Download Quantitative Demand Analysis

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?
Elasticity
Relative 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)
EZ 
%Q X Q X Q X Q X Z


%Z
Z Z
Z Q X
• Discrete variables (schedule, points) => approximate arc elasticity (averages)
Q X 2  Q X1
Q X
(Q X 2  Q X1 ) 2 Q X 2  Q X1 Z 2  Z1
%Q X
QX
arc E Z 



Z
Z 2  Z1
%Z
Z 2  Z1 Q X 2  Q X1
( Z 2  Z1 ) 2
Z
Own Price Elasticity of
Demand
EQX , PX
%QX

%PX
d
• Negative according to the “law of demand”
Elastic:
EQ X , PX  1
Inelastic: EQ X , PX  1
Unitary:
EQ X , PX  1
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!
E Q X ,PX
%Q X d %Q X d


 8.64
%PX
 3%
%Q X d  3% 8.64   25 .92 %
Perfectly Elastic &
Inelastic Demand
Price
Price
D
D
Quantity
Quantity
Perfectly Elastic
Perfectly Inelastic
EQX , PX  
EQX , PX  0
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.
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 – .02Q
For linear demand MR has the same
intercept and twice the slope of AR
• Arc MR = TR / Q
= (TR2-TR1) / (Q2-Q1)
• Max TR: dTR / dQ = MR = 0
Solve for Q*
800
600
400
P or AR
200
0
-200 0
10
20
30
40
50
-400
60
MR
70
-600
-800
14
12
10
8
6
4
2
0
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.
When demand
is elastic,
price cut
increases
total revenue
Price (dollars per pizza)
At low prices
and large
quantities, the
elasticity is small.
Elastic
demand
25.00
Total Revenue (billions of dollars)
At high prices
and small
quantities, the
elasticity is large.
Demand Curve or
Average Revenue
20.00
15.00
Unit
elastic
12.50
10.00
Inelastic
demand
5.00
0
350.00
312.50
300.00
Marginal Revenue
25
50
Maximum
total revenue
250.00
When demand
is inelastic,
price cut decreases
total revenue
200.00
150.00
100.00
50.00
0
25
50
Quantity (pizza per hour)
Cross Price Elasticity of
Demand
EQX , PY
%QX

%PY
Substitutes (EQx,Py > 0)
Complements (EQx,Py < 0)
d
Example: Impact of a change
in a competitor’s price
• 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!
E Q X , PY
%Q X d %Q X d


 9.06
%PY
 4%
%Q X  4%  9.06   36 .24 %
d
Income Elasticity
E QX ,I
%Q X d

%I
Inferior Good (EQx,I < 0)
Normal 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 Elasticity
of Demand
A relationship is
described as
When its
magnitude is
Which means that
Perfectly elastic
or infinitely elastic
Infinity
The smallest possible increase in price causes
an infinitely large decrease in quantity demanded
Elastic
Less than infinity
but greater than 1
% decrease in quantity demanded
exceeds % increase in price
Unit elastic
1
% decrease in quantity demanded
equals % increase in price
Inelastic
Greater than zero
but less than 1
% decrease in quantity demanded
is less than % increase in price.
Perfectly inelastic
Zero
or completely inelastic
The quantity demanded is the same
at all prices
Glossary of Cross Elasticity
of Demand
A relationship is
described as
When its
magnitude 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.
Substitutes
Positive, less
than infinity
If the price of one good increases, the quantity
demanded 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 Elasticity
of Demand
Which means that
A relationship is
described as
When its
magnitude is
Negative income elastic
(inferior good)
Less than zero
Positive income elastic
(normal good – every
normal is not superior)
Greater than zero The percent increase in the quantity demanded
is less than the percentage increase in income.
Positive income elastic
(superior good – every
superior is normal)
Greater than 1
When income increases, quantity demanded
decreases.
The percentage increase in the quantity demanded
is greater than the percentage increase in income.