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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. - PowerPoint PPT Presentation
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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
Z%
Q%E
12
1212
12
XX
12
12
XX
12
12
XX
XX
X
X
XZ QQ
ZZ
ZZ
2)ZZ(
ZZ
2)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
Factors Affecting 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.
MR
Demand and Revenue• Demand Function
Q = 70,000 – 100P• Inverse Demand Function
P = 700 – .01Q• Total Revenue
TR = P * Q = 700Q – .01Q2 • Average Revenue
AR = TR / Q = 700 – .01Q = P• Marginal Revenue
MR = dTR / dQ = 700 – .02QFor linear demand MR has the sameintercept and twice the slope of AR
• Arc MR = TR / Q = (TR2-TR1) / (Q2-Q1)
• Max TR: dTR / dQ = MR = 0Solve for Q*
-800
-600
-400
-200
0
200
400
600
800
0 10 20 30 40 50 60 70
P or AR
0
2
4
6
8
10
12
14
0 10 20 30 35 40 50 60 70
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
Unitelastic
Elasticdemand
Quantity (pizza per hour)
Pric
e (d
olla
rs p
er p
izza
)
15.00
Inelastic demand
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
Negative income elastic(inferior good)
Less than zero When income increases, quantity demanded decreases.
Greater than zeroPositive income elastic(normal good – every normal is not superior)
The percent increase in the quantity demandedis less than the percentage increase in income.
Positive income elastic(superior good – everysuperior is normal)
Greater than 1 The percentage increase in the quantity demanded is greater than the percentage increase in income.
