Principles of Economics DBM1313 Chapter 3: Theory of Demand & Elasticity of Demand
CHAPTER 3 2015/chapter 3 pp… · Chapter Outline • The elasticity concept ... demand curve Own...
Transcript of CHAPTER 3 2015/chapter 3 pp… · Chapter Outline • The elasticity concept ... demand curve Own...
CHAPTER 3
Quantitative Demand Analysis
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Chapter Outline• The elasticity concept• Own price elasticity of demand
– Elasticity and total revenue– Factors affecting the own price elasticity of demand– Marginal revenue and the own price elasticity of demand
• Cross-price elasticity– Revenue changes with multiple products
• Income elasticity• Other Elasticities
– Linear demand functions– Nonlinear demand functions
• Obtaining elasticities from demand functions– Elasticities for linear demand functions– Elasticities for nonlinear demand functions
• Regression Analysis– Statistical significance of estimated coefficients– Overall fit of regression line– Regression for nonlinear functions and multiple regression
3-2
Chapter Overview
Introduction• Chapter 2 focused on interpreting demand
functions in qualitative terms:
– An increase in the price of a good leads quantity demanded for that good to decline.
– A decrease in income leads demand for a normal good to decline.
• This chapter examines the magnitude of changes using the elasticity concept, and introduces regression analysis to measure different elasticities.
3-3
Chapter Overview
The Elasticity Concept
• Elasticity
– Measures the responsiveness of a percentage change in one variable resulting from a percentage change in another variable.
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The Elasticity Concept
The Elasticity Formula
• 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
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The Elasticity Concept
Measurement Aspects of Elasticity
• 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.
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The Elasticity Concept
Own Price Elasticity• 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.
𝐸𝑄𝑋𝑑,𝑃𝑋 =%Δ𝑄𝑋
𝑑
%Δ𝑃𝑋– Sign: negative by law of demand.– Magnitude of absolute value relative to unity:
• 𝐸𝑄𝑋𝑑,𝑃𝑋> 1: Elastic.
• 𝐸𝑄𝑋𝑑,𝑃𝑋 < 1: Inelastic.
• 𝐸𝑄𝑋𝑑,𝑃𝑋 = 1: Unitary elastic.
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Own Price Elasticity of Demand
Extreme Elasticities
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Quantity
Demand
Price
Perfectly Inelastic
𝐸𝑄𝑋
𝑑,𝑃𝑋= 0
Demand
𝐸𝑄𝑋𝑑,𝑃𝑋= −∞
Perfectly elastic
Own Price Elasticity of Demand
Linear Demand, Elasticity, and Revenue
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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 − 0.5𝑄Demand: 𝑄 = 80 − 2𝑃
• Revenue = $30 × 20 = $600
• Elasticity: −2 ×$30
20= −3
• Conclusion: Demand is elastic.
Observation: Elasticity varies along a linear (inverse) demand curve
Own Price Elasticity of Demand
Total Revenue Test
• 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.
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Own Price Elasticity of Demand
Factors Affecting the Own Price Elasticity
• Three factors can impact the own price elasticity of demand:
– Availability of consumption substitutes.
– Time/Duration of purchase horizon.
– Expenditure share of consumers’ budgets.
– Product durability
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Own Price Elasticity of Demand
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 as follows:
𝑀𝑅 = 𝑃1 + 𝐸
𝐸– When −∞ < 𝐸 < −1 then, 𝑀𝑅 > 0.– When 𝐸 = −1 then, 𝑀𝑅 = 0.– When −1 < 𝐸 < 0 then, 𝑀𝑅 < 0.
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Own Price Elasticity of Demand
Demand and Marginal Revenue
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Quantity0
𝑃
MR
3
Price
6
Demand
Own Price Elasticity of Demand
1
6
Unitary
Marginal Revenue (MR)
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.
𝐸𝑄𝑋𝑑,𝑃𝑌=%Δ𝑄𝑋
𝑑
%Δ𝑃𝑌– If 𝐸𝑄𝑋𝑑,𝑃𝑌
> 0, then 𝑋 and 𝑌 are substitutes.
– If 𝐸𝑄𝑋𝑑,𝑃𝑌< 0, then 𝑋 and 𝑌 are complements.
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Cross-Price Elasticity
Cross-Price Elasticity in Action• 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.
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Cross-Price Elasticity
Cross-Price Elasticity
• 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 + 𝐸𝑄𝑋𝑑,𝑃𝑋+ 𝑅𝑌𝐸𝑄𝑌𝑑,𝑃𝑋
×%∆𝑃𝑋
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Cross-Price Elasticity
Cross-Price Elasticity in Action• 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.
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Cross-Price Elasticity
Income Elasticity• Income elasticity
– Measures responsiveness of a percent change in demand for good X due to a percent change in income.
𝐸𝑄𝑋𝑑,𝑀=%Δ𝑄𝑋
𝑑
%Δ𝑀– If 𝐸𝑄𝑋𝑑,𝑀
> 0, then 𝑋 is a normal good.
– If 𝐸𝑄𝑋𝑑,𝑀< 0, then 𝑋 is an inferior good.
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Income Elasticity
Income Elasticity in Action• Suppose that the income elasticity of demand for
transportation is estimated to be 1.80. If income is projected to decrease by 15 percent,
• what is the impact on the demand for transportation?
1.8 =%Δ𝑄𝑋
𝑑
−15– Demand for transportation will decline by 27 percent.
• is transportation a normal or inferior good?– Since demand decreases as income declines,
transportation is a normal good.
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Income Elasticity
Other Elasticities
• 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.
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Other Elasticities
Elasticities for Linear Demand Functions
• From a linear demand function, we can easily compute various elasticities.
• Given a linear demand function:
𝑄𝑋𝑑 = 𝛼0 + 𝛼𝑋𝑃𝑋 + 𝛼𝑌𝑃𝑌 + 𝛼𝑀𝑀 + 𝛼𝐻𝑃𝐻
– Own price elasticity: 𝛼𝑋𝑃𝑋
𝑄𝑋𝑑.
– Cross price elasticity: 𝛼𝑌𝑃𝑌
𝑄𝑋𝑑.
– Income elasticity: 𝛼𝑀𝑀
𝑄𝑋𝑑.
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Obtaining Elasticities From Demand Functions
Elasticities for Linear Demand Functions In Action• The daily demand for Invigorated PED shoes is estimated to
be
𝑄𝑋𝑑 = 100 − 3𝑃𝑋 + 4𝑃𝑌 − 0.01𝑀 + 2𝐴𝑋
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: −325
65= −1.15.
– Cross-price elasticity: 435
65= 2.15.
– Income elasticity: −0.0120,000
65= −3.08.
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Obtaining Elasticities From Demand Functions
Elasticities for Nonlinear Demand Functions
• One non-linear demand function is the log-linear demand function:
ln𝑄𝑋𝑑
= 𝛽0 + 𝛽𝑋 ln 𝑃𝑋 + 𝛽𝑌 ln 𝑃𝑌 + 𝛽𝑀 ln𝑀 + 𝛽𝐻 ln𝐻
– Own price elasticity: 𝛽𝑋.
– Cross price elasticity: 𝛽𝑌.
– Income elasticity: 𝛽𝑀.
3-23
Obtaining Elasticities From Demand Functions
Elasticities for Nonlinear Demand FunctionsIn Action
• An analyst for a major apparel company estimates that the demand for its raincoats is given by
𝑙𝑛 𝑄𝑋𝑑 = 10 − 1.2 ln 𝑃𝑋 + 3 ln𝑅 − 2 ln𝐴𝑌
where 𝑅 denotes the daily amount of rainfall and 𝐴𝑌the level of advertising on good Y. What would be the impact on demand of a 10 percent increase in the daily amount of rainfall?
𝐸𝑄𝑋𝑑,𝑅= 𝛽𝑅 = 3.
So, 𝐸𝑄𝑋𝑑,𝑅=
%∆𝑄𝑋𝑑
%∆𝑅⇒ 3 =
%∆𝑄𝑋𝑑
10.
A 10 percent increase in rainfall will lead to a 30 percent increase in the demand for raincoats.
3-24
Obtaining Elasticities From Demand Functions