Chapter 2
Supply and
Demand
Talk is cheap because supply
exceeds demand.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
Chapter 2 Outline
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
Demand
Supply
Market Equilibrium
Shocking the Equilibrium: Comparative Statistics
Elasticities
Effects of a Sales Tax
Quantity Supplied Need Not Equal Quantity
Demanded
When to Use the Supply-and-Demand Model
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-2
2.1 Demand
• The quantity of a good or service that consumers
demand depends on price and other factors such as
consumers’ incomes and the prices of related goods.
• The demand function describes the mathematical
relationship between quantity demanded (Qd), price
(p) and other factors that influence purchases:
•
•
•
•
p
ps
pc
Y
=
=
=
=
per unit price of the good or service
per unit price of a substitute good
per unit price of a complementary good
consumers’ income
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-3
2.1 Demand
• We often work with a linear demand function.
• Example: estimated demand function for pork in
Canada.
•
•
•
•
•
Qd
p
pb
pc
Y
= quantity of pork demanded (million kg per year)
= price of pork (in dollars per kg)
= price of beef, a substitute good (in dollars per kg)
= price of chicken, another substitute (in dollars per kg)
= consumers’ income (in dollars per year)
• Graphically, we can only depict the relationship between
Qd and p, so we hold the other factors constant.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-4
2.1 Demand Example: Canadian Pork
Assumptions about
pb, pc, and Y to
simplify equation
• pb = $4/kg
• pc = $3.33/kg
• Y = $12.5 thousand
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-5
2.1 Demand Example: Pork
• Changing the ownprice of pork simply
moves us along an
existing demand
curve.
• Changing one of the
things held constant
(e.g. pb, pc, and Y)
shifts the entire
demand curve.
• pb to $4.60 /kg
Q = 286-20p+20∆pb
= 286-20p + 20*0.6
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-6
2.1 Summing Demand Functions
• Q1= D1(p)
• Q2= D2(p)
• Q =Q1+Q2
=D1(p)+D2(p)
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-7
2.2 Supply
• The quantity of a good or service that firms
supply depends on price and other factors
such as the cost of inputs that firms use to
produce the good or service.
• The supply function describes the
mathematical relationship between quantity
supplied (Qs), price (p) and other factors that
influence the number of units offered for sale:
• p = per unit price of the good or service
• ph = per unit price of other production factors
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-8
2.2 Supply
• We often work with a linear supply function.
• Example: estimated supply function for pork in
Canada.
• Qs = quantity of pork supplied (million kg per year)
• p = price of pork (in dollars per kg)
• ph = price of hogs, an input (in dollars per kg)
• Graphically, we can only depict the relationship
between Qs and p, so we hold the other factors
constant.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-9
2.2 Supply Example: Canadian Pork
• Assumption about ph
to simplify equation
• ph = $1.50/kg
dQs
 40
dp
dp
1

 slope
dQs 40
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-10
2.2 Supply Example: Canadian Pork
• Changing the ownprice of pork simply
moves us along an
existing supply
curve.
• Changing one of the
things held constant
(e.g. ph) shifts the
entire supply curve.
• ph to $1.75 /kg
Q= 88+40p-60∆ph
Q =88+40p-60*.25
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-11
2.2 Summing Supply Functions
The Sum of Domestic and Foreign Supply
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-12
2.3 Market Equilibrium
• The interaction between consumers’ demand
curve and firms’ supply curve determines the
market price and quantity of a good or service
that is bought and sold.
• Mathematically, we find the price that equates
the quantity demanded, Qd, and the quantity
supplied, Qs:
• Given Qd  286 20 p and Qs  88 40 p ,find p such that
Qd = Qs: 286 20 p  88  40 p
p = $3.30
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-13
2.3 Market Equilibrium
• Graphically, market equilibrium occurs where
the demand and supply curves intersect.
• At any other price, excess supply or excess
demand results.
• Natural market forces push toward equilibrium Q
and p.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-14
2.4 Shocking the Equilibrium:
Comparative Statics
• Changes in a factor that affects demand, supply, or a
new government policy alters the market price and
quantity of a good or service.
• Changes in demand and supply factors can be
analyzed graphically and/or mathematically.
• Graphical analysis should be familiar from your
introductory microeconomics course.
• Mathematical analysis simply utilizes demand and
supply functions to solve for a new market
equilibrium.
• Changes in demand and supply factors can be large or
small.
• Small changes are analyzed with Calculus.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-15
2.4 Shocking the Equilibrium: Comparative
Statics with Discrete (large) Changes
• Graphically analyzing the effect of an increase
in the price of hogs
• When an input gets more expensive, producers
supply less pork at every price.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-16
2.4 Shocking the Equilibrium: Comparative
Statics with Discrete (large) Changes
• Mathematically analyzing the effect of an
increase in the price of hogs Qs  73 40 p
• If ph increases by $0.25, new ph = $1.75 and
Qd  Qs
286 20 p  73  40 p
p  $3.55
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
Qd  286 203.55  215
Qs  73 403.55  215
2-17
2.4 Shocking the Equilibrium:
Comparative Statics with Small Changes
• Demand and supply functions are written as
general functions of the price of the good,
holding all else constant.
• Supply is also a function of some exogenous (not
in firms’ control) variable, a.
• Because the intersection of demand and
supply determines the price, p, we can write
the price as an implicit function of the supplyshifter, a:
Q  S  p(a), a 
s
• In equilibrium:
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-18
2.4 Shocking the Equilibrium:
Comparative Statics with Small Changes
• Given the equilibrium condition
, we differentiate with
respect to a using the chain rule to determine
how equilibrium is affected by a small change
in a:
• Rearranging:
• dp/da has the same sign as dS/da
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-19
Solved Problem 2.1
• ∆p & ∆Q when ∆ph? Do Comparative Statics
286-20p =178+40p-60ph
p=1.8 + ph
• dp/ph=1
• Q=D(p(ph))=286-20p(ph)
• dQ/dph=(dD/dp)(dp/ph)=-20*1=-20
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-20
2.5 Elasticities
• The shape of demand and supply curves
influence how much shifts in demand or
supply affect market equilibrium.
• Shape is best summarized by elasticity.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-21
2.5 Elasticities
• Elasticity indicates how responsive one
variable is to a change in another variable.
• The price elasticity of demand measures how
sensitive the quantity demanded of a good,
Qd, is to changes in the price of that good, p.
• If Qd  a  bp, then
and elasticity
can be evaluated at any point on the demand
curve.
• Arc versus point elasticity
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-22
2.5 Example: Elasticity of Demand
• Previous pork demand was Qd  286  20 p
• Calculating price elasticity of demand at
equilibrium (p=$3.30 and Q=220):
• Interpretation:
• negative sign consistent with downward-sloping
demand
• a 1% increase in the price of pork leads to a
0.3% decrease in quantity of pork demanded
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-23
2.5 Elasticity of Demand
• Elasticity of demand varies along a linear
demand curve
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-24
2.5 Constant Elasticity Demand Curves
• Q= Apε where 0>ε>-1
• take natural log:
ln Q = lnp + εlnp
dlnQ/dp=ε/p
(dQ/Q)/dp=ε/p
• (dQ/Q)/(dp/p)=ε
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-25
2.5 Factors Affecting Demand
Elasticity
1. Availability of Substitutes
2. Time Horizon
3. Necessities vs. Luxuries
4. Purchase Size
More Inelastic
More Elastic
Fewer Substitutes
More Substitutes
Short Run (less time)
Long Run (more time)
Necessities
Luxuries
Small Part of Budget
Large Part of Budget
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-26
Determinants of Elasticity of Demand
1. The availability of substitutes strongly
influences the sensitivity of quantity
demanded to changes in price.
– For goods with fewer substitutes, consumers
are unable to adjust quantity demanded
significantly in response to a price increase
making demand inelastic.
– For goods with many substitutes, consumers
can easily reduce quantity demanded as
price rises by switching to those other
products making demand elastic.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-27
Determinants of Elasticity of Demand
2. The time horizon influences the
elasticity of demand for a good.
– Immediately following a price increase,
consumers may not be able to alter
their consumption patterns, making
demand inelastic.
– Over time, however, consumers can
adjust their behavior by finding
substitutes making demand elastic.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-28
Determinants of Elasticity of Demand
3. The nature of the good to the consumer
can also affect the elasticity of demand.
– For goods considered as necessities,
consumers are more reluctant to reduce
quantity demanded when the price rises
making demand inelastic.
– When goods are considered luxuries,
consumers will cut back on their
purchases when the price rises, making
demand elastic.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-29
Determinants of Elasticity of Demand
4. The size of the purchase relative to the
consumer’s budget will influence the elasticity
of demand.
– Consumers are less concerned about price
changes when purchases of a good
represent a small portion of their incomes
making demand inelastic.
– Consumers become much more concerned
(even worried) about price changes when
purchases of a good account for a large
portion of their incomes making demand
elastic.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-30
2.5 Other Elasticities
• There are other common elasticities that are
used to gauge responsiveness.
• income elasticity of demand
• cross-price elasticity of demand
• elasticity of supply
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-31
2.5 Elasticity of Supply
Elasticity of Supply Captures the Sensitivity of Quantity Supplied to
Changes in Price
Price per
Unit
The Same
Price Increase
Inelastic Supply
Elastic Supply
$50
$40
…Causes a Small Increase in
Quantity Supplied if Supply is
Inelastic
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
80 85
170
Quantity
…Causes a Big Increase in Quantity
Supplied if Supply is Elastic
2-32
2.5 Factors Affecting Supply
Elasticity
1. Change in Per-Unit Costs with
Increased Production
2. Time Horizon
3. Share of Market for Inputs
4. Geographic Scope
More Inelastic
More Elastic
Difficult to Increase Production at
Constant Unit Cost
Easy to Increase Production at
Constant Unit Cost
Raw Materials
Manufactured Goods
Short Run
Long Run
Large Share of Market for Inputs
Small Share of Market for Inputs
Global Supply
Local Supply
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-33
Determinants of Elasticity of Supply
1. The main determinant of the elasticity of
supply is how quickly per-unit costs
increase with an increase in production.
– If increased production requires much
higher costs, then the supply curve will be
inelastic.
– If production can increase with constant
costs then the supply curve will be elastic.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-34
Determinants of Elasticity of Supply
2. The time horizon influences the elasticity of
supply for a good.
– Immediately following a price increase,
producers can expand output only using
their current capacity making supply
inelastic.
– Over time, however, producers can expand
their capacity making supply elastic.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-35
Determinants of Elasticity of Supply
3. The elasticity of supply for a good relates
to its share of the market for the inputs
used in production.
– Supply is elastic when the industry can
be expanded without causing a big
increase in the demand for the industry’s
inputs.
– Supply is inelastic when industry
expansion causes a significant increase in
the demand for the industry’s inputs.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-36
Determinants of Elasticity of Supply
4. The geographic scope of the market
determines the elasticity of supply for a good.
– The wider the scope of the market of a
good, the less elastic its supply.
– The narrower the scope of the market of a
good, the more elastic its supply.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-37
2.5 Supply Elasticity
Constant-Elasticity Supply Curves
Q= Apη where 1>η>0
take natural log:
ln Q = lnp + ηlnp
(dQ/Q)/(dp/p)=η
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-38
Solved Problem 2.3
• What would be the effect of the Arctic National Wildlife
Refuge (ANWR) on the world price of oil given that ε=-0.4,
η=0.3, and the pre-ANWR world Q1=82 m barrels/day &
p1=$50/barrel, ANWR production is 0.8 m barrels/day.
• pre-ANWR world linear Demand and Supply functions
Demand: Qd = a0 - a1P
Supply: Qs = b0 + b1P
Use elasticity = (P/Q) × (ΔQ/ΔP) to compute a1 and b1.
-0.4 = -(50/82)a1
0.3 = (50/82)b1
a1 = 0.656
b1 = 0.492
Solve for a0 and b0
Qd = a0 - a1P
Qs = b0 + b1P
82 = a0 - 0.656(50)
82 = b0 + 0.492(50)
a0 = 114.8
b0 = 57.4
Qd = 114.8 – 0.656P
Qs = 57.4 + 0.492P
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-39
Solved Problem 2.3
• post-ANWR supply function:
Qs = 57.4 + 0.8 + 0.492P
Qs = 58.2 + 0.492P
• New equilibrium p and Q?
58.2 + 0.492P = 114.8 – 0.656P
p2=$49.30 that is 1.4% decrease in p
Q2=82.46 that is 0.56% increase in Q
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-40
2.6 Effects of a Sales Tax
• Two types of sales taxes:
• Ad valorem tax is in percentage terms
• California’s state tax rate is 8.25%, so a $100
purchase generates $8.25 in tax revenue
• Specific (or unit) tax is in dollar terms
• U.S. gasoline tax is $0.18 per gallon
• Ad valorem taxes are much more common.
• The effect of a sales tax on equilibrium price
and quantity depends on elasticities of
demand and supply.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-41
2.6 Equilibrium Effects of a Sales
Tax
• Consider the effect of a $1.05 per unit
(specific) sales tax on the pork market that is
collected from pork producers.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-42
2.6 How Specific Tax Effects
Depend on Elasticities
• If a unit tax, , is collected from pork producers, the
price received by pork producers is reduced by this
amount and our equilibrium condition becomes:
• Differentiating with respect to :
• Rearranging indicates how the tax changes the price
consumers pay:
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-43
2.6 How Specific Tax Effects
Depend on Elasticities
• The equation
can be expressed in terms of
elasticities by multiplying through by p/Q:
• Tax incidence on consumers, the amount by which the price
to consumers rises as a fraction of the amtount of the tax, is
now easy to calculate given elasticities of demand and
supply.
• Tax incidence on firms, the amount by which the price paid
to firms rises, is simply 1 – dp/dτ
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-44
2.6 Important Questions About Tax
Effects
• Does it matter whether the tax is collected from producers
or consumers?
• Tax incidence is not sensitive to who is actually taxed.
• A tax collected from producers shifts the supply curve back.
• A tax collected from consumers shifts the demand curve
back.
• Under either scenario, a tax-sized wedge opens up between
demand and supply and the incidence analysis is identical.
• Does it matter whether the tax is a unit tax or an ad
valorem tax?
• If the ad valorem tax rate is chosen to match the per unit
tax divided by equilibrium price, the effects are the same.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-45
2.6 Important Questions About Tax
Effects
• Does it matter whether the tax is a unit tax or
an ad valorem tax?
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-46
2.7 Quantity Supplied Need Not
Equal Quantity Demanded
• Price determines whether Qs = Qd
• A price ceiling legally limits the amount that can be
charged for a product.
• Effective ceilings force the price below equilibrium price.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-47
2.7 Quantity Supplied Need Not
Equal Quantity Demanded
• Price determines whether Qs = Qd
• A price floor legally inflates the price of a product
above some level.
• Effective floor forces the price above equilibrium price.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-48
2.8 When to Use the Supply-andDemand Model
• This model is appropriate in markets that are
perfectly competitive:
1. There are a large number of buyers and sellers.
2. All firms produce identical products.
3. All market participants have full information
about prices and product characteristics.
4. Transaction costs are negligible.
5. Firms can easily enter and exit the market.
• We will talk more about the perfectly
competitive market in Chapter 8.
Copyright © 2011 Pearson Addison-Wesley. All rights reserved.
2-49