Chapter 11 Monopoly

Objective How does a monopolist set its price and output? What is wrong with monopoly? What are some other pricing strategies a monopolist can use?

Causes of a Monopoly Barriers to entry – Legal barriers to entry. Technical barriers to entry Diminishing average cost over a broad range of output like a natural monopoly. Special knowledge of a low-cost method of production. Ownership of a key resource Possession of unique managerial talent. Legal barriers to entry. Patents and copyrights. Exclusive franchise or license.

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

Revenue Analysis for a Monopoly

A Monopoly’s Revenue ∆TR/∆Q = MR 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 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 P Q TR MR $5 3 15 $1 $4 4 16 $4 $4 $4 $4 Note that MR<P

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

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

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

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

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

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

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*

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

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|)

Optimal Price and Quantity Results Deadweight loss Dollar measure - Loss to society Profit maximization results in units not produced where marginal social benefit > marginal social cost Some of the consumer surplus under perfect competition is transferred to the monopolist.

The socially optimal price D d MR MC Compared to perfect competition, a monopoly produces less output and charges a higher price b p q f Quantity

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

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 Price 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 MR Fee e d Unit Price MC b a Quantity

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

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

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

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

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…… D d Transactions represented by the blue line are not undertaken MR MC p q b f Quantity

Two part Tariff may not be optimal when consumers are not identical Price DElizabeths B Half the consumers are type A and half are B The monopoly sets a fee=A+B/2 The Elizabeths are willing to pay the fixed fee, but the Geoffreys are not DGeoffreys A p* q1 q2 Quantity

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

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

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: Demand MR P1 Q 1 Demand P2 Q 2 Marginal cost MR

Price Discrimination 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

Practice Questions: #1 Given: Find 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: Find 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?