Elasticities

1. CHAPTER 2
Elasticities

2. Learning Objectives
What will you learn in this module?
 What is price elasticity of demand?
 What is the difference between inelastic and elastic
demand for goods?
 Why firms want to know the price elasticity of demand for
their products?
 What are the THREE (3) important factors that influences
the elasticity of demand for a product?

3. Consumer Demand
• In the previous module, we can see that the demand
for a firm's product, depends on
• its price,
• the prices of substitutes or complements,
• consumer incomes and
• other variables.

4. Consumer Demand
In this module, we will go through the important elements:
• Demand for a firm’s product depends on various factors,
managers must understand the directions of the changes in
prices and income on consumer demand to make a good
decision.
• Important to understand what is elasticity, it explains the
magnitude of changes in price and quantity of a good.
• Demand Function: different factors influence consumer
demand, the Regression analysis is used to estimate the
parameters (factors) of demand functions.

5. THE ELASTICITY

6. The Elasticity
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What is Elasticity?
• the responsiveness or sensitivity of one variable to
changes in other variable.
• The elasticity between two variables, quantity ( and , can
be expressed mathematically as:
• When a functional relationship exists, like , the elasticity
is:

7. How to measuring Elasticity
• Two Important aspects of elasticity:
1. Sign determines the relationship: either positive or
negative.
2. Value: absolute value is greater than 1 or less than 1.
The absolute Magnitude of elasticity:
• 𝐸 𝑄,𝑃 > 1 Q is highly responsive to changes in 𝑃.
• 𝐸 𝑄,𝑃 < 1 Q is slightly responsive to changes in P.
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8. Price Elasticity
• What is own price elasticity of demand?
 Measures the responsiveness of a percentage change
in the quantity demanded of good X to a percentage
change in the price of X.
𝐸 𝑄 𝑋
𝑑
,𝑃 𝑋
=
%Δ𝑄 𝑋
𝑑
%Δ𝑃𝑋
 Sign: negative by law of demand.
 Magnitude of absolute value relative to unity:
• 𝐸 𝑄 𝑋
𝑑
,𝑃 𝑋
> 1: price elasticity of demand is Elastic.
• 𝐸 𝑄 𝑋
𝑑
,𝑃 𝑋
< 1: price elasticity of demand is Inelastic.
• 𝐸 𝑄 𝑋
𝑑
,𝑃 𝑋
= 1: price elasticity is Unitary elastic.
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9. A VIDEO ABOUT
For more Video on Demand Elasticity
https://www.youtube.com/watch?v=HHcblIxiAAk
For more video on Price Elasticity
https://www.youtube.com/watch?v=VhKI8cOaYL
I

10. Linear Demand
Quantity
Price
Demand
$40
0
$20
$10
20 30
$5
40
$15
$30
$25
$35
10 50 60 70 80
Linear Inverse Demand: 𝑃 = 40 − 0.5𝑄
Demand: 𝑄 = 80 − 2𝑄
• Revenue = $30 × 20 = $600
• Elasticity: −2 ×
$30
20
= −3
• Conclusion: Demand is elastic.
• Revenue = $10 × 60 = $600
• Elasticity: −2 ×
$10
60
= −0.333
• Conclusion: Demand is
inelastic.
Elasticity varies along
a linear (inverse)
demand curve

11. Elasticity and Total Revenue
• Total revenue is maximized when demand is unitary
elastic
• Elastic demand: A price increase (decrease) leads to a
decrease (increase) in total revenue.
• Inelastic demand: A price increase (decrease) leads to
an increase (decrease) in total revenue.
• Perfectly elastic: infinite elasticity of demand
• Perfectly inelastic: demand elasticity is zero
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𝐸 𝑄 𝑋
𝑑
,𝑃 𝑋
= 0
𝐸 𝑄 𝑋
𝑑
,𝑃 𝑋
= −∞

12. Factors Affecting their Own Price
Elasticity
• Three factors can influence the own price
elasticity of demand:
1. Availability of consumption substitutes: one key
determinant of elasticity of demand of the good is
the number of its close substitute goods
2. Time/Duration of purchase horizon: demand is
more elastic in the short term than in the long term.
3. Expenditure share of consumers’ budgets: small
share of consumer’s budget is more inelastic than
consumers spend large proportion of their income.
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13. A VIDEO ABOUT
For more video on Factors Affecting their Own Price
Elasticity
https://www.youtube.com/watch?v=mKSBYx3VPPA

14. Elasticity and Marginal Revenue
• The marginal revenue can be derived from a market
demand curve.
 Marginal revenue measures the additional revenue due to a
change in output.
• This link relates marginal revenue to the own price
elasticity of demand:
• When then, . demand is elastic
• When then, . demand is unitary elastic
• When then, . demand is inelastic
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15. The figure showsthe MarginalRevenueassociatedwith eachprice-outputpairon the demandcurve.
Noticethat for a lineardemand curve, the marginalrevenuescheduleliesexactlyhalfwaybetween the
demandcurve and the verticalaxis.Furthermore, marginalrevenueis lessthan the pricefor each unit
sold.
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Quantity0
𝑃
MR
3
Price
6
Demand
1
6
Unitary
Marginal Revenue (MR)

16. Cross-Price Elasticity
• Cross-price elasticity
Measures responsiveness of a percent change in demand for good
X due to a percent change in the price of good Y.
𝐸 𝑄 𝑋
𝑑
,𝑃 𝑌
=
%Δ𝑄 𝑋
𝑑
%Δ𝑃𝑌
• If 𝐸 𝑄 𝑋
𝑑
,𝑃 𝑌
> 0, then 𝑋 and 𝑌 are substitutes.
• If 𝐸 𝑄 𝑋
𝑑
,𝑃 𝑌
< 0, then 𝑋 and 𝑌 are complements.
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17. Cross-Price Elasticity
• Suppose the cross-price elasticity of demand between
clothing and food is -0.18. If the price of food is projected
to increase by 10 percent, how much will demand for
clothing change?
−0.18 =
%∆𝑄 𝐶𝑙𝑜𝑡ℎ𝑖𝑛𝑔
𝑑
10
⇒ %∆𝑄 𝐶𝑙𝑜𝑡ℎ𝑖𝑛𝑔
𝑑
= −1.8
• That is, demand for clothing is expected to decline by 1.8 percent
when the price of food increases 10 percent.
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18. Cross-Price Elasticity
• Cross-price elasticity is important for firms selling multiple
products.
• Price changes for one product that affect changes in demand for
other products.
• Assessing the overall change in revenue from a price
change for one good when a firm sells two different goods
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19. Income Elasticity
• What is Income elasticity
 Measures responsiveness of a percent change in demand for good
X due to a percent change in income (M).
𝐸 𝑄 𝑋
𝑑
,𝑀 =
%Δ𝑄 𝑋
𝑑
%Δ𝑀
• If 𝐸 𝑄 𝑋
𝑑
,𝑀 > 0, then 𝑋 is a normal good.
• If 𝐸 𝑄 𝑋
𝑑
,𝑀 < 0, then 𝑋 is an inferior good.
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20. A VIDEO ABOUT
For more information on Cross-Price and
Income Elasticity
https://www.youtube.com/watch?v=QLMJDo9dc
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21. Elasticities for Linear Demand
Functions
• From a linear demand function, we can compute various
elasticities of demand.
• Given a linear demand function:
𝑄 𝑋
𝑑
= 𝛼0 + 𝛼 𝑋 𝑃𝑋 + 𝛼 𝑌 𝑃𝑌 + 𝛼 𝑀 𝑀 + 𝛼 𝐻 𝑃 𝐻
 Own price elasticity: 𝛼 𝑋
𝑃 𝑋
𝑄 𝑋
𝑑.
 Cross price elasticity: 𝛼 𝑌
𝑃 𝑌
𝑄 𝑋
𝑑.
 Income elasticity: 𝛼 𝑀
𝑀
𝑄 𝑋
𝑑.
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22. Regression Analysis
• How does manager obtain information on the demand
function?
• Published studies.
• Hire consultant.
• To estimate the demand function using Statistical technique called
regression analysis
• using data on quantity, price, income and other important variables.
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23. Conclusion
• Elasticities are tools used 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.
• Other things, including cost functions.
• Managers can quantify the impact of changes in prices,
income, advertising, etc.
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24. SHORT QUIZ
On Key Terms and Concepts
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25. Review the following key concepts and terms
Elasticity
Own price elasticity of demand
Cross price elasticity of demand
Arc elasticity of demand
Inelastic demand
Income elasticity
Perfectly Inelastic demand
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