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1.5: Monopoly I: Behavior

ECON 326 · Industrial Organization · Spring 2020

Ryan Safner
Assistant Professor of Economics
safner@hood.edu
ryansafner/IOs20
IOs20.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

  • Market power: ability to raise \(p>MC(q)\) and not lose all 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 \(p^*\) and quantity \(q^*\)

    • Must search for \((q^*,p^*)\) that maximizes \(\pi\)

The Monopolist's Choice

  • 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!

The Monopolist's Choice II

  • As monopolist chooses to produce more \(q^*\), must lower the price on all units to sell them

The Monopolist's Choice 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 Choice 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, \(\Delta q^*\), revenues would change by:

\(R(q)=\)\(p \Delta q\) \(+\) \(q \Delta p\)

Monopoly and Revenues I

  • If a monopolist increases output, \(\Delta q^*\), revenues would change by:

\(R(q)=\)\(p \Delta q\) \(+\) \(q \Delta p\)

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

Monopoly and Revenues I

  • If a monopolist increases output, \(\Delta q^*\), revenues would change by:

\(R(q)=\)\(p \Delta q\) \(+\) \(q \Delta p\)

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

  • Price effect: lowers price per unit \((\Delta p)\) on all units sold \((q)\)

Monopoly and Revenues I

  • If a monopolist increases output, \(\Delta q^*\), revenues would change by:

\(R(q)=\)\(p \Delta q\) \(+\) \(q \Delta p\)

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

  • Price effect: lowers price per unit \((\Delta p)\) on all units sold \((q)\)

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

$$\frac{\Delta R(q)}{\Delta q}=MR(q)=p+\frac{\Delta p}{\Delta q}q$$

Monopoly and Revenues I

  • If a monopolist increases output, \(\Delta q^*\), revenues would change by:

\(R(q)=\)\(p \Delta q\) \(+\) \(q \Delta p\)

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

  • Price effect: lowers price per unit \((\Delta p)\) on all units sold \((q)\)

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

$$\frac{\Delta R(q)}{\Delta q}=MR(q)=p+\frac{\Delta p}{\Delta q}q$$

  • Compare: demand for a competitive firm is perfectly elastic: \(\frac{\Delta p}{\Delta}q=0\), 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: $$MR(q)=p+\frac{\Delta p}{\Delta q}q$$

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: $$MR(q)=p+\frac{\Delta p}{\Delta q}q$$

  • Recognize that \(\frac{\Delta p}{\Delta q}\) is the slope, \(b\), \(\left(\frac{rise}{run} \right)\)

Monopoly and Revenues II

$$\begin{align*} MR(q)&=p+(b)q\\ MR(q)&=(a+bq)+bq\\ \mathbf{MR(q)}&=\mathbf{a+2bq}\\ \end{align*}$$

Monopoly and Revenues III

$$\begin{align*} p(q)&=a-bq\\ MR(q)&=a-2bq\\ \end{align*}$$

  • 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

Price Elasticity \(MR(q)\) \(R(q)\)
\(\vert \epsilon \vert >1\) Elastic \(+\) Increasing
\(\vert \epsilon \vert =1\) Unit \(0\) Maximized
\(\vert \epsilon \vert <1\) Inelastic \(-\) Decreasing

  • Strong relationship between price elasticity of demand and monopoly pricing

  • Monopolists only produce where demand is elastic, with positive \(MR(q)\)!

  • Check back later in today's class notes for more

Measuring Markup Prices

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

  • Monopolists mark up price above \(MC(q)\)

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

Measuring Markup Prices

  • Size of markup depends on price elasticity of demand
    • \(\downarrow\) price elasticity: \(\uparrow\) 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

$$L=\frac{p-MC(q)}{p} = -\frac{1}{\epsilon}$$

  • \(L=0 \implies\) perfect competition
    • (since \(P=MC)\)
  • As \(L\rightarrow 1 \implies\) more market power

The Lerner Index II

The more (less) elastic a good, the less (more) the optimal markup: \(L=\frac{p-MC(q)}{p}=-\frac{1}{\epsilon}\)

"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: \(\pi=[p-AC(q)]q\)

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: \(\pi=[p-AC(q)]q\)

  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: \(\pi=[p-AC(q)]q\)

  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:

$$\begin{align*} C(q)&=2.5q^2+25,000\\ MC(q)&=5q\\ \end{align*}$$

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

$$q=300-0.2p$$

  1. Find Apple's profit-maximizing quantity and price.
  2. How much total profit does Apple earn?
  3. How much of Apple's price is markup over (marginal) cost?
  4. 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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