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4.1: Monopoly

ECON 306 · Microeconomic Analysis · Fall 2019

Ryan Safner
Assistant Professor of Economics
safner@hood.edu
ryansafner/microf19
microF19.classes.ryansafner.com

Market Power I

Adam Smith

1723-1790

"People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the public, or in some contrivance to raise prices, (Book I, Chapter 2.2)"

Smith, Adam, 1776, An Enquiry into the Nature and Causes of the Wealth of Nations

Market Power

  • All sellers would like to raise prices and extract more revenue from consumers

  • Competition from other sellers drives prices down to match MC(q) (and bids costs and rents upwards to match prices)

  • If a firm in a competitive market raised p>MC(q), would lose all of its customers

  • A firm with market power has the ability to raise price above its marginal cost and not lose all of its customers

Monopoly

  • We start with a simple model of monopoly: a market with a single seller

  1. Firm's products may have few close substitutes

  2. Barriers to entry, making entry costly

  3. Firm is a "price-searcher": can set optimal price p∗ in addition to quantity q∗

    • Must search for (q∗,p∗) that maximizes π

The Monopolist's Problem

The Monopolist's Problem I

  • The monopolist's profit maximization problem:

  1. Choose: < output and price: (qo,po)>

  2. In order to maximize: < profits: π>

The Monopolist's Problem II

  • Monopolist is constrained by relationship between quantity and price that consumers are willing to pay

  • Market (inverse) demand describes maximum price consumers are willing to pay for a given quantity

  • Implications:

    • Monopolies can't set a price "as high as it wants"
    • Monopolies can still earn losses (and exit in the long run)

The Monopolist's Problem II

  • As monopolist chooses to produce more q∗, must lower the price on all units to sell them

The Monopolist's Problem II

  • As monopolist chooses to produce more q∗, must lower the price on all units to sell them

  • Price effect: lost revenue from lowering price on all sales

The Monopolist's Problem II

  • As monopolist chooses to produce more q∗, must lower the price on all units to sell them

  • Price effect: lost revenue from lowering price on all sales

  • Output effect: gained revenue from increase in sales

Monopoly and Revenues I

  • If a monopolist increases output, Δq∗, revenues would change by:

R(q)=pΔq + qΔp

Monopoly and Revenues I

  • If a monopolist increases output, Δq∗, revenues would change by:

R(q)=pΔq + qΔp

  • Output effect: increases number of units sold (Δq) times price p per unit

Monopoly and Revenues I

  • If a monopolist increases output, Δq∗, revenues would change by:

R(q)=pΔq + qΔp

  • Output effect: increases number of units sold (Δq) times price p per unit

  • Price effect: lowers price per unit (Δp) on all units sold (q)

Monopoly and Revenues I

  • If a monopolist increases output, Δq∗, revenues would change by:

R(q)=pΔq + qΔp

  • Output effect: increases number of units sold (Δq) times price p per unit

  • Price effect: lowers price per unit (Δp) on all units sold (q)

  • Divide both sides by Δq to get Marginal Revenue, MR(q):

ΔR(q)Δq=MR(q)=p+ΔpΔqq

Monopoly and Revenues I

  • If a monopolist increases output, Δq∗, revenues would change by:

R(q)=pΔq + qΔp

  • Output effect: increases number of units sold (Δq) times price p per unit

  • Price effect: lowers price per unit (Δp) on all units sold (q)

  • Divide both sides by Δq to get Marginal Revenue, MR(q):

ΔR(q)Δq=MR(q)=p+ΔpΔqq

  • Compare: demand for a competitive firm is perfectly elastic: ΔpΔq=0, so we saw MR(q)=p!

Monopoly and Revenues II

  • If we have a linear inverse demand function of the form p=a+bq
    • a is the choke price (intercept)
    • b is the slope

Monopoly and Revenues II

  • If we have a linear inverse demand function of the form p=a+bq

    • a is the choke price (intercept)
    • b is the slope

  • Marginal revenue again is defined as: MR(q)=p+ΔpΔqq

Monopoly and Revenues II

  • If we have a linear inverse demand function of the form p=a+bq

    • a is the choke price (intercept)
    • b is the slope

  • Marginal revenue again is defined as: MR(q)=p+ΔpΔqq

  • Recognize that ΔpΔq is the slope, b, (riserun)

Monopoly and Revenues II

  • If we have a linear inverse demand function of the form p=a+bq

    • a is the choke price (intercept)
    • b is the slope

  • Marginal revenue again is defined as: MR(q)=p+ΔpΔqq

  • Recognize that ΔpΔq is the slope, b, (riserun)

MR(q)=p+(b)qMR(q)=(a+bq)+bqMR(q)=a+2bq

Monopoly and Revenues III

p(q)=a−bqMR(q)=a−2bq

  • Marginal revenue starts at same intercept as Demand (a) with twice the slope (2b)

Monopoly and Revenues: Example

Example: Suppose the market demand is given by:

q=12.5−0.25p

  1. Find the function for a monopolist's marginal revenue curve.

  2. Calculate the monopolist's marginal revenue if the firm produces 6 units, and 7 units.

Revenues and Price Elasticity of Demand

  • Marginal revenue is stgonly related to price elasticity of demand:

Revenues and Price Elasticity of Demand

  • Marginal revenue is stgonly related to price elasticity of demand:

p+(ΔpΔq)q=MR(q)Definition of MR(q)

Revenues and Price Elasticity of Demand

  • Marginal revenue is related to price elasticity of demand:

p+(ΔpΔq)q=MR(q)Definition of MR(q)pp+(ΔpΔq)qp=MR(q)pDividing both sides by p

Revenues and Price Elasticity of Demand

  • Marginal revenue is related to price elasticity of demand:

p+(ΔpΔq)q=MR(q)Definition of MR(q)pp+(ΔpΔq)qp=MR(q)pDividing both sides by p1+(ΔpΔq×qp)⏟1ϵ=MR(q)pSimplifying

Revenues and Price Elasticity of Demand

  • Marginal revenue is related to price elasticity of demand:

p+(ΔpΔq)q=MR(q)Definition of MR(q)pp+(ΔpΔq)qp=MR(q)pDividing both sides by p1+(ΔpΔq×qp)⏟1ϵ=MR(q)pSimplifying1+1ϵ=MR(q)pRecognize price elasticity ϵ=ΔqΔp×pq

Revenues and Price Elasticity of Demand

  • Marginal revenue is related to price elasticity of demand:

p+(ΔpΔq)q=MR(q)Definition of MR(q)pp+(ΔpΔq)qp=MR(q)pDividing both sides by p1+(ΔpΔq×qp)⏟1ϵ=MR(q)pSimplifying1+1ϵ=MR(q)pRecognize price elasticity ϵ=ΔqΔp×pqp(1+1ϵ)=MR(q)Multiplying both sides by p

Revenues and Price Elasticity of Demand II

  • Here is finally further evidence for pthe relationship we showed in lesson 1.9
(https://microf19.classes.ryansafner.com/slides/09-slides#28) on price elasticity of demand! - Revenue-maximizing price and quantity where demand is unit elastic `MR(q)=p(1+1ϵ)
|PriceEl∗icity|MR(q)∣R(q)|⊢----------⊢-------⊢------|∣|ϵ|>1El∗ic∣+|Increasing|∣|ϵ|=1Unit∣0|Maξmized|∣|ϵ|<1I≠l∗ic∣−|Decreasing|-Monopolists⋅only⋅∏ucewheredemandisel∗ic,withpositiveMR(q)`! ]

Measuring Markup Prices

  • How much does a monopolist mark up price over cost?

Measuring Markup Prices

  • How much does a monopolist mark up price over cost?

MR(q)=MC(q)

Measuring Markup Prices

  • How much does a monopolist mark up price over cost?

MR(q)=MC(q)p(1+1ϵ)=MC(q)

Measuring Markup Prices

  • How much does a monopolist mark up price over cost?

MR(q)=MC(q)p(1+1ϵ)=MC(q)p=MC(q)1+1ϵ

Measuring Markup Prices

p=MC(q)1+1ϵ

  • Perfect competition: p=MC(q) (allocatively efficient)

  • Monopolists mark up price above MC(q)

  • Size of markup depends on price elasticity of demand

    • ↓ price elasticity: ↑ markup
    • i.e. the less responsive to prices consumers are, the higher the monopolist can charge

The Lerner Index I

  • Lerner Index measures market power as % of firm's price that is markup above (marginal) cost

L=p−MC(q)p=−1ϵ

  • L=0⟹ perfect competition
    • (since P=MC)
  • As L→1⟹ more market power

The Lerner Index II

The more (less) elastic a good, the less (more) the optimal markup: L=p−MC(q)p=−1ϵ

"Inelastic" Demand Curve

"Elastic" Demand Curve

Profit-Maximizing Price and Quantity (Graph)

  • Profit-maximizing quantity is always q∗ where MR(q) = MC(q)

Profit-Maximizing Price and Quantity (Graph)

  • Profit-maximizing quantity is always q∗ where MR(q) = MC(q)

  • But monopolist faces entire market demand

    • Can charge as high as consumers are WTP

Profit-Maximizing Price and Quantity (Graph)

  • Profit-maximizing quantity is always q∗ where MR(q) = MC(q)

  • But monopolist faces entire market demand

    • Can charge as high as consumers are WTP

  • Break even price p=AC(q)min

Profit-Maximizing Price and Quantity (Graph)

  • Profit-maximizing quantity is always q∗ where MR(q) = MC(q)

  • But monopolist faces entire market demand

    • Can charge as high as consumers are WTP

  • Break even price p=AC(q)min

  • Shut-down price p=AVC(q)min

Monopolist's Supply Decisions

  1. Produce the optimal amount of output q∗ where MR(q)=MC(q)

Monopolist's Supply Decisions

  1. Produce the optimal amount of output q∗ where MR(q)=MC(q)

  2. Raise price to maximum consumers are WTP: p∗=Demand(q∗)

Monopolist's Supply Decisions

  1. Produce the optimal amount of output q∗ where MR(q)=MC(q)

  2. Raise price to maximum consumers are WTP: p∗=Demand(q∗)

  3. Calculate profit with average cost: π=[p−AC(q)]q

Monopolist's Supply Decisions

  1. Produce the optimal amount of output q∗ where MR(q)=MC(q)

  2. Raise price to maximum consumers are WTP: p∗=Demand(q∗)

  3. Calculate profit with average cost: π=[p−AC(q)]q

  4. Shut down in the short run if p<AVC(q)

    • Minimum of AVC curve where MC(q)=AVC(q)

Monopolist's Supply Decisions

  1. Produce the optimal amount of output q∗ where MR(q)=MC(q)

  2. Raise price to maximum consumers are WTP: p∗=Demand(q∗)

  3. Calculate profit with average cost: π=[p−AC(q)]q

  4. Shut down in the short run if p<AVC(q)

    • Minimum of AVC curve where MC(q)=AVC(q)

  5. Exit in the long run if p<AC(q)

    • Minimum of AC curve where MC(q)=AC(q)

The Profit Maximizing Quantity & Price: Example

Example: Consider the market for iPhones. Suppose Apple's costs are:

C(q)=2.5q2+25,000MC(q)=5q

The demand for iPhones is given by (quantity is in millions of iPhones):

q=300−0.2p

  1. Find Apple's marginal revenue function.
  2. Find Apple's profit-maximizing quantity and price.
  3. How much total profit does Apple earn?
  4. How much of Apple's price is markup over (marginal) cost?
  5. What is the price elasticity of demand at Apple's profit-maximizing output?

Market Power I

Adam Smith

1723-1790

"People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the public, or in some contrivance to raise prices, (Book I, Chapter 2.2)"

Smith, Adam, 1776, An Enquiry into the Nature and Causes of the Wealth of Nations

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