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