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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)
Total revenue & total cost
(dollars per day)
Price Taking Firm
TR
300
225
Economic
profit =
TR - TC
183
100
Economic
loss
0
4
9
12
Quantity (sweaters per day)
Marginal revenue & marginal cost
(dollars per day)
Profit-Maximizing Output for a
Price Taking Firm
30
25
Profitmaximization
point
MC
D=AR=MR
20
10
8 9 10
Quantity (sweaters per day)
Total revenue & total cost
(dollars per day)
Total Revenue, Total Cost,
and Economic Profit for a Price
Setting Firm
300
225
183
100
0
4
9
12
Quantity (sweaters per day)
Price and cost (dollars per hour)
A Price Setting Firm’s Profit
Maximizing Output
MC
20
dP(Q )
MR (Q )  P(Q )  Q
dQ
14
10
D
MR
0
1
2
3
4
5
Quantity (haircuts per hour)
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
Marginal revenue & marginal cost
(dollars per day)
A Firm’s Supply Curve
MC curve
= Supply curve
31
MR2
25
MR1
AVC
s
17
MR0
7
9 10
Quantity (sweaters per day)
Marginal revenue & marginal cost
(dollars per day)
A Firm’s Supply Curve
S
31
25
s
17
7
9 10
Quantity (sweaters per day)
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
Price (cents per kilowatt-hour)
Natural Monopoly
15
10
5
ATC
D
0
1
2
3
4
Quantity (millions of kilowatt-hours)
Monopoly PriceSetting 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.
Price and cost (dollars per hour)
A Monopoly’s Output and Price
MC
20
Profit = $12
($4 x 3 units)
14
ATC
Economic
profit $12
10
D
MR
0
1
2
3
4
5
Quantity (haircuts per hour)
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
P
AR = P(Q) =50 – Q2/2
30
Profit = profit margin X Q*
= (P* - AC) Q*
MC = AC
10
MR = 50 – Q2
40
Q
Price-cost Margin and Elasticity
MR 
dTR
dQ
dP(Q )
dQ
 Q dP (Q ) 
 P 1 

P dQ 

 dP(Q ) / P 
 P1 

dQ
/
Q



1 


 P 1 

 ex ,Px 
 P(Q )  Q

1 


 P 1 

 | ex ,Px | 
Price-cost market and

Equating MC with MR, we have
MC
price - cost margin



1 

 MR  P1 

|
e
|
x , Px 

P  MC
1


P
| e x ,Px |
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).
Price
Monopoly and
Competition Compared
PA
Single-price
monopoly
restricts output,
raises price
MC
PM
Equilibrium
in competitive
industry
PC
MR
0
QM
QC
D
Quantity
Price
Inefficiency of Monopoly
PA
Consumer
surplus
Monopoly
MC
PM
Deadweight
loss
PC
Monopoly’s
gain
MR
0
QM
QC
D
Quantity
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
2 segmented markets, 2
separate price in general.
b
b/2
B/2
B
q
More generally, the problem is
max Q1 ,Q2 P1 (Q1 )Q1  P2 (Q2 )Q2   TC (Q1  Q2 )

Optimal output for the two markets are given by
P1 (Q1 ) TC
P1  Q1

0
Q1
Q1
P2  Q2
P2 (Q2 ) TC

0
Q2
Q21
P1 (Q1 )
P2 (Q2 )
MC1  P1  Q1
 P2  Q2
 MC 2
Q1
Q2
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-sosmart 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$250)
– tennis ball--HK’s price is two or three times that in
the US
Competitive Markets
Market Equilibrium
Equilibrium is defined as the price at which the
quantity demanded equals the quantity supplied
(so markets clear)

–



While all five conditions for perfect competition are
(obviously) never fully satisfied, the model is still useful
as frame of reference.
When a market is out of equilibrium, market
forces push the price towards equilibrium
Excess supply (a.k.a., surplus) -- This triggers a
price decrease
Excess demand (a.k.a., shortage) --This
triggers a price increase
Price ($ per ton-mile)
Market Equilibrium (cont.)
a
surplus when
market price = 22
supply
22
b
20
equilibrium
c
0
demand
8
10
11
Quantity (Million ton-miles a year)
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
Wage ($ per hour)
Net inc. in seller surplus = fdge -ghb
Net inc. in buyer surplus = - (fdge +egb)
Net inc. in SW = - (ghb + egb)
a
4.20
4.00
f
d
excess supply
e
g
b
equilibrium
h
c
0
supply
demand
8
10
11
Quantity (Billion worker-hours a week)
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?
Price ($ per ticket)
Net
Net
Net
Net
804 f
800 d
794
0
j
inc.
inc.
inc.
inc.
in
in
in
in
$10
e
g
supply
b
h
900
buyer surplus = -(fdge + egb)
seller surplus = -(djhg + ghb)
tax revenue = fdge + djhg
SW = -(egh + ghb)
demand
920
Quantity (Thousand tickets a year)
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