Quantitative Demand Analysis

Headlines:In 1989 Congress passed and president signed a minimum-wage bill. The purpose of this bill was to increase the purchasing power of unskilled workers.

We know that the consequences of price floor is decrease in demand. Now lets quantify it.

How many minimum-wage workers lost their jobs?

What happened to the total wage bill of firms that hire unskilled workers?

ElasticityRelative measure. Sign and magnitude show type of relationship and extent of demand response to a change in its determinant “Z”.

EZ = %QX / %Z

• Percentage <=> proportion

• Units-free measure: % independent of the units of measurement

• Continuous variables (function, curve) => precise point elasticity (derivative)

• Discrete variables (schedule, points) => approximate arc elasticity (averages)

X

XXXXZ Q

Z

Z

Q

ZZ

QQ

Z%

Q%E

12

1212

12

XX

12

12

XX

12

12

XX

XX

X

X

XZ QQ

ZZ

ZZ

QQ

2)ZZ(

ZZ

2)QQ(

QQ

Z

ZQ

Q

Z%

Q%Earc

Own Price Elasticity of Demand

• Negative according to the “law of demand”

Elastic:

Inelastic:

Unitary:

X

dX

PQ P

QE

XX

%

%,

1, XX PQE

1, XX PQE

1, XX PQE

%92.2564.8%3Q%

64.8%3

Q%

P%

Q%E

dX

dX

X

dX

P,Q XX

Example: Quantifying the Change• According to an FTC Report by Michael Ward, AT&T’s own

price elasticity of demand for long distance services is -8.64.

• If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T?

• Calls would increase by 25.92 percent!

Perfectly Elastic & Inelastic Demand

Perfectly Elastic

D

Price

Quantity

Perfectly Inelastic

D

Price

Quantity

XX PQE , 0,

XX PQE

Determinants of Own Price Elasticity

• Available Substitutes

• The more substitutes available for the good, the more elastic the demand.

• Time

• Demand tends to be more inelastic in the short term than in the long term.

• Time allows consumers to seek out available substitutes.

• Expenditure Share

• Goods that comprise a small share of consumer’s budgets tend to be more inelastic than goods for which consumers spend a large portion of their incomes.

Own-Price Elasticity and Total Revenue

• Elastic

• An increase (a decrease) in price leads to a decrease (an increase) in total revenue.

• Inelastic

• An increase (a decrease) in price leads to an increase (a decrease) in total revenue.

• Unitary

• Total revenue is maximized at the point where demand is unitary elastic.

350.00 25 50

12.50

5.00

10.00

20.00

25.00

0 25 50

150.00

200.00

250.00

312.50

Tot

al R

even

ue (

bill

ions

of

doll

ars)

Maximum total revenue

When demandis inelastic, price cut decreasestotal revenue

Unit elastic|EP| = 1 MR = 0

Elastic demand|EP| > 1 MR > 0

Quantity (pizza per hour)

Pric

e (d

olla

rs p

er p

izza

)

15.00

Inelastic demand|EP| < 1 MR < 0

300.00

100.00

50.00

0

When demandis elastic, price cut increasestotal revenue

At high prices and small quantities, the elasticity is large.

At low prices and large quantities, the elasticity is small.

Demand Curve orAverage Revenue

Marginal Revenue

Cross Price Elasticity of Demand

Substitutes (EQx,Py > 0)

Complements (EQx,Py < 0)

Y

dX

PQ P

QE

YX

%

%,

%24.3606.9%4Q%

06.9%4

Q%

P%

Q%E

dX

dX

Y

dX

P,Q YX

• According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is 9.06.

• If MCI and other competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services?

• AT&T’s demand would fall by 36.24 percent!

Example: Impact of a change in a competitor’s price

Income Elasticity

Normal Good (EQx,I > 0)

I%

Q%E

dX

I,QX

Inferior Good (EQx,I < 0)

Superior Good (EQx,I > 1)

Uses of Elasticities• Pricing

• Managing cash flows

• Impact of changes in competitors’ prices

• Impact of economic booms and recessions

• Impact of advertising campaigns

• And lots more: CDC study

Du Pont antitrust law suit

Glossary of Price Elasticityof Demand

A relationship isdescribed as

When itsmagnitude is

Which means that

Perfectly elasticor infinitely elastic

Unit elastic

Inelastic

Perfectly inelasticor completely inelastic

Infinity The smallest possible increase in price causes an infinitely large decrease in quantity demanded

Less than infinitybut greater than 1

Greater than zerobut less than 1

Elastic

1

Zero

% decrease in quantity demanded exceeds % increase in price

% decrease in quantity demanded equals % increase in price

% decrease in quantity demanded is less than % increase in price.

The quantity demanded is the same at all prices

Glossary of Cross Elasticityof Demand

A relationship isdescribed as

When itsmagnitude is

Which means that

Perfect substitutes Infinity The smallest possible increase in price of one good causes an infinitely large in the demand of the other good.

Positive, lessthan infinity

Substitutes If the price of one good increases, the quantitydemanded of the other good also increases.

Independent Zero The demand for one good remains constant,regardless of the price of the other good.

Complements Less than zero The demand for one good decreases when the price of the other good increases.

Glossary of Income Elasticityof Demand

A relationship isdescribed as

When itsmagnitude is

Which means that

Positive income elastic(superior good)

Greater than 1 The percent increase in the quantity demandedis greater than the percentage increase in income.

Greater than zeroPositive income inelastic(normal good)

The percent increase in the quantity demandedis less than the percentage increase in income.

Negative income elastic(inferior good)

Less than zero When income increases, quantity demanded decreases.