3.Baye Chapter 3.pptx

Chapter 3
Quantitative Demand Analysis

© 2022 by McGraw-Hill Education. All Rights Reserved. 2
Learning Objectives
Explain Explain how regression analysis may be used to estimate demand functions and how to interpret and use the output of a regression.
Show Show how to determine elasticities from linear and log-linear demand functions.
Explain Explain the relationship between marginal revenue and the own price elasticity of demand.
Discuss Discuss three factors that influence whether the demand for a given product is relatively elastic or inelastic.
Illustrate Illustrate the relationship between the elasticity of demand and total revenues.
Apply Apply various elasticities of demand as a quantitative tool to forecast changes in revenues, prices, and/or units sold.

Elasticity
–A measure of the responsiveness of one variable to changes in another variable;
the percentage change in one variable that arises due to a given percentage
change in another variable.
© 2022 by McGraw-Hill Education. All Rights Reserved. 3-3
The Elasticity Concept

The elasticity between two variables, 𝐺 and 𝑆, is mathematically expressed
as:
𝐸𝐺,𝑆 =
%Δ𝐺
%Δ𝑆
When a functional relationship exists, like 𝐺 = 𝑓 𝑆 , the elasticity is:
𝐸𝐺,𝑆 =
𝑑𝐺
𝑑𝑆
𝑆
𝐺
The Elasticity Concept

Important aspects of the elasticity:
–Sign of the relationship:
• Positive
• Negative
–Absolute value of elasticity magnitude relative to unity:
• 𝐸𝐺,𝑆 > 1 𝐺 is highly responsive to changes in 𝑆.
• 𝐸𝐺,𝑆 < 1 𝐺 is slightly responsive to changes in 𝑆.
Measurement Aspects of Elasticity

Own Price Elasticity of Demand
Own price elasticity of demand
– Measures the responsiveness of a percentage change in the quantity demanded of good X to a
percentage change in its price.
𝐸𝑄𝑋
𝑑
,𝑃𝑋
=
%Δ𝑄𝑋
𝑑
%Δ𝑃𝑋
– Sign: negative by law of demand.
– Magnitude of absolute value relative to unity:
• 𝐸𝑄𝑋
𝑑
,𝑃𝑋
> 1: Elastic.
• 𝐸𝑄𝑋
𝑑
,𝑃𝑋
< 1: Inelastic.
• 𝐸𝑄𝑋
𝑑
,𝑃𝑋
= 1: Unitary elastic.

Linear Demand, Elasticity, and Revenue (Figure 3.1)
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 − 2𝑃
• Revenue = $30 × 20 = $600
• Elasticity: −2 ×
$30
20
= −3
• Conclusion: Demand is elastic.
• Revenue = $20 × 40 = $800
$20
40
= −1
• Conclusion: Demand is unitary elastic.
• Revenue = $10 × 60 = $600
$10
60
= −0.333
• Conclusion: Demand is inelastic.
Observation: Elasticity
varies along a linear
(inverse) demand curve

Elasticity and Total Revenue (Figure 3.1)
• Total Revenue is maximized
when elasticity is = 1, Unitary
Elastic
• In the elastic range, total
revenue can be increased by
decreasing price.
• In the inelastic range, total
revenue can be increased by
increasing price.

When demand is elastic:
– A price increase (decrease) leads to a decrease (increase) in total revenue.
When demand is inelastic:
– A price increase (decrease) leads to an increase (decrease) in total revenue.
When demand is unitary elastic:
–Total revenue is maximized.
Total Revenue Test

Perfectly Elastic and Inelastic Demand (Figure 3.2)
Quantity
Demand
Price
Perfectly Inelastic
𝐸𝑄𝑋
𝑑
,𝑃𝑋
= 0
Demand
𝐸𝑄𝑋
𝑑
,𝑃𝑋
= −∞
Perfectly
elastic

Three factors can impact the own price elasticity of demand:
1. Availability and number of substitutes
2. Time/duration of purchase horizon
3. Expenditure share of consumers’ budgets
Factors Affecting the Own Price Elasticity

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 as
follows:
𝑀𝑅 = 𝑃
1 + 𝐸
𝐸
–When −∞ < 𝐸 < −1 then, 𝑀𝑅 > 0.
–When 𝐸 = −1 then, 𝑀𝑅 = 0.
–When −1 < 𝐸 < 0 then, 𝑀𝑅 < 0.
Marginal Revenue and the Own Price Elasticity of
Demand

Demand and Marginal Revenue (Figure 3.3)
Quantity
0
𝑃
MR
3
Price
6
Demand
1
6
Unitary
Marginal Revenue (MR)

Cross-price elasticity
–Measures the responsiveness of a percent change in demand for good X due to a
percent change in the price of good Y.
𝐸𝑄𝑋
𝑑
,𝑃𝑌
=
%Δ𝑄𝑋
𝑑
%Δ𝑃𝑌
–If 𝐸𝑄𝑋
𝑑
,𝑃𝑌
> 0, then 𝑋 and 𝑌 are substitutes.
–If 𝐸𝑄𝑋
𝑑
,𝑃𝑌
< 0, then 𝑋 and 𝑌 are complements.
Cross-Price Elasticity

Suppose it is estimated that 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, by how much will demand for clothing change?
−0.18 =
%∆𝑄𝐶𝑙𝑜𝑡ℎ𝑖𝑛𝑔
𝑑
10
⇒ %∆𝑄𝐶𝑙𝑜𝑡ℎ𝑖𝑛𝑔
𝑑
= −1.8
–That is, demand for clothing is expected to decline by 1.8 percent when the price
of food increases 10 percent.
Cross-Price Elasticity in Action

• Cross-price elasticity is important for firms selling multiple products.
–Price changes for one product impact demand for other products.
• Assessing the overall change in revenue from a price change for one
good when a firm sells two goods is:
∆𝑅 = 𝑅𝑋 1 + 𝐸𝑄𝑋
𝑑
,𝑃𝑋
+ 𝑅𝑌𝐸𝑄𝑌
𝑑
,𝑃𝑋
× %∆𝑃𝑋
Cross-Price Elasticity

Suppose a restaurant earns $4,000 per week in revenues from hamburger
sales (X) and $2,000 per week from soda sales (Y).
If the own price elasticity for burgers is 𝐸𝑄𝑋,𝑃𝑋
= −1.5 and the cross-price
elasticity of demand between sodas and hamburgers is 𝐸𝑄𝑌,𝑃𝑋
= −4.0,
what would happen to the firm’s total revenues if it reduced the price of
hamburgers by 1 percent?
∆𝑅 = $4,000 1 − 1.5 + $2,000 −4.0 −1% = $100
–That is, lowering the price of hamburgers 1 percent increases total revenue by
$100.
Cross-Price Elasticity in Action

Income elasticity
–Measures the responsiveness of a percent change in demand for good X due to a
percent change in income.
𝐸𝑄𝑋
𝑑
,𝑀 =
%Δ𝑄𝑋
𝑑
%Δ𝑀
–If 𝐸𝑄𝑋
𝑑
,𝑀 > 0, then 𝑋 is a normal good.
–If 𝐸𝑄𝑋
𝑑
,𝑀 < 0, then 𝑋 is an inferior good.
Income Elasticity

Suppose that the income elasticity of demand for organic potatoes is
estimated to be 2.26. If income is projected to decrease by 10 percent,
what is the impact on the demand for organic potatoes?
2.26 =
%Δ𝑄𝑋
𝑑
−10
–Demand for organic potatoes will decline by 22.6 percent.
Are organic potatoes a normal or inferior good?
–Since demand decreases as income declines, organic potatoes are a normal good.
Income Elasticity in Action

Own advertising elasticity of demand for good X is the ratio of the
percentage change in the consumption of X to the percentage change in
advertising spent on X.
Cross-advertising elasticity between goods X and Y would measure the
percentage change in the consumption of X that results from a 1 percent
change in advertising toward Y.
Other Elasticities

From a linear demand function, we can easily compute various elasticities.
Given a linear demand function:
𝑄𝑋
𝑑
= 𝛼0 + 𝛼𝑋𝑃𝑋 + 𝛼𝑌𝑃𝑌 + 𝛼𝑀𝑀 + 𝛼𝐻𝑃𝐻
–Own price elasticity: 𝐸𝑄𝑥,𝑝𝑥 = 𝛼𝑋
𝑝𝑥
𝑄𝑥
–Cross price elasticity: 𝐸𝑄𝑥,, 𝑃𝑦 = 𝛼𝑌
𝑝𝑦
𝑄𝑥
–Income elasticity: 𝐸𝑄𝑥,𝑀 = 𝛼𝑀
𝑀
𝑄𝑥
Elasticities for Linear Demand Functions

Elasticities for Linear Demand Functions In Action
The daily demand for Invigorated PED shoes is estimated to be:
𝑄𝑋
𝑑
= 100 − 3𝑃𝑋 + 4𝑃𝑌 − 0.01𝑀 + 2𝑃𝐴𝑋
Suppose good X sells at $25 a pair, good Y sells at $35, the company utilizes 50
units of advertising, and average consumer income is $20,000. Calculate the own
price, cross-price and income elasticities of demand.
– 𝑄𝑋
𝑑
= 100 − 3 $25 + 4 $35 − 0.01 $20,000 + 2 50 = 65 units.
– Own price elasticity: −3(
25
65
) = −1.15.
– Cross-price elasticity: 4(
35
65
) = 2.15.
– Income elasticity: −0.01(
20,000
65
) = −3.08.

A log-linear specification is appropriate if quantity demanded is not
linearly related to the explanatory variables:
ln 𝑄𝑋
𝑑
= 𝛽0 + 𝛽𝑋 ln 𝑃𝑋 + 𝛽𝑌 ln 𝑃𝑌 + 𝛽𝑀 ln 𝑀 + 𝛽𝐻 ln 𝐻
–Own price elasticity: 𝛽𝑋.
–Cross price elasticity: 𝛽𝑌.
–Income elasticity: 𝛽𝑀.
Elasticities for Nonlinear Demand Functions

An analyst for a major apparel company estimates that the demand for its
raincoats is given by
𝑙𝑛 𝑄𝑋
𝑑
= 10 − 1.2 ln 𝑃𝑋 + 3 ln 𝑅 − 2 ln 𝐴𝑌
where 𝑅 denotes the daily amount of rainfall and 𝐴𝑌 the level of advertising on good Y.
What would be the impact on demand of a 10 percent increase in the
daily amount of rainfall?
𝐸𝑄𝑋
𝑑
,𝑅 = 𝛽𝑅 = 3. So, 𝐸𝑄𝑋
𝑑
,𝑅 =
%∆𝑄𝑋
𝑑
%∆𝑅
⇒ 3 =
%∆𝑄𝑋
𝑑
10
A 10 percent increase in rainfall will lead to a 30 percent increase in the demand for
raincoats
Elasticities for Nonlinear Demand Functions In Action

Data-Driven Demand Curves
• Recall from Chapter 1, Table 1-3
the example relating quantity and
price for television using data
from 10 outlets.
• Suppose now that the data were
generated as part of a field
experiment. Using regression
analysis, the demand curve is
estimated to be
Q = 1631.47 – 2.60P

Regression techniques can also be applied to estimate log-linear demand
functions, a common application for nonlinear functions.
See the Excel file Demo03-05.xls at www.mhhe.com/baye10e
Regression for Nonlinear Functions
and Multiple Regression

Using Multiple Regression to Estimate Demand Curves with
Multiple Explanatory Variables
• Functional relationships with multiple variables:
• For linear demand relationship
𝑄𝑋
𝑑
= 𝛼0 + 𝛼𝑋𝑃𝑋 + 𝛼𝑀𝑀 + 𝛼𝐻𝑃𝐻 + 𝑒
• Or for non-linear relationship
ln 𝑄𝑋
𝑑
= 𝛽0 + 𝛽𝑋 ln 𝑃𝑋 + 𝛽𝑀 ln 𝑀 + 𝛽𝐻 ln 𝑃𝐻 + 𝑒

3.Baye Chapter 3.pptx

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to 3.Baye Chapter 3.pptx

Similar to 3.Baye Chapter 3.pptx (20)

Recently uploaded

Recently uploaded (15)

3.Baye Chapter 3.pptx