Chapter 17

The Age of Entrepreneurship:

Monopoly

DefinitionsRevenue = 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 Monopoly’s Total, Average, and Marginal Revenue

A Monopoly’s 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 Monopoly’s RevenueAn 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.

$5 $5 $5

$4 $4 $4 $4

P Q TR MR

$5 3 15$1

$4 4 16

Note that MR<P

MR=P + (Δp/Δq)(q)

Total Revenue

Quantity

Price

$1110

9876543210

–1–2–3–4

1 2 3 4 5 6 7 8

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 Elasticity10

Quantity 0

Price

pMAX

A

p1

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 quantity13

The profit-maximizing price and quantity equate marginal cost with marginal revenue

Quantity 0

Price

D

MR

MC

α

q*

ρp*

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 Tariffs20

Quantity 0

Price

MR

ed

MCb

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 Profit21

Quantity 0

Price

MR

ed

MCb

a

c

Unit Price

The producer earns a higher profit

Profit

Two-Part Tariffs and A Higher Profit

22

Quantity 0

Price

MR

e

MCUnit Price

The producer earns a higher profit if he lowers the price to MC and charges a higher fee

Profit

Two-Part Tariffs and Efficiency23

Quantity 0

Price

MR

e

MCUnit 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

DGeoffreysDElizabeths

p*

q1 q2

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

MRDemand

Q 2

MR

Q 1

(b) Senior citizen demand(b) Demand by people below age 60

PP1

P2

The relative prices charged will depend on the price elasticity of demand in each market:

21

21

11

11

P

P

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 MRg=MRe=MCt

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?