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Chapter 17

Chapter 17. The Age of Entrepreneurship: Monopoly. Definitions. Revenue = price * quantity TR= pq Profit = Revenue – Costs π = TR – C Marginal revenue= Δ TR/ Δ q Change in total revenue from selling an extra unit of output. A Monopoly’s Total, Average, and Marginal Revenue.

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Chapter 17

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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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