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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