect the price that prevails in the market through her own actions. • Sometimes this is thought of as the degree to which a firm can raise price above marginal cost.

  13. Shutdown Condition • In the short run, the monopolist shuts down if the profit-maximising price does not cover AVC (or average non-sunk costs). • In the long run, the monopolist shuts down if the profit-maximising price does not cover AC.

  14. Example: Profit maximisation • Suppose: P(Q) = 100 – Q TC(Q) = 100 + 20Q + Q2 • Marginal revenue is: MR = dTR = 100 – 2Q dQ • Marginal cost is: MC = dTC = 20 + 2Q dQ • MR = MC ==> 100 – 2Q = 20 + 2Q ==> Q* = 20 P* = 80

  15. Example: Profit maximisation • In equilibrium Q* = 20 P* = 80 • Observe that: AVC = 20 + Q* = 40 AC = 100 + 20 + Q* = 45 Q* • Hence, P* > AVC and P* > AC

  16. Price Example: Positive Profits for Monopolist 100 Demand curve 100 Quantity

  17. Price Example: Positive Profits for Monopolist 100 MR Demand curve 50 100 Quantity

  18. Price Example: Positive Profits for Monopolist MC 100 MR 20 Demand curve 50 100 Quantity

  19. Price Example: Positive Profits for Monopolist MC 100 MR 20 Demand curve 20 50 100 Quantity

  20. Price Example: Positive Profits for Monopolist MC 100 E 80 MR 20 Demand curve 20 50 100 Quantity

  21. Price Example: Positive Profits for Monopolist MC AVC 100 E 80 MR 20 Demand curve 20 50 100 Quantity

  22. Price Example: Positive Profits for Monopolist MC AVC 100 E 80 AC MR 20 Demand curve 20 50 100 Quantity

  23. Price Example: Positive Profits for Monopolist MC AVC 100 E 80 : Profits AC MR 20 Demand curve 20 50 100 Quantity

  24. Profit Maximisation Notes: A monopolist has less incentive to increase output than the perfect competitor: for the monopolist, an increase in output causes a reduction in its price. Profits can remain positive in the long run because of the assumption that there are barriers to entry.

  25. Profit Maximisation Notes: • A monopolist does not have a supply curve: because price is determined endogenously by the demand: • The monopolist picks a preferred point on the demand curve. • Alternative view: the monopolist chooses output to maximize profits subject to the constraint that price be determined by the demand curve.

  26. Inverse Elasticity Pricing Rule • We can rewrite the MR curve as follows: MR = P + dP · Q dQ = P + dP · Q · P dQ P = P 1 + dP · Q dQ P = P 1 + 1  ( ) ( )

  27. Inverse Elasticity Pricing Rule • Given that  is the price elasticity of demand: • When demand is elastic ( < -1), then the marginal revenue is positive (MR > 0). • When demand is unit elastic ( = -1), then the marginal revenue is zero (MR= 0). • When demand is inelastic ( > -1), then the marginal revenue is negative (MR < 0).

  28. Price Example: Elastic Region of Linear Demand Curve a Demand a/b Quantity

  29. Price Example: Elastic Region of Linear Demand Curve a MR Demand a/2b a/b Quantity

  30. Price Example: Elastic Region of Linear Demand Curve a Elastic region ( < -1), MR > 0 MR Demand a/2b a/b Quantity

  31. Price Example: Elastic Region of Linear Demand Curve a Elastic region ( < -1), MR > 0 Inelastic region (0>>-1), MR<0 MR Demand a/2b a/b Quantity

  32. Price Example: Elastic Region of Linear Demand Curve a Elastic region ( < -1), MR > 0 Unit elastic (=-1), MR=0 Inelastic region (0>>-1), MR<0 MR Demand a/2b a/b Quantity

  33. Inverse Elasticity Pricing Rule • A monopolist will only operate on the elastic region of the market demand curve • Note: As demand becomes more elastic at each point, marginal revenue approaches price.

  34. The Lerner Index of Market Power • The monopolist will produce at MR = MC, but we also found that: MR = P 1 + 1  • Then: P 1 + 1 = MC  or: P – MC = –1 P  ( ) ( )

  35. The Lerner Index of Market Power Definition: The Lerner Index of market power is the price-cost margin, (P*-MC)/P*. • It measures the monopolist's ability to price above marginal cost, which in turn depends on the elasticity of demand. • The Lerner index ranges between 0 (for the competitive firm) and 1 (for a monopolist facing a unit elastic demand).

  36. The Welfare Economics of Monopoly • A monopoly equilibrium entails a dead-weight loss. • For the following analysis, suppose the supply curve in perfect competition is equal to the marginal cost curve of the monopolist.

  37. Example: Welfare Effects of Perfect Competition Supply PC Demand QC MR

  38. Example: Welfare Effects of Perfect Competition Supply : Consumer Surplus PC : Producer Surplus Demand QC MR

  39. Example: Welfare Effects of Monopoly MC PC Demand QC MR

  40. Example: Welfare Effects of Monopoly MC PM PC Demand QM QC MR

  41. Example: Welfare Effects of Monopoly MC PM : Consumer Surplus PC Demand QM QC MR

  42. Example: Welfare Effects of Monopoly MC PM : Consumer Surplus : Producer Surplus PC Demand QM QC MR

  43. Example: Welfare Effects of Monopoly MC PM : Consumer Surplus : Producer Surplus PC : Deadweight Loss Demand QM QC MR

  44. Summary A monopoly market consists of a single seller facing many buyers (utilities, postal services). A monopolist's profit maximization condition is to set marginal revenue equal to marginal cost. Marginal revenue generally is lower than price. How much less depends on the elasticity of demand.

  45. Summary A monopolist never produces on the inelastic portion of demand since, in the inelastic region, raising price and reducing quantity make total revenues rise and total costs fall! The Lerner Index is a measure of market power, often used in antitrust analysis. A monopoly equilibrium entails a dead-weight loss.

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