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Revenue and Pricing Strategies in Monopoly Markets

This chapter explores the revenue and pricing strategies used by monopolies, including total, average, and marginal revenue. It also discusses the relationship between marginal revenue and price, the effects of an increase in sales on total revenue, and the optimization of price and quantity for maximum profit.

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Revenue and Pricing Strategies in Monopoly Markets

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  1. Chapter 17 The Age of Entrepreneurship: Monopoly

  2. Definitions • Revenue = price * quantity • TR=pq • Profit = Revenue – Costs • π = TR – C • Marginal revenue= ΔTR/Δq • Change in total revenue from selling an extra unit of output

  3. A Monopoly’s Total, Average, and Marginal Revenue

  4. A Monopoly’s Revenue • Marginal Revenue • ∆TR/∆Q = MR • How does MR compare to P in a monopoly market? • To sell an extra unit the monopolist has to lower price. • He sells the extra unit at the new price (thus total revenue rises), but lowers price on all previous units sold (which reduces total revenue) • MR<P

  5. A Monopoly’s Revenue An increase in sales has two effects on total revenue • The output effect—revenue earned on the extra unit • The price effect—revenue lost on previous units. • MR=P + (Δp/Δq)(q) $5 $5 $5 $4 $4 $4 $4 Note that MR<P

  6. Price Total Revenue increases and then decreases. Total Revenue $11 10 9 8 7 6 5 4 Total Revenue 3 2 1 0 –1 Quantity 1 2 3 4 5 6 7 8 9 –2 –3 –4

  7. Marginal Revenue is the slope of the total revenue curve • Marginal revenue is positive (negative) when total revenue is increasing (decreasing) • Marginal revenue is zero when total revenue reaches a maximum Total Revenue Q Marginal Revenue Q

  8. Marginal Revenue • Marginal revenue curve • Below demand curve • Slope = 2* Slope of demand curve • MR=P + (Δp/Δq) (q) • MR=p-|Δp/Δq|(q)=p(1-1/|ξ|) • ξ = elasticity of demand

  9. Price Marginal revenue and demand • Inverse demand function p= f(q)=A-bq • Price – from any given quantity • Demand function: q = f(p)= (A-p)/b • quantity demanded at each price a p = A - bq MR = A - 2bq 0 D Quantity The marginal revenue curve is steeper than the demand curve. With a straight-line demand curve, the slope of the marginal revenue curve is twice the slope of the demand curve

  10. Price Demand and Elasticity pMAX |ξ|>1 |ξ|=1 p1 μ |ξ|<1 Quantity demanded: q = A - bp 0 Quantity A

  11. Pricing and Quantity Decisions • The Elasticity Rule • The firm will never choose a point on inelastic portion of demand curve • When |ξ|<1, then marginal revenue is negative • Selling an extra unit of output will reduce profit • It increases costs and • decreases revenue

  12. Optimal Price and Quantity Results • Profit-maximizing quantity, q* • Increase production if MR>MC • Until MR=MC • Profit-maximizing price, p* • On demand curve, at q*

  13. Price ρ α Optimal price and quantity MC The profit-maximizing price and quantity equate marginal cost with marginal revenue MR p* 0 D Quantity q*

  14. Optimal Price and Quantity Results • # 2: Profit-maximizing price • On the demand curve • At optimal quantity • MR=p(1-1/|ξ|) • p=MR(1-1/|ξ|); • MR=MC • p=MC(1-1/|ξ|)

  15. Optimal Price and Quantity Results • Deadweight loss • Dollar measure - Loss to society • For • Marginal social benefit > marginal social cost • No production • Profit-maximizing firm

  16. Optimal Price and Quantity Results • Societal consumer surplus • Difference – consumers • Willing to pay • Selling price (pays) • Producer surplus • Difference – producer • Receives (selling price) • Cost of production

  17. Price f b The socially optimal price d MC The price-quantity combination that maximizes the sum of consumer surplus and producer surplus equates marginal cost with price (willingness to pay). p MR 0 D Quantity q

  18. Two-Part Tariffs • Monopolist charges • A lump sum fee • A unit price • The two part tariff allows the monopoly to • Capture consumer surplus • Earn extra-normal profit • Sell the optimal output level

  19. Two-Part Tariffs • Assume there are identical consumers in the market • Consumers buy more of the good as its price declines • Each gets the same consumer surplus

  20. Price Two-Part Tariffs c The producer charges each consumer, in addition to the per-unit price, a fixed fee equal to her share of the consumer surplus: Fee=CS/N d e Unit Price MR a MC b 0 Quantity Fee

  21. Price Two-Part Tariffs and Profit c The producer earns a higher profit d e Unit Price Profit MR a MC b 0 Quantity

  22. Price Two-Part Tariffs and A Higher Profit The producer earns a higher profit if he lowers the price to MC and charges a higher fee e Profit MR MC 0 Quantity Unit Price

  23. Price Two-Part Tariffs and Efficiency • The producer is efficient: • He sells the socially optimal amount • Sets a price equals MC e Profit MR MC 0 Quantity Unit Price

  24. Price MC Two-Part Tariffs when the monopoly realizes a loss AC p A two-part tariff enables the monopolist to earn positive profits E c 0 Quantity q

  25. Problems with uniform Pricing • When consumers are not identical • Some buyers with a willingness to pay above marginal cost do not buy because the price is high • Lowering price to capture this market segment may reduce monopoly profit.

  26. Price f b When the monopoly charges a single price…… d Transactions represented by the blue line are not undertaken MC p MR 0 D Quantity q

  27. Price Two part Tariff may not be optimal when consumers are not identical The Elizabeths are willing to pay the fixed fee, but the Geoffreys are not p* B A DGeoffreys DElizabeths 0 Quantity q1 q2

  28. Non uniform pricing / Price Discrimination • Separate consumers • Groups/ markets • Slightly different products • Tastes • No reselling • Different prices

  29. Price Discrimination • Price discrimination • Charge different prices to different consumers • Segmented markets • Physical separation/other characteristics • Arbitrage - impossible

  30. Demand MR Demand Q 1 Q 2 Price Discrimination: the Market for Movie Tickets (b) Demand by people below age 60 (b) Senior citizen demand P The relative prices charged will depend on the price elasticity of demand in each market: P1 P2 Marginal cost MR

  31. Price Discrimination • #4: Price Discrimination in Segmented Markets • Produce q* (profit maximizing quantity) • Marginal revenue (any market) = marginal cost • Marginal revenue (one market) = Marginal revenue (other) market • MRg=MRe=MCt

  32. Practice Questions: #1 • Given: • Inverse demand: P=100 - Q • MC constant at $50 and no fixed costs • Find • Socially optimal output level • Monopoly output and price • If the monopoly can charge a fee in addition to the above price, what is the fee? The profit? • What is the optimal price and fee? The profit?

  33. Practice Questions: #2 • Given: • Two groups of buyers: P1=130-2Q1 and P2=60-Q2 • MC constant at $50 and no fixed costs • Find • Price and quantity to each group • Is the monopoly output socially efficient?

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