1

Demand and Supply:Elasticity

Principles MicroeconomicsProfessor Dalton

ECON 202 – Spring 2013Boise State University

2

Elasticity

Elasticity - measure of responsiveness

Measures how much a dependent variable changes due to a change in an independent variable

Elasticity = %Δ X / %Δ Y • Elasticity can be computed for any two

related variables

3

Elasticity Measures

Elasticities economists are interested in:• a change in price on the quantity demanded• a change in income on the demand function

for a good• a change in the price of a related good on

the demand function for a good• a change in the price on the quantity

supplied

4

Price Elasticity of Demand

The “law of demand” tells us that as the price of a good increases the quantity that will be bought decreases but does not tell us by how much.

The price elasticity of demand, ε, is a measure of that information

“If you change price by 5%, by what percent will the quantity purchased change?

5

ε % Q

% P

At a point on a demand function this can be calculated by:

ε =

Q2 - Q1

Q1

P2 - P1

P1

Q2 - Q1 = Q

P2 - P1 = P=

QQ1

PP1

Price Elasticity of Demand

6

Q

Q1

P

P1

ε =

Price decreases from $7 to $5

3

Px

Qx/t

D

$5B

5

$7A

P1 =

P2 =

P2- P1 = 5 - 7 = P = -2P = -2

Q1 = Q2 =

Q2 - Q1 = 5 - 3 = Q = +2

Q = +2

+2

7

3[2/3 = .66667]

[-2/7=-.28571]

= % Q = 67%

% P = -28.5%= -2.3 [rounded]

The “own” price elasticity of demandat a price of $7 is -2.3

This is “point” price elasticity. It is calculated at a pointon a demand function. It is not influenced by the directionor magnitude of the price change.

.

There is a problem! If theprice changes from $5 to$7 the coefficient of elasticity is different!

-2

7

3

Px

Qx/t

D

$5B

5

$7A

Q

Q1

P

P1

ε =

When the price increases from $5 to $7,

P1 =

P2 =P = +2

+2

5

Q1=Q2=

Q = -2

-2

5 = % Q = -40%

% P = 40%= -1 [this is called “unitary elasticity]

the ε = -1 [“unitary”]

ep = -1

In the previous slide, when the price decreased from $7 to $5, ε = -2.3

ep = -2.3The point price elasticity is different at every point!

There is an easier way!

8

An easier way!

Q1PP1

ε =

QQ1 =

Q

Q1

P1

P*

By rearranging terms

=P1

Q1*

Q

Pthis is the slope of thedemand function

this is a point onthe demandfunction

Q P1

Q1

= *Pε

Given that when:P1 = $7, Q1 = 3

P2 = $5, Q2= 5

P2- P1 = 5 - 7 = P = -2

Q2 - Q1 = 5 - 3 = Q = +2

Then,Q

P +2 -2

= = -1

This is the slope of the demand Q = f(P)

-1

P1 = $7, Q1 = 3

7

3= -2.33

On linear demand functions the slope remains constant so you just put in P and Q

9

Use of Price Elasticity

Ruffin and Gregory [Principles of Economics, Addison-Wesley, 1997, p 101] report that:• short run εof gasoline is = .15 (inelastic)• long run εof gasoline is = .78 (inelastic)• short run εof electricity is = . 13

(inelastic)• long run εof electricity is = 1.89 (elastic)

Why is the long run elasticity greater than short run?

What are the determinants of elasticity?

10

Determinants of Price Elasticity

Availability of substitutes• greater availability of substitutes makes a good

more elastic Proportion of budget expended on good

• higher proportion – more elastic Time to adjust to the price changes

• longer time period means more adjustments possible and increases elasticity

Price elasticity for “brands” tends to be more elastic than for the category

11

P

Q/t

D1

D1 is a “perfectly elastic”demand function.

ε % Q

% P

For an infinitesimally smallchange in price, Q changes by infinity.

= undefined

perfectly elasticε = undefined

.

Buyers are very responsive to price changes. An infinitely small change in pricechanges Q by infinity.

D2

perfectlyinelasticε = 0

D2 is a “perfectly inelastic” demand function, no matter howmuch the price changes the same amount is bought. Buyersare not responsive to price changes! ε = 0, perfectly inelastic.

0

P 0= 0

.

As the demand function becomes more horizontal, [buyers are more responsiveto price changes],ε approaches infinity.

De

12

Income Elasticity

Income elasticity [ey] is a measure of the effect of an income change on demand.

When ey > 0, the good is a normal or superior good an increase in income increases demand, a decrease in income decreases demand.

0 < ey < 1 is a normal good

1 < ey is a superior good

When ey < 0, the good is an inferior good

13

Examples of Income Elasticity

normal goods, [0 < ey < 1 ], (between 0 and 1) • coffee, beef, Coca-Cola, food, Physicians’

services, hamburgers, . . .

Superior goods, [ ey > 1], (greater than 1)

• movie tickets, foreign travel, wine, new cars, . .

Inferior goods, [ey < 0], (negative)

• “top ramen,” flour, lard, beans, . . .

14

Cross-Price Elasticity

Cross-price elasticity [exy] is a measure of how responsive the demand for a good is to changes in the prices of related goods.

Given a change in the price of good Y, what is the effect on the demand for good X?

exy is defined as:

PQ

ey

xxy

%

%

15

Cross-Price Elasticity

In the case of beef and pork•the ebp is not the same as epb

•ebp is the % change in the demand for beef with respect to a % change in the price of pork

•epb is the % change in the demand for pork with respect to a % change in the price of beef

16

The cross elasticity of the demand for beef with respect to the

price of pork, ebeef-pork or ebp can be calculated:

ebp =% Q of beef

%P of pork

An increase in the price of pork,

+ Pp

“causes” an increase in the demand for beef.

+ Qb+ebppositive

cross elasticity is positive

ebp =% Q of beef

%P of pork

A decrease in the price of pork,

- Pp

“causes” a decrease in the demand for beef.

- Qb+ebppositive

If goods are substitutes, exy will be positive. The greater the coefficient, the more likely they are good substitutes.

Cross-Price Elasticity

17

Cross-Price Elasticity

•exy > 0 suggests substitutes, the higher the coefficient the better the substitute

•exy < 0 suggests the goods are complements, the greater the absolute value the more complimentary the goods are

•exy = 0 suggests the goods are not related

•exy can be used to define markets in legal proceedings

18

Elasticity of Supply

Elasticity of supply is a measure of how responsive sellers are to changes in the price of the good.

Elasticity of supply [es] is defined:

seQuantity Supplied

price%

%

19

Q /t

P

Given a supply function,

supply

at a price [P1], Q1 is produced and offeredfor sale.

P1

Q1

At a higher price [P2],

P2

a largerquantity, Q2, will be producedand offered for sale.

Q2

+P

+Q

The increase in price [ P ], inducesa larger quantity goods [ Q]for sale.

The more responsive sellers are to

P, the greater the absolute value of es.

[The supply function is “flatter”ormore elastic]

Elasticity of supply

es = %Qsupplied

%P

20

Q /ut

PThe supply function is amodel of sellers behavior.

Sellers behavior is influenced by:1. technology

2. prices of inputs3. time for adjustment

market periodshort runlong runvery long run

4. expectations 5. anything that influences costs of production

taxesregulations, . . .

Se

a perfectly elastic supply [es is undefined.]

Sia perfectly inelasticsupply, es = 0

as supply approaches horizontal es

approaches infinity

21

Elasticity

Price elasticity of demand • elastic, inelastic or unitary elasticity

Income elasticity • superior, normal, and inferior

Cross-Price elasticity• complements/substitutes

Price elasticity of supply• Elastic, inelastic