econ6021 (nov 2004) price taking, price setting, and competitive market

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ECON6021 (Nov 2004) Price Taking, Price Setting, and Competitive Market

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ECON6021 (Nov 2004)

Price Taking, Price Setting, and Competitive Market

This lecture will introduce:

Profit maximization Price Taking Firm

– Supply curve– Application: multi-plant firm

Price Setting Firm– Price-cost margin– Price discrimination

Competitive Market– Efficiency of Competitive Market

Marginal Analysis

Firm’s objective– to maximize profit π=TR-TC

If MR > MC, the extra revenue from selling one more unit exceeds the extra cost.

If MR < MC, the extra revenue from selling one more unit is less than the extra cost.

If MR = MC economic profit is maximized.

Profit Maximization

π is maximized if– MR = MC and MR cuts MC from above– So long as it is worthwhile producing

This holds for whatever market structure such as– Perfect competition (price taking firm) – Monopoly (price setting firm)

Price Taking FirmT

otal

rev

enu

e &

tot

al c

ost

(do

llar

s pe

r d

ay)

Quantity (sweaters per day)0 4 9 12

100

300

183

225

Economicloss

Economicprofit =TR - TC

TR

Profit-Maximizing Output for a Price Taking Firm

Quantity (sweaters per day)

8 9 10

10

20

30

Mar

gin

al r

even

ue

& m

argi

nal

cos

t (

dol

lars

per

day

)

25

Profit-maximizationpoint

D=AR=MR

MC

Total Revenue, Total Cost,and Economic Profit for a Price Setting Firm

Quantity (sweaters per day)

Tot

al r

even

ue

& t

otal

cos

t (

doll

ars

per

day

)

0 4 9 12

100

300

183

225

A Price Setting Firm’s Profit Maximizing Output

Pri

ce a

nd

cos

t (do

llar

s pe

r ho

ur)

0 1 2 3 4 5

10

14

20

Quantity (haircuts per hour)

D

MR

MC

dQ

QdPQQPQMR

)()()(

Price Taking Firm

Characteristics of Perfect Competition

– Many firms, each selling an identical product

– Many buyers

– No restrictions on entry into the industry

– Firms in the industry have no advantage over potential new

entrants

– Firms and buyers are well informed about prices of the

products of each firm in the industry

As a result of these characteristics, perfect competitors are

price takers.

Price takers -- firms that cannot influence the market price

A Firm’s Supply CurveM

argi

nal

rev

enu

e &

mar

gin

al c

ost

(d

olla

rs p

er d

ay)

Quantity (sweaters per day)

7 9 10

17

25

31

MC curve = Supply curve

AVC

MR0

s

MR2

MR1

A Firm’s Supply Curve

Quantity (sweaters per day)

7 9 10

17

25

31

Mar

gin

al r

even

ue

& m

argi

nal

cos

t (

dol

lars

per

day

)S

s

Application: Multi-plant firm

Suppose a perfectly competitive firm has two plants producing identical goods with marginal cost functions MC1(Q1) and MC2(Q2).

It is straightforward to show that it show produce Q1 and Q2 in the two plant so that

MC1(Q1) = MC2(Q2) = P

where P is market price.

Price Setting Firm

Price Setting Firm and How Monopoly Arises

The simplest form of price setting firm is monopoly

A monopoly is an industry that produces a good or service – for which no close substitute exists and – in which there is one supplier that is

protected from competition by a barrier preventing the entry of new firms.

Barriers to Entry

Key input owned by a firm– DeBeers, a South African firm that controls

more than 80 percent of the world’s supply of natural diamonds.

But most monopolies arise from two other types of barrier: legal barriers and natural barriers

Barriers to Entry

Legal Barriers to Entry– In a legal monopoly competition and entry is restricted by the

granting of a public franchise, government license, patent, or copyright.

– E.g. Microsoft is the only firm that is allowed to produce Window 98, etc. HK Town gas. China light

Natural Barriers to Entry– A natural monopoly results from a situation in which one firm can

supply the entire market at a lower price than two or more firms can.

– Example: Electric utility– A market used to be thought as a natural monopoly may turn out

to be no longer the case as technology progresses

Natural Monopoly

Quantity (millions of kilowatt-hours)

5

10

15

0 1 2 3 4

D

Pri

ce (c

ents

per

kil

owat

t-ho

ur)

ATC

Monopoly Price-Setting Strategies Price discrimination is the practice of

selling different units of a good or service for different prices.

A single-price monopoly is a firm that must sell each unit of its output for the same price.

Single-Price Monopoly

The firm’s demand curve is the market demand curve.

Marginal revenue is not the same as the market price.

There is no supply curve for a monopoly.

Price and Output Decision

The competitive firm is a price taker, whereas the monopoly influences its price.

For the monopoly, price exceeds marginal revenue, thus price exceeds marginal cost.

Profit is maximized where MC = MR Monopolists can earn economic profits--firms

cannot enter due to barriers to entry.

A Monopoly’s Output and PriceP

rice

an

d c

ost (

doll

ars

per

hour

)

0 1 2 3 4 5

10

14

20

Quantity (haircuts per hour)

ATCEconomicprofit $12

Profit = $12($4 x 3 units)

D

MR

MC

An example: Linear Demand Q = 100 – 2P; AC=MC=10

Inverse demand: P = 50 – Q/2 TR = P*Q = (50 – Q/2) Q = 50Q – Q2/2 MR = 50 – Q

– Remark: if P = A – BQ, then MR = A – 2BQ MR = MC → 50 – Q = 10 → Q = 40 Substituting Q = 40 into inverse

demand, P = 50 – 40/2 = 30

Optimal output, profit margin, and profit

MC = AC

AR = P(Q) =50 – Q2/2

Q

P

Profit = profit margin X Q*= (P* - AC) Q*

30

10

40

MR = 50 – Q2

Price-cost Margin and Elasticity

||

11

11

/

/)(1

)(1

)()(

,

,

Pxx

Pxx

eP

eP

QdQ

PQdPP

dQ

QdP

P

QP

dQ

QdPQQP

dQ

dTRMR

Price-cost market and

||

1margincost -price

||

11

,

,

Pxx

Pxx

eP

MCPe

PMRMC

Equating MC with MR, we have

The more elastic the demand, the smaller the price-cost margin Price-cost margin, a.k.a. price-cost markup, or Lerner Index of market power (1934).

Competition and Efficiency

Efficiency is achieved when all the gains from trade have been realized (social welfare is maximized).

Monopoly andCompetition Compared

Pri

ce

Quantity

PA

PM

PC

0

DMR

MC

QM QC

Single-pricemonopolyrestricts output,raises price

Equilibriumin competitiveindustry

Inefficiency of MonopolyP

rice

Quantity

PA

PM

0

DMR

MC

QM QC

PC

Consumersurplus

Monopoly’sgain

Deadweightloss

Monopoly

Gains from Monopoly

Economies of Scale and Scope– Lowers average total cost and a greater

range of goods produced

Incentives to Innovate – The attempt to apply new knowledge in the

production process and obtain a patent

Price Discrimination Arcadia Publisher is planning to publish a book.

– loyalty to the author is fixed at $2M– production cost=$0 per copy– two groups of buyers

• 100K group 1 readers--each willing to pay up to $30• 400K group 2 readers--each willing to pay up to $5

If p= $30, only group 1 readers will buy the book. Arcadia obtains $30x100K =$3M (gross of loyalty)

If p= $5, both groups of readers will buy the book. Arcadia obtains $5x500K=$2.5M (gross of loyalty)

Hence, charging $30 is better.

Price Discrimination

Now suppose Arcadia knows that all group 1 readers are in HK and group 2 readers are in Chile. Then it can charges a fee of $30 for a book sold in HK and $5 for a book sold in Chile.

Price discrimination leads to– greater profits– greater social welfare!!

Determination of differentiated prices under constant marginal cost

A

q b b/2 B B/2

2 segmented markets, 2 separate price in general.

More generally, the problem is

)()()(max 21222111, 21QQTCQQPQQPQQ

Optimal output for the two markets are given by

22

2222

1

11111

212

2222

11

1111

)()(

0)(

0)(

MCQ

QPQP

Q

QPQPMC

Q

TC

Q

QPQP

Q

TC

Q

QPQP

Equalization of marginal cost and marginal revenue in each segment

Evidence of Geographic Price Discrimination

Parallel imports--unauthorized flows of genuine products across countries that compete with authorized distribution channels (ranging from deluxe cars to cheap beer)

It is often thought that parallel imports of HK made movie and music products back into HK market adversely affects the very survival of HK movie and music industry.

Price Discrimination: How to separate different customers

Coupons--those people who have lower time cost will collect and use coupons to get a discount; they are likely to have lower maximum willingness to pay as well (Sincere VIP card works similarly)

In 1999, CTI charged different fees for its registered IDD users--37cents/min to US for smart users who made a double registration; $2.9 /min for not-so-smart users who did not (c.w. HKTC’s 001 and 0060).

Educational edition--software companies charge a substantial lower price to teachers and students for their software

Price Discrimination: How to separate different customers

Hardcover vs paperback--readers of lower maximum willingness to pay are more patient; hence publishing a paperback later attract these buyers without affecting sale to hardcover buyers (compared w. seasonal sales in department stores)--production differentiation in general

Different prices for different geographic locations– golf clubs are much more expensive in HK than in

the US (HK$4.5K vs US$250)– tennis ball--HK’s price is two or three times that in

the US

Competitive Markets

Market Equilibrium

Equilibrium is defined as the price at which the quantity demanded equals the quantity supplied (so markets clear)

– While all five conditions for perfect competition are (obviously) never fully satisfied, the model is still useful as frame of reference.

When a market is out of equilibrium, market forces push the price towards equilibrium

Excess supply (a.k.a., surplus) -- This triggers a price decrease

Excess demand (a.k.a., shortage) --This triggers a price increase

0

20

8 10 11

supply

demand

a

b

c

equilibrium

Quantity (Million ton-miles a year)

Pri

ce (

$ p

er

ton

-mil

e)

Market Equilibrium (cont.)

22

surplus when market price = 22

Invisible Hand

Social welfare (SW) = net gains from production and trade In the absence of tax, SW = buyer surplus + seller surplus In the presence of tax, SW = buyer surplus + seller surplus

+ tax revenue An outcome is efficient if the SW cannot be further

increased. [taxation cannot increase SW, to be shown shortly]

Perfect competition is efficient, in which– marginal benefit = price– marginal cost = price– single price in market

Price Ceiling

Upper limit that sellers can lawfully charge and buyers can lawfully pay rent control regulated price for electricity

Price Floor

Lower limit that sellers can charge and buyers can pay minimum wage agricultural price supports

Minimum Wage: Equilibrium

0

4.20

8 10 11

supply

demand

a

b

c

equilibrium

excess supply

Quantity (Billion worker-hours a week)

Wage (

$ p

er

hour)

4.00

Net inc. in seller surplus = fdge -ghbNet inc. in buyer surplus = - (fdge +egb)Net inc. in SW = - (ghb + egb)

ef

d g

h

Minimum Wage: Losses

deadweight losses -- sellers willing to provide item at price that buyers willing to pay, but provision doesn’t occur

price elasticities of demand and supply

Can tax improve SW?Net inc. in buyer surplus = -(fdge + egb) Net inc. in seller surplus = -(djhg + ghb) Net inc. in tax revenue = fdge + djhgNet inc. in SW = -(egh + ghb)

0

800

900

e

Quantity (Thousand tickets a year)

Pri

ce (

$ p

er

tick

et)

supply

demand

$10

b

h

804

794

920

f

d

j

g

Tax: Does it matter whom the tax is imposed upon: sellers or buyers? If an excise tax of $10 is levied on sellers, the

sellers will be willing to supply the same quantity as before only when the price is increased by $10. [upper shifting of supply, demand unmoved]

If an excise tax of $10 is levied directly on buyers, the buyers will buy the same quantity as before only when the price charged by sellers is reduced by $10. [downward shifting of demand, supply unmoved.]

The outcomes under the two scenarios are the same