Chapter 3 Applying the Supply-and- Demand Model. Copyright © 2012 Pearson Education. All rights...

Chapter 3

Applying the Supply-and-Demand Model

Copyright © 2012 Pearson Education. All rights reserved.3 - 23 - 2

Topic

• How the shapes of demand and supply curves matter?

• Sensitivity of quantity demanded to price.

• Sensitivity of quantity supplied to price.

• Long run versus short run.

• Effects of a sales tax.

Copyright © 2012 Pearson Education. All rights reserved.3 - 33 - 3

How Shapes of Demand and Supply Matter?

• The shapes of the demand and supply curves determine by how much a shock affects the equilibrium price and quantity.

• Example: processed pork (same as Chapter 2) Supply depends on the price of pork and the

price of hogs.

Copyright © 2012 Pearson Education. All rights reserved.3 - 4

A $0.25 increase in the price of hogs causes the supply of pork to shift to the left.

A $0.25 increase in the price of hogs causes the supply of pork to shift to the left

Figure 3.1 How the Effect of a Supply Shock Depends on the Shape of the Demand Curve

D1

S1S2

3.553.30

3.6753.30

176 215 2200 176 2200

D2

S1S2

Q, Million kg of pork per year

p,

$ p

er k

g

p,

$ p

er k

g (a) (b)

e2

e1

e2

e1

This shift of the supply curve causes a movement along the demand curve…

and a reduction in quantity. But equilibrium quantity does not change since

consumption is not sensitive to price



Figure 3.1 How the Effect of a Supply Shock Depends on the Shape of the Demand Curve

(cont.)

3.30

220


p,

$ p

er k

g

2051760

(c)

e1

e2D3

S1S2

When demand is very sensitive to price… a shift in the supply

curve to S2… has no effect on the

equilibrium price and a substantial effect

on the quantity


Sensitivity of Quantity Demanded to Price

• Elasticity – the percentage change in a variable in response to a given percentage change in another variable.

• Price elasticity of demand () – the percentage change in the quantity demanded in response to a given percentage change in the price.


Sensitivity of Quantity Demanded to Price (cont.)

• Formally,

where indicates change.

• Example If a 1% increase in price results in a 3% decrease in quantity

demanded, the elasticity of demand is = -3%/1% = -3.

Q

p

p

Q

pp

QQ

p

Q

%

%


Sensitivity of Quantity Demanded to Price (cont.)

• Along linear demand curve with a function of:

Where -b is the slope or

the elasticity of demand is

bpaQ

p

Qb

(3.3) Q

pb

Q

p

p

Q


Sensitivity of Quantity Demanded to Price: Example

• The estimated linear demand function for pork is:

Q = 286 -20p where Q is the quantity of pork demanded in million

kg per year and p is the price of pork in $ per year. At the equilibrium point of p = $3.30 and Q = 220

the elasticity of demand for pork is

3.0220

30.320

Q

pb


Elasticity: An Application and a Practice Problem

• Varian (2002) found that the price elasticity of demand for internet use was -2.0 for those who used a 128 Kbps service -2.9 for those who used a 64 Kbps service.

• Practice problem: A 1% increase in the price will result in a 2%

reduction in the demand for high speed connection; and a 2.9% reduction in the demand for slower speed connection


Solved Problem 3.1

• Calculate the elasticity of demand for the linear pork demand curve D in panel a of Figure 3.1 at the equilibrium e1 where p=$3.30 and Q=220. The estimated linear demand function for pork, which holds constant other factors that influence demand besides price (Equation 2.3), is Q=286 – 20p, where Q is the quantity of pork demanded in million kg per year and p is the price of pork in dollars per kg.


Solved Problem 3.1: Answer

• Substitute the slope coefficient, the price, and the quantity values into Equation 3.3.

• By inspection, the slope coefficient for this demand equation is b = 20 (and a = 286). Substituting b = 20, p = $3.30, and Q = 220 into Equation 3.3, we find that the elasticity of demand at the equilibrium e1 in panel a of Figure 3.1 is

• Comment: Thus, at the equilibrium, a 1% increase in the price of pork leads to a –0.3% fall in the quantity of pork demanded: A price increase causes a less than proportionate fall in the quantity of pork demanded.


Elasticity Along a Demand Curve

• The elasticity of demand varies along most demand curves. Along a downward-sloping linear demand curve the

elasticity of demand is a more negative number the higher the price is.


Figure 3.2 Elasticity Along the Pork Demand Curve

p, $

pe

r kg

a/2 = 143a/5 = 57.2

D

a = 286220


0

11.44

a/b = 14.30

3.30

a/(2b) = 7.15

Elastic < –1 = –4

= –0.3

Inelastic 0 > > –1

Perfectlyinelastic

Perfectly elastic

Q = 286 -20p

= -bp

Q = -20 x 11.4457.2 = -4

3.30 220 = -0.3

Unitary: = -1


Elasticity Along The Demand Curve: Practice Problem

• According to Agcaoli-Sombilla (1991), the elasticity of demand for rice is -0.47 in Austria; -0.8 in Bangladesh, China, India, Indonesia, and Thailand; -0.25 in Japan; -0.55 in the EU and the US; and -0.15 in Vietnam. In which countries is the demand for rice

inelastic?• In all the countries, since in all cases > -1.

In which country is the least elastic?• In Vietnam, where = -0.15


Elasticity Along the Demand Curve (cont.)

• Along a horizontal demand curve, elasticity is infinite – perfectly elastic demand a increase in price causes an infinite

change in quantity demanded

• Along a vertical demand curve, elasticity is zero – perfectly inelastic demand A change in the price does not cause a

change in the quantity demanded


Figure 3.3 Vertical and Horizontal Demand Curvesp,

Pri

ce p

er

un

it

(a) Perfectly Elastic Demand

Q, Units pertime period

p*

(b) Perfectly Inelastic Demand

p, P

rice

pe

r u

nit

Q* Q, Units pertime period

(c) Individual’s Demand for Insulin

p*

p, P

rice

of

insu

lin d

ose

Q* Q, Insulindoses per day


Demand Elasticity and Revenue

• Any shock that changes the equilibrium price will affect an industry’s revenue

• Whether revenue increases or decreases when the equilibrium price changes depends on elasticity With elastic demand, a higher price reduces

revenue With inelastic demand, a higher price

increases revenue


Figure 3.4 Effect of a Price Change on Revenue

An increase in price to p2 reduces quantity

Revenue decreases by B, but increases by C, resulting in revenue of A+C

Revenue = A + B


Solved Problem 3.2

• Does revenue increase or decrease if the demand curve is inelastic at the initial price? How does it change if the demand curve is elastic?

• Answer Consider the extreme case where the demand curve

is perfectly inelastic and then generalize to the inelastic case.

Show that if the demand curve is elastic at the initial price, then area C is relatively small.


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Solved Problem 3.2: Answer


Solved Problem 3.2

• Does revenue increase or decrease if the demand curve is inelastic at the initial price? How does it change if the demand curve is elastic?


Effect of elasticity on revenue:

0 0

Quantity, Q, units per year

Quantity, Q, units per year

Elastic demand Inelastic demand

CAB

CB A

Price Price


Demand Elasticities Over Time

• Demand elasticities may be different in the short-run and the long-run

• The difference depends on substitution and storage opportunities

• For most goods elasticities tend to be larger in the long-run

• For easily storable or durable goods, the reverse is true


Sensitivity of Quantity Demanded to Income

• Formally,

where Y stands for income.

• Example If a 1% increase in income results in a 3% increase in

quantity demanded, the income elasticity of demand is = 3%/1% = 3.

Q

Y

Y

Q

YY

QQ

Y

Q

%

%


Sensitivity of Quantity Demanded to Income: Example

• The estimated demand function for pork is:

Q = 171 – 20p + 20pb + 3pc + 2Y where p is the price of pork, pb is the price of beef,

pc is the price of chicken and Y is the income (in thousands of dollars).

Question: what would be the income elasticity of demand for Pork if Q = 220 and Y = 12.5

Answer:• Since = 2, then

114.0220

5.1222

Q

Y

Q

Y

Y

Q

Y

Q


Sensitivity of Quantity Demanded to the Price of a Related Good

• Formally,

where Po stands for price of another good.

• Example If a 1% increase in the price of a related good results in a

3% decrease in quantity demanded, the cross-price elasticity of demand is = -3%/1% = -3.

Q

p

p

Q

ppQQ

p

Q o

o

o

oo

%

%


Sensitivity of Quantity Demanded to the Price of a Related Good

• If the cross-price elasticity is positive, the goods are substitutes Question: can you think of any examples of two

goods that are substitutes?• Roses and carnations; tea and coffee

• If the cross-price elasticity is negative, the goods are complements Question: can you think of any examples of two

goods that are complements?• Peanut butter and jelly; cheese and wine


Sensitivity of Quantity Demanded to the Price of a Related Good: Example

• Again, the estimated demand function for pork is:

Q = 171 – 20p + 20pb + 3pc + 2Y Question: what would be the cross-price elasticity

between the price of beef and the quantity of pork if Q = 220 and pb = $4?

Answer:• Since = 20, then

364.0220

42020

Q

p

Q

p

p

Q bb

b

bp

Q


Sensitivity of Quantity Supplied to Price

• Formally,

where Q indicates quantity supplied.

• Example If a 1% increase in price results in a 3% increase in quantity

supplied, the elasticity of supply is = 3%/1% = 3.

Q

p

p

Q

pp

QQ

p

Q

%

%


Sensitivity of Quantity Supplied to Price: Example

• The estimated linear supply function for pork is:

Q = 88 - 40p where Q is the quantity of pork supplied in million

kg per year and p is the price of pork in $ per year. At the equilibrium, where p = $3.30 and Q = 220,

the elasticity of supply is:

6.0220

30.340

Q

P

p

Q


Sensitivity of Quantity Supplied to Price (cont.)

• Along linear supply curve with a function of:

Where h is the slope or

the elasticity of supply is

hpgQ

p

Qh

Q

ph

Q

p

p

Q


Figure 3.5 Elasticity Along the Pork Supply Curve


Supply Elasticities Over Time

• Supply elasticities may differ in the short-run and the long-run

• The difference depends on the ability to convert fixed inputs into variable inputs


Solved Problem 3.3

• What would be the effect of ANWR production on the world price of oil given that ε = –0.4,η = 0.3, the pre-ANWR daily world production of oil is Q1 = 84 million barrels per day, the pre-ANWR world price is p1 = $70 per barrel, and daily ANWR production would be 0.8 million barrels per day? For simplicity, assume that the supply and demand curves are linear and that the introduction of ANWR oil would cause a parallel shift in the world supply curve to the right by 0.8 million barrels per day.


Solved Problem 3.3


Effects of a Sales Tax

1. What effect does a sales tax have on equilibrium prices and quantity?

2. Is it true, as many people claim, that taxes assessed on producers are passed along to consumers?

3. Do the equilibrium price and quantity depend on whether the tax is assessed on consumers or on producers?


Two Types of Sales Taxes

• Ad valorem tax - for every dollar the consumer spends, the government keeps a fraction, α, which is the ad valorem tax rate

• Specific tax - where a specified dollar amount, , is collected per unit of output


Figure 3.6 Effect of a $1.05 Specific Tax on the Pork Market Collected from Producers

• A tax on producers shifts the supply curve downward by the amount of the tax (= $1.05)….

• which causes the market price to increase…

• After the tax, buyers pay an additional

$.70 per unit ($4.00 - $3.30)

sellers receive $0.35 less per unit ($3.30 - $2.95)

and the government collects $216.3 in revenue.

p, $

pe

r kg

Q2 = 206 Q1 = 220176

T = $216.3 million


0

p2 = 4.00

p3 = 3.30

p2 – = 2.95

= $1.05 S1

e1

e2

S2

D


How Specific Tax Effects Depend on Elasticities

• The government raises the tax from zero to , so the change in the tax is = – 0 = . The price buyers pay increases by:

• If = -0.3 and = 0.6, a change of a tax of = $1.05 causes the price buyers pay to rise by

p

70.0$05.1$]3.0[6.0

6.0

p


Solved Problem 3.4

• If the supply curve is perfectly elastic and demand is linear and downward sloping, what is the effect of a $1 specific tax collected from producers on equilibrium price and quantity, and what is the incidence on consumers? Why?


Solved Problem 3.4


Figure 3.7 Effect of a $1.05 Specific Tax on Pork Collected from Consumers

p,

$ p

er

kg

Q2 = 206 Q1 = 220176

T = $216.3 million

Q, Million kg of pork per year0

p = 4.00

p = 3.30

p2 – = 2.95

= $1.05

Wedge, = $1.05

D1

D2

e2

e2S

The tax shifts the demand curve down by τ = $1.05…

but the new equilibrium is the same as when the tax is applied to suppliers


Figure 3.8 Comparison of an Ad Valorem and a Specific Tax on Pork


Solved Problem 3.5

• If the short-run supply curve for fresh fruit is perfectly inelastic and the demand curve is a downward-sloping straight line, what is the effect of an ad valorem tax on equilibrium price and quantity, and what is the incidence on consumers? Why?


Solved Problem 3.5


Figure 3.9 Effect of a Specific Gasoline (Carbon) Tax in the Long Run and in the

Short Run

Chapter 3 Applying the Supply-and- Demand Model. Copyright © 2012 Pearson Education. All rights...

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