Transcript Power Division Ministry of Power, Energy & Mineral Resources

BUS 525: Managerial
Economics
Lecture 3
Quantitative Demand Analysis
Overview
I. The Elasticity Concept
– Own Price Elasticity
– Elasticity and Total Revenue
– Cross-Price Elasticity
– Income Elasticity
II. Demand Functions
– Linear
– Log-Linear
III. Regression Analysis
The Elasticity Concept
• Elasticity is a measure of the responsiveness of a variable
to a change in another variable: the percentage change
in one variable that arises due to a given percentage
change in another variable
– How responsive is variable “G” to a change in variable “S”?
EG , S
%G

%S
If EG,S > 0, then S and G are directly related.
If EG,S < 0, then S and G are inversely related.
If EG,S = 0, then S and G are unrelated.
The Elasticity Concept Using
Calculus
• An alternative way to measure the
elasticity of a function G = f(S) is
EG , S
dG S

dS G
If EG,S > 0, then S and G are directly related.
If EG,S < 0, then S and G are inversely related.
If EG,S = 0, then S and G are unrelated.
Own Price Elasticity of
Demand
A measure of the responsiveness of the demand for a good to
changes in the price of that good: the percentage change in the
quantity demanded of the good divided by the percentage
change in the price of the good
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
Perfectly Elastic &
Inelastic Demand
Price
Price
D
D
Quantity
PerfectlyElastic( EQX ,PX  )
Quantity
PerfectlyInelastic(EQX ,PX  0)
Elasticity, Total Revenue and
Linear Demand
P
100
TR
0
10
20
30
40
50
Q
0
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
80
800
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
80
1200
60
800
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
80
1200
60
40
800
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
80
1200
60
40
800
20
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
Elastic
80
1200
60
40
800
20
0
10
20
30
40
50
Q
0
10
20
Elastic
30
40
50
Q
Elasticity, Total Revenue and
Linear Demand
P
100
TR
Elastic
80
1200
60
Inelastic
40
800
20
0
10
20
30
40
50
Q
0
10
Elastic
20
30
40
Inelastic
50
Q
Own-Price Elasticity
and Total Revenue
• Elastic
– Increase (a decrease) in price leads to a
decrease (an increase) in total revenue.
• Inelastic
– 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.
Elasticity, Total Revenue and
Linear Demand
P
100
TR
Unit elastic
Elastic
Unit elastic
80
1200
60
Inelastic
40
800
20
0
10
20
30
40
50
Q
0
10
Elastic
20
30
40
Inelastic
50
Q
Class Exercise I
• Research department of an airline
estimates that the own price
elasticity of demand for a particular
route is -1.7. If the airline cuts price
by 5 percent, will the ticket sales
increase enough to increase overall
revenues?
• If so, by how much?
Factors Affecting
Own Price Elasticity
– Available substitutes
• The more substitutes available for the good, the
more elastic the demand.
• Broader categories of goods have more inelastic
demand than more specifically defined categories.
– 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.
Some Elasticity Estimates
Table 3-2 Selected Own Price Elasticities
Market
Own Price Elasticity
Transportation
-0.6
Motor vehicles
-1.4
Motorcycles and bicycles
-2.3
Food
-0.7
Cereal
-1.5
Clothing
-0.9
Women’s clothing
-1.2
Table 3-3 Selected Short and Long-Term Own Price Elasticities
Market
Short-Term Own Price
Elasticity
Long-Term Own Price
Elasticity
Transportation
-0.6
-1.9
Food
-0.7
-2.3
Alcohol and tobacco
-0.3
-0.9
Recreation
-1.1
-3.5
Clothing
-0.9
-2.9
1-18
The Arc Price Elasticity of
Demand
How can the percentage changes in Q
and P be calculated in order to derive
the own price elasticity of demand?
Q
EQX,PX
--------------(Q1 + Q2)/2
=-----------------P
-------------(P1 + P2)/2
Q
-------------(Q1 + Q2)
= -------------------P
------------(P1 + P2)
Class Exercise II
•
Consider a Demand Curve
Q = 40,000,000 - 2,500P
•
Calculate arc elasticity of demand from the given data
Price
16,000
P2=12,500
P1=12,000
0
B
A
8,750,000
10,000,000
40,000,000
Q
How sensitive are consumers to a
change in the avg. price of
automobiles?
We calculate the arc price elasticity of
demand between A and B as:
Ep =
10,000,000-8,750,000
-----------------------------(10,000,000+8,750,000)/2
-------------------------------- = - 3.267
12,000 - 12,500
----------------------(12,000 + 12,500)/2
Interpretation
 Between points A and B (or between
the price range from $12,000 to
$12,500), a one-percent increase in
the average price of cars will bring
about, on average, a reduction of
sales by 3.267%, ceteris paribus.
 Because the price elasticity of
demand is calculated between two
points on a given demand curve, it is
called the arc price elasticity of
demand.
Caveat
• Elasticity measure depends on
the price at which it is measured.
• It is not generally a constant
(because the demand curve is not
likely to be a straight line).
The Point Price Elasticity of Demand
It measures the price
elasticity of demand at a
given price or a particular
point on the demand curve.
Q
P
ep = (-----)(----)
P
Q
Class Exercise III
Qxd = -2,500Px + 1,000M + 0.05PY - 1,000,000H+
0.05AX
Other things being equal,
if P1 = $12,000, Q1 = 10,000,000.
• Calculate point elasticity of demand.
• What's the point elasticity of demand at
P2 = $12,500?
• Calculate arc elasticity of demand.
Calculation of the point elasticity using
the demand for automobile equation
Qxd = -2,500Px + 1,000M + 0.05PY - 1,000,000H+ 0.05AX
Other things being equal,
if P1 = $12,000, Q1 = 10,000,000.
The point price elasticity is:
Q
P
ep = (-----) (---)
P
Q
= (-2,500)(12,000/10,000,000)
=-3
Point price elasticity (cont.)
What's the point elasticity of demand at
P2 = $12,500?
At this price, Q = 8,750,000.
Hence,
ep =
=
=
Q
P
(-----) (---)
P
Q
(-2,500)(12,500/8,750,000)
- 3.571
Two versions of the elasticity of
demand – Point vs. Arc
Price
16,000
12,500
12,000
ep= -3.571
Ep= -3.267
ep= -3.0
8,750,000 10,000,00
0
Q
From Concept to Applications
We began with a definition of the
elasticity of demand based on,
EQx, Px =
%in Qxd
--------------%  in Px
If we know the price elasticity of
demand (Ep), the formula will let us
answer a number of "what if" questions.
Examples
(1) How great a price reduction is
necessary to increase sales by
10%?
(2) What will be the impact on sales
of a 5% price increase?
(3) Given marginal cost and price
elasticity information, what is the
profit-maximizing price?
Class Exercise IV
Supposing that the elasticity of
demand for diesel is -0.5, how much
prices must go up to reduce gasoline
use by 1%?
The price increase needed to
reduce diesel consumption by 1%
Supposing that the elasticity of
demand for diesel is -0.5, how much
prices must go up to reduce gasoline
use by 1%?
- 0.01
- 0.5 = ---------- ,
%Pd
%Pd = (-0.01/-0.5) = + 0.02 or 2%
Marginal Revenue and the Own
Price Elasticity Of Demand
• Demand and marginal revenue
– For a linear demand curve marginal revenue curve lies
exactly halfway between the demand curve and the
vertical axis
– Marginal revenue is less than the price of each unit sold
– When demand is elastic (-∞<E<-1), marginal revenue is
positive
– When demand is unitary elastic (E=-1), marginal
revenue is zero
– When demand is inelastic (-1<E<0), marginal revenue
is negative
Cross Price Elasticity of
Demand
A measure of the responsiveness of the demand for
a good to changes in the price of a related good:
the percentage change in the quantity demanded of
the good divided by the percentage change in the
price of a related good
d
EQX , PY
%QX

%PY
If EQX,PY > 0, then X and Y are substitutes.
If EQX,PY < 0, then X and Y are complements.
Income Elasticity
A measure of the responsiveness of the demand for a
good to changes in consumer income: the percentage
change in the quantity demanded divided by the
percentage change in income
EQX , M
%QX

%M
d
If EQX,M > 0, then X is a normal good.
If EQX,M < 0, then X is a inferior good.
Some Elasticity Estimates
Table 3-4 Selected Cross-Price Elasticities
Cross-Price Elasticity
Transportation and recreation
-0.05
Food and recreation
-0.15
Clothing and food
-0.18
Table 3-5 Selected Income Elasticities
Income Elasticity
Transportation
1.80
Food
0.80
Ground beef, nonfed
-1.94
Table 3-6 Selected Long-Term Advertising Elasticities
Advertising Elasticity
Clothing
0.04
Recreation
0.25
1-36
Other Elasticities
Advertising elasticity
A measure of the responsiveness of the demand for a
good to changes in advertising expenditure: the
percentage change in the quantity demanded divided by
the percentage change in advertising expenditure
%QX

%Ax
d
EQX , A
Class Exercise V
• Advertising elasticity of recreation :
0.25
• How much should advertising
increase to increase the demand for
recreation by 15%?
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!
Example 1: Pricing and Cash
Flows
• According to a BTRC Report by
Zahid Hussain, BTCL’s own price
elasticity of demand for long
distance services is -8.64.
• BTCL needs to boost revenues in
order to meet it’s marketing goals.
• To accomplish this goal, should
BTCL raise or lower it’s price?
Answer: Lower price!
• Since demand is elastic, a reduction
in price will increase quantity
demanded by a greater percentage
than the price decline, resulting in
more revenues for BTCL.
Example 2: Quantifying
the Change
• If BTCL lowered price by 3 percent,
what would happen to the volume of
long distance telephone calls routed
through BTCL?
Answer
• Calls would increase by 25.92 percent!
EQX , PX
%QX
 8.64 
%PX
d
%QX
 8.64 
 3%
d
 3%   8.64  %QX
d
%QX  25.92%
d
Example 3: Impact of a change
in a competitor’s price
• According to an BTRC Report by
Zahid Hussain, BTCL’s cross price
elasticity of demand for long distance
services is 9.06.
• If competitors reduced their prices
by 4 percent, what would happen to
the demand for BTCL’s services?
Answer
• BTCL’s demand would fall by 36.24 percent!
EQX , PY
%QX
 9.06 
%PY
%QX
9.06 
 4%
d
 4%  9.06  %QX
d
%QX  36.24%
d
d
Interpreting Demand
Functions
• Mathematical representations of
demand curves.
• Example: d
QX  10  2PX  3PY  2M
• X and Y are substitutes (coefficient of
PY is positive).
• X is an inferior good (coefficient of M is
negative).
Linear Demand Functions
• General Linear Demand Function:
QX  0   X PX  Y PY  M M  H H
d
P
EQX , PX   X X
QX
Own Price
Elasticity
EQX , PY
PY
 Y
QX
Cross Price
Elasticity
M
EQX , M   M
QX
Income
Elasticity
Class Exercise 6
• Given the demand curve,
Qxd = 100- 3Px+4Py-.01M+2Ax
• If Px=25, Py= 35, M= 20,000, Ax =50
• Calculate (a) own price, (b) cross
price, and © income elasticity of
demand
Example of Linear Demand
•
•
•
•
•
Qxd = 100- 3Px+4Py-.01M+2Ax.
Own-Price Elasticity: (-3)Px/Qx.
If Px=25, Py= 35, M= 20,000, Ax =50
Q=65 [since 100 – 3(25) +4(35) -.01(20,000)+2(50)] = 65
Own price elasticity of demand at Px=25, Q=65:
E
=(-3)(25)/65= - 1.15
• Cross price elasticity of demand at Py=35, Q65
E
=(4)(35)/65= 2.15
• Income elasticity of demand at M=20,000
E
=(-0.1)(20,000)/65= -3.08
QX , PX
QX , Py
QX , M
Elasticities for Nonlinear Demand
Functions
• Qxd = c PxβxPy βyMβMHβH
• General Log-Linear Demand Function:
ln QX d  0   X ln PX  Y ln PY  M ln M  H ln H
Own PriceElasticity:  X
Cross PriceElasticity:  Y
IncomeElasticity:
M
Example of Log-Linear
Demand
• ln(Qd) = 10 - 2 ln(P).
• Own Price Elasticity: -2.
Graphical Representation of
Linear and Log-Linear
Demand
P
P
D
Linear
D
Q
Log Linear
Q
Regression Analysis
• One use is for estimating demand
functions.
• Important terminology and concepts:
–
–
–
–
–
Least Squares Regression: Y = a + bX + e.
Confidence Intervals.
t-statistic.
R-square or Coefficient of Determination.
F-statistic.
An Example
• Use a spreadsheet to estimate the
following log-linear demand
function.
ln Qx  0   x ln Px  e
Summary Output
Regression Statistics
Multiple R
0.41
R Square
0.17
Adjusted R Square
0.15
Standard Error
0.68
Observations
41.00
ANOVA
df
Regression
Residual
Total
Intercept
ln(P)
SS
1.00
39.00
40.00
MS
F
3.65
18.13
21.78
Coefficients Standard Error
7.58
1.43
-0.84
0.30
3.65
0.46
t Stat
5.29
-2.80
Significance F
7.85
0.01
P-value
0.000005
0.007868
Lower 95%
Upper 95%
4.68
10.48
-1.44
-0.23
Interpreting the Regression
Output
• The estimated log-linear demand function
is:
– ln(Qx) = 7.58 - 0.84 ln(Px).
– Own price elasticity: -0.84 (inelastic).
• How good is our estimate?
– t-statistics of 5.29 and -2.80 indicate that the
estimated coefficients are statistically different
from zero.
– R-square of .17 indicates we explained only 17
percent of the variation in ln(Qx).
– F-statistic significant at the 1 percent level.
Conclusion
• Elasticities are tools you can use to quantify
the impact of changes in prices, income, and
advertising on sales and revenues.
• Given market or survey data, regression
analysis can be used to estimate:
– Demand functions.
– Elasticities.
– A host of other things, including cost functions.
• Managers can quantify the impact of changes
in prices, income, advertising, etc.
Lessons:
(1) The first lessons in business:
Never lower your price in the inelastic
range of the demand curve. Such a
price decrease would reduce total
revenue and might at the same time
increase average production cost.
(2)When the demand is inelastic, raise
the price to increase revenue and,
possibly, profit.
(3)When demand is elastic, price
increases should be avoided.
Lessons (Cont.)
(4)But should we always cut price
when the demand is elastic?
Even over the range where demand
is elastic, a firm will not necessarily
find it profitable to cut prices; the
profitability of such an action
depends on whether the marginal
revenues generated by the price
reduction exceed the marginal cost
of the added production.
Another Example: Optimal Pricing
Step 1 – Using the relationship between MR and Ep
Given, TR = PQ,
TR
MR = ------Q
 (PQ)
=--------Q
Q
P
= P(-----) + Q (-----)
Q
Q
Q
P
= P (1 + ----- -----) = P ( 1 +
P
Q
1
----)
ep
Optimal Pricing (Cont.)
Optimal Price is when MC = MR
i.e., MC = P (1 + 1/ep)
MC
P = ------------(1 + 1/ep)
That is, the profit-maximizing
price is determined by MC and ep
Predicting Revenue Changes
from Two Products
Suppose that a firm sells to related goods. If the price of
X changes, then total revenue will change by:
 


R  [RX 1  EQX , PX  RY EQY , PX ]  %PX