Download - 03.FMG_24-Theory_of_Demand.pdf
FMG 24: Theory Of Demand
Managerial Economics
Dr. Subhasis Bera
The amount of a particular goods or services that a consumer is willing to buy at a
particular price during a specified period under a given set of economic conditions is
called demand.
Demand of a product depends on numbers of variables known as determinants of
demand and demand function is expressed as
Quantity of Product X demanded = Qx
= f (Price of X, Prices of Related Goods, Expectations of Price Changes,
Consumer Incomes, Demanded Tastes and Preferences, Advertising Expenditures, and
so on)
Mathematically we can express this function as
Changes in demand is sensitive to the change of any one these variable.
, ,..., ,..., , ,..x x yQ f P P I T A
What is Demand?
A good Manager needs to have clear idea about the sensitivity of demand
Changes in the demand leads to a change in the total revenue as TR=P.Q
Therefore managerial decision regarding entering into a market or setting up price will be
based on the comparison of the sensitivity of demand among various markets.
In a market, as a result of change in P, there will be a change in Q depending on the slope
of demand curve. Therefore a manager can a take a decision on the basis of the slope of
demand curve.
However units of measurement are different in different market.
How a Manager will compare sensitivity of demand in two different market?
Measures of Sensitivity of Demand
Now it is important to know how demand changes as a result of change in the determinants
of price to understand the change in Total Revenue (TR). Other than slope of the demand
curve, Elasticity concept can help in this regard. Elasticity is a unit free measurement
therefore can be utilised to compare sensitivity of demand in two different market. This
helps a manager can understand how many extra unit he can sell due to a change in price.
There are three types of elasticity
1. Own price elasticity
2. Cross price elasticity
3. Income elasticity
There are two ways to measure the elasticity
1. Point elasticity
2. Arc elasticity
Elasticity of Demand
The point elasticity concept is used to measure the effect on a dependent variable Y of a
very small or marginal change in an independent variable X.
Although the point elasticity concept can often give accurate estimates of the effect on Y of
very small (say, less than 5 percent) changes in X, it is not used to measure the effect on Y
of large-scale changes, because elasticity typically varies at different points along a
function.
Point Elasticity
Changes in the quantity demanded due to one percent change in the price of the same
commodity is known as Price elasticity.
percenatge change in the quantity demanded for XPrice elasticity of X = =
percentage change in the price of XPx
.100
.100
x
x
Px
x
x
Q
Q
P
P
x xPx
x x
P Q
Q p
Price Elasticity of Demand
if E < 0, goods are Normal or Inferior
Changes in the quantity demanded due to one percent change in the Income of the
consumer is known as Income elasticity.
When good X is a normal good, an increase in income leads to an increase in the
consumption of X. Thus, when X is a normal good then
When X is an inferior good , an increase in income leads to a decrease in the consumption
of X. Thus, when X is an inferior good then
percenatge change in the quantity demanded for XIncome elasticity of X = =
Percentage change in the income of the consumerMx
x
x
Mx
Q
Q
M
M
xYx
x
QM
Q M
0Mx
0Mx
Income Elasticity of Demand
Problem 1: Your firm’s research department has estimated the income elasticity ofdemand for FMCG product to be - 1.94. You have just read in The Wall Street Journal thatdue to an upturn in the economy, consumer incomes are expected to rise by 10 percentover the next three years. As a manager of a FMCG company, how will this forecast affecton purchases of FMCG product?
Solution: here
And
Now putting these value in the income elasticity formula we get
Solving this equation for yields
Since FMCG product has an income elasticity of -1.94 and consumer income is expectedto rise by 10 percent, you can expect to sell 19.4 percent less FMCG product over the nextthree years.
Therefore, you should decrease of FMCG product by 19.4 percent, unless something elsechanges.
1.94Mx
10M
% change in quantity demanded1.94
10
19.4xQ
Income Elasticity of Demand: Demonstration Problem
Changes in the quantity demanded for the commodity X due to one percent change in the
price of the commodity Y is known as Cross Price elasticity.
percenatge change in the quantity demanded for XCross Price elasticity of X = =
Percentage change in the price of Yxy
x
xxy
y
y
Q
Q
P
P
y xxy
x y
P Q
Q p
Cross Price Elasticity of Demand
If call rate goes up people will
buy less number of Mobile
Handset
(in case of Complementary)
If price of iphone goes up
people will buy more number of
Samsung Mobile Handset
(in case of Substitute goods)
Our demand function is Q = 8,500 – 5,000P + 3,500PV + 150 I + 1,000A
When P = $7, PV = $3, and I = $40,000 and A = $20,
Then demand Q = 10,000
In the above equation and
Therefore point elasticity = ЄA = point advertising elasticity
i.e., 1 per cent change in advertising will result in a 2 per cent change in demand.
5000Q
P
1000
Q
A
percentage change in quantity demanded
percentage change in advertising expenditure
x
x
A q
q A
201000 2
10000
Point Elasticity: Limitation
Now assume that advertising expenditure increases from $20 to $50 (i.e., ∂A = 30) and demand
increases by 30,000(i.e.,=∂qx ) ( i.e., total demand is now (10,000 + 30,000 = 40,000)
Therefore advertising elasticity
Now if we move in the opposite direction i.e., there is a decrease in the advertising expenditure
then advertising elasticity
The indicated elasticity A = 1.25 is now quite different. This problem occurs because elasticities are
not typically constant but vary at different points along a given demand function.
To overcome the problem of changing elasticity along a demand function, the arc elasticity formula
was developed to calculate an average elasticity for incremental as opposed to marginal changes.
x
x
A q
q A
20 30000
10000 302
x
x
A q
q A
50 30000
400001 2
3. 5
0
Point Elasticity: Limitation- continuation
To overcome the problem of changing elasticities along a demand function, the arc
elasticity formula was developed to calculate an average elasticity for incremental as
opposed to marginal changes.
Arc elasticity measures the average elasticity over a given range of a function.
Arc elasticity is measured as
Change in qAverage q
Change in PAverage P
2 1
2 1
2 1
2 1
q - q/2
- P/2
q q
PP P
2 1
2 1
q P P
P q q
P
Q
A
B
q1 q2
p1
p2
Arc Elasticity
Demand
Curve
Changes in the price changes the demand hence the total revenue.
Elasticity and Total Revenue
Decision to change price to change total revenue will depend on elasticity of demand
Here D2D2 is more elastic than the demand curve D1D1
Px
P1
P2
Q1 Q2Qx
A
B
D1
D1
Px
P1
P2
Q1 Q2Qx
A
B
D2
D2
Loss In Revenue
Gain In Revenue
As a result of change in Price P, quantity demanded Q change. Therefore, the Total
Revenue = TR =P.Q also change
Relation between Elasticity and Total Revenue
Now if then
Or,
Or,
Or,
Or,
TR pq
( )Therefore, .
d TR dpMR p q
dq dq
. 0dp
p qdq
1 . 0q dp
pp dq
1 . 0q dp
p dq
1e
( )0
d TR
dq
Therefore when |e| > 1 TR increases as a result of
decrease in the price
Similarly we can prove that when |e| < 1 then TR
decreases as a result of decrease in the price.
When |e| = 1 then TR remain unchanged 1
1 0e
1
1e
1
1e
Relation Between Elasticity and Total Revenue: Mathematical
With the help of elasticity producer can determine the profit max price of his product
provided that he has price elasticity data and marginal cost.
Although there is no unanimous agreement but still price elasticity information is useful for
policy formulation especially in the case of energy sectors.
1q dp
MR pp dq
1 11 1MR p AR
e e
.TR p qAR p
q q
Relation between AR, MR and Elasticity
Responsiveness of a demand for a product, as a result of change in price, changes
depending on the following factors
Determinants of Elasticity of Demand
The number of close substitute of the product
The cost of switching between the products
The degree of necessity
Nature of demand ( whether subject to
habitual consumption)
Peak and off peak demand
1
2
3
4
5
Elasticity is a unit free measurement.
Concept of elasticity is very important in economic analysis especially when one wants
to compare the changes in the demand or supply in various market.
Price elasticity of demand affects a business's ability to increase the price of a product.
Elastic goods are more sensitive to increases in price, while inelastic goods are less
sensitive.
Assuming that there are no costs in producing the product, businesses would simply
increase the price of a product until demand falls. Things become more complicated,
however, after introducing costs.
Since the main profits of a company come from products in higher demand, it is
important to understand the changes in demand due to change in the price of the
product.
Application of Elasticity of Demand
Price
Elas
ticAs Price increases
Total Revenue Falls.
If Price falls Total Revenue Increases
It is Advisable to reduce price to generate more
revenue
Price
Inelas
tic
As Price increases Total Revenue
Increases.
If Price falls Total Revenue Falls
It is Advisable to increase price to generate more
revenue
Unit
Price
Elas
tic
As Price increases Total Revenue
remain Unchanged.
If Price falls Total Revenue Remain
Unchanged
It is Advisable not to change price
The Government
The Business Sector
Input Price
Application of Elasticity of Demand
Firms use price discounts, specials, coupons, and rebate programs to measure the price
sensitivity of demand for their products. Armed with such knowledge, and detailed unit
cost information, firms have all the tools necessary for setting optimal prices.
The relation between marginal revenue, price, and the point price elasticity of demand
follows directly from the mathematical definition of a marginal relation. In equation below,
the link between marginal revenue, price, and the point price elasticity of demand is
Now if e < 1 then MR > P and the gap between MR and P will fall as |e| increases.
Now since MR = MC from the profit maximization condition, we can write the above
equation as
Therefore optimal profit making price will be
11MR p
e
11MC p
e
*
11
P
MCP
Application of Elasticity of Demand: Optimum Price
People may not react to the price change quickly. There may be some other demand
factors that customer will consider before considering the change in price.
But in the long run demand is more elastic since customers adjust their demand
accordingly.
Time Effect on the Elasticity of Demand
Suppose Delhi Dare Devils offered Rs. 200 off the Rs. 1200 regular price of reservedseats and sales spurted from 3200 to 4000 seats per game.
Now demand curve is P = a + b Q
Here 3200 seats were sold at a regular price of Rs. 1200 per game and 4000 seats weresold at the discount price of Rs. 1000.
This indicates that two points on the team’s linear demand curve are identified.
Now we have 1200 = a + b. 3200
And 1000 = a +b. 4000
Subtracting 2 from 1 we get 200 = - b. 800
Or, b = - 0.25
Now substitute b in 1 or in 2 and get 1200 = a + (-0.25) 3200
Or, a =1200+ 800 = 2000
Therefore demand curve is P = 2000 + (-0.25).Q
Demand Curve Estimation
Demand is more dynamic than an economic analysis can capture in linear demand
analysis. There are numbers of factor that change at much faster speed than the process of
adjustment conducted by the clients.
Problems of Estimation of Demand
Researcher/ Manager has to do a survey to collect
qualitative as well as quantitative information for
estimating Demand.
Question 1 Question 2 Question 3 Question 4 Question 5
What is your
Monthly
Income?
What Price
Currently do
you Pay?
Would you pay a
medium increase
in price?
Would you pay a
Higher increase in
price?
What is the highest
Price you would
like to pay?
What would you do
if the Price is too
high?
Estimation of Demand : Sample Questionnaire Idea
Respondent must understand the purpose of the study
Company can give some money to customer and ask
them to shop in a simulated shop to understand their
preference pattern.
One major problem with this direct approach that
consumer knows that he/she is being monitored hence
will not reveal his/her true preference.
Another problem is that in this method sample error is
much higher than survey method.
Estimation of Demand : Market Experiment
There are various ways of doing market experiment.
In some select cities firm may change the price and observe the change in demand to
estimate relation between p and Q.
Sometime it is difficult to estimate demand accurately as there are interplay betweendemand and supply.
Change in Price may not be an indication of changes in demand alone. Changes in thesupply also have effect on the price and therefore it is difficult to have relation between Pand Qd while other assumption holds.
Since there are other unobservable variables those have impact on the demand, we needto take into account of all these variable to estimate demand more accurately. Regressionanalysis is one method with which we can include them in our model using a term called“disturbance- term”.
We use regression method to estimate the demand. We have to estimate the parameter insuch a way so that sum of the square of the error will be minimum.
Demand specifications can be of various types.
1) Linear
2) Multiplicative
3) Log model. It can be semilog or log log.
After specification of the model i.e., identifying the variables we need to use a method toestimate the parameters. Most common method is OLS method.
1P A IQ P A I
Estimation of Demand
How to do Regression in MS Excel 2007
How to do Regression in MS Excel 2007
How to do Regression in MS Excel 2007
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8301
R Square 0.689
Adjusted R Square 0.6393
Standard Error 1.7183
Observations 30
ANOVA
df SS MS F Significance F
Regression 4 163.55237 40.888094 13.84829
8
4.384E-06
Residual 25 73.814293 2.9525717
Total 29 237.36667
Coefficients Standard
Error
t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 27.261 3.4103023 7.9936982 2.384E-08 20.237279 34.284577 20.237279 34.28457688
X Variable 1 -0.0834 0.0186916 -4.4612825 0.0001506 -0.1218848 -0.0448925 -0.1218848 -0.044892537
X Variable 2 0.0038 0.0116303 0.3249293 0.7479381 -0.020174 0.027732 -0.020174 0.027731974
X Variable 3 -0.0732 0.0200602 -3.6468858 0.0012194 -0.1144722 -0.0318426 -0.1144722 -0.031842565
X Variable 4 -0.276 0.9132764 -0.3021558 0.7650328 -2.1568796 1.6049761 -2.1568796 1.604976133
How to do Regression in MS Excel 2007: Interpretation of the result
In the table above first we need to look at the sign of the coefficient and then to P values. If
p values are less than 0.005 than we can say that the values of the estimates are significant
and we can rely on the coefficient.
Once we find that coefficients are significant we can say look at the values of the
coefficient to conclude about the relationship between explanatory and dependent
variable. In general, in case of linear model, coefficient represents the elasticity.
Therefore from the value we can say about the change in demand due to a change in the
explanatory.
Interpretation of The Result
The regression result mentioned above are based on a sample across the country which
may not be a true representation of the population. The basic test of the statistical
significance of each estimated regression coefficient is called t-test. To test this we need to
calculate the t statistics.
Where,
After calculating the t-statistics we compare the value with the t-table. Conventionally, we
select 0.05 level of significance i.e., we can be 95 per cent confident that results obtained
from sample are representative of the population.
S.E. of
bt
b
Statistical Evaluation of Regression Results: t test
Another test is called F-test which is often used in conjunction with R2. Instead of testing
the significance of each coefficient, this test is applied to test the overall significance of the
regression equation. Therefore F-test measures the significance of the R2. To test this we
need to calculate the F-statistics
As a rule of thumb, a calculated F statistics greater than 3 permits rejection of the
hypothesis that there is no relation between the dependent and explanatory variables at
0.05 per cent level of significance.
2
1, 2
explained variation/(k-1) ( 1)
Unexplained Variation /(n-k)1
( )
k n k
R
kF
R
n k
Statistical Evaluation of Regression Results: F test
Now you need to estimate demand function
using a sample data from Claroline and
explain each of the coefficient.
Estimation of Demand Curve using a sample Data
Thank You!
The concept of elasticity demand is of great use to the government in formulating
its revenue-collecting and welfare policies.
while levying and collecting taxes, the government has to keep in mind the
response of the market.
For example, basic necessities of life have a very low elasticity of demand and the
government, by taxing them, can collect a large amount of tax revenue without
reducing their demand by the consumers. However, while taxing such goods, it has
also to think of the fact that this may lead to an undue burden upon the consumers.
They may reduce their consumption of some other (non-taxed or taxed at lower
rates) goods which happen to be health giving and nutritious, such as milk, cereals
and vegetables. However, if the good in question is considered a harmful one and
has an elastic demand, then the government can deliberately levy a huge tax on it
with the objective of reducing its consumption.
Use of Elasticity of Demand: The Government
When a firm changes Px, its total revenue changes both on account of the change in
Px and the resultant change in Dx. Therefore, a firm finds that while determining
the price of its product, it should take into account its elasticity of demand as well.
Business firms also realize that they can charge higher prices with a limited
reduction in demand only in the short run. If faced with persistent high price, the
consumers shift their demand to lower priced substitutes in the long run.
Use of Elasticity of Demand: The Business Sector
With an objective of profit maximization a firm also needs to consider the input price. i.e.,
the respective elasticities of demand for the productive resources.
If price elasticity of input is higher then the price of the product produced by the firm will
also be sensitive enough. However how much a firm can charge that will again depend on
the price elasticity of demand of the product.
Use of Elasticity of Demand: Input Market