Chapter 17 The Age of Entrepreneurship: Monopoly

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 2

A Monopolys Total, Average, and Marginal Revenue

A Monopolys 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

A Monopolys Revenue An increase in sales has two effects on total revenue The output effectrevenue earned on the extra unit The price effectrevenue lost on previous units. $5 $4 PQTRMR $5315 $1 $4416 Note that MR<P MR=P + (Δp/Δq)(q)

Total Revenue Quantity Price $ –1 –2 –3 – Total Revenue increases and then decreases. 9 Total Revenue

Q Total Revenue Q Marginal Revenue 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

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 8

Marginal revenue and demand 9 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 Quantity 0 Price D p = A - bq MR = A - 2bq a 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

Demand and Elasticity 10 Quantity 0 Price p MAX A p1p1 μ |ξ|>1 |ξ|=1 |ξ|<1 Quantity demanded: q = A - bp

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 11

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* 12

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

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|) 14

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

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 16

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

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 18

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

Two-Part Tariffs 20 Quantity 0 Price MR e d MC b a c Fee Unit Price 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

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

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

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

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

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.

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

B 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 Quantity 0 Price D Geoffreys D Elizabeths p* q1q1 q2q2 A

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

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

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

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 MR g =MR e =MC t

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?

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?