Quantitative Demand Analysis Elasticity of Demand

1
Session 3

• Quantitative Demand Analysis Elasticity of
  Demand

2
Overview

• I. Elasticities of Demand
• Own Price Elasticity
• Elasticity and Total Revenue
• Cross-Price Elasticity
• Income Elasticity
• II. Demand Functions
• Linear
• Log-Linear

3
Demand Function Faced by a Firm

• Q ao a1Px a2N a3M a4Py a5H ...
• as are the coefficients to be estimated by
  regression analysis
• demand will then determine the type quantity of
  inputs firm will use

4
Elasticities of Demand

• How responsive is variable G to a change in
  variable S

S and G are directly related
- S and G are inversely related
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Price Elasticity

• Responsiveness of quantity demanded to a change
  in price
• Ep DQd/DP
• Ep dQ/dP (P/Q)

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Own Price Elasticity of Demand

• Negative according to the law of demand

Elastic
Inelastic
Unitary
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Own Price Elasticity Also called Point Price
Elasticity

• Ep DQ/DP
• DQ/DP X P/Q
• Gives elasticity at a given point on the demand
  curve
• If Ep -5, then quantity demand declines 5 for
  each 1 increase in price

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Perfectly Elastic Inelastic Demand
Price
Price
D
D
Quantity
Quantity
Perfectly Elastic
Perfectly Inelastic
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Price Elasticity

• Why is elasticity important?
• It is useful to know by how much quantity
  demanded will fall when price goes up
• Elasticity Worksheets pp. 2-20 2-24 in
  handouts

10
Own-Price Elasticity and Total Revenue

• Elastic
• Increase (a decrease) in price leads to a
  decrease (an increase) in total revenue.
• Inelastic
• Increase (a decrease) in price leads to an
  increase (a decrease) in total revenue.
• Unitary
• Total revenue is maximized at the point where
  demand is unitary elastic.

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Elasticity, TR, and Linear Demand
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Elasticity, Total Revenue, and Marginal Revenue

• A linear demand curve is elastic above midpoint,
  unitary at midpoint and inelastic below midpoint
• So a reduction in price leads to an increase in
  TR down to midpoint and to a decline thereafter
• MR is positive when TR increases, zero when TR is
  max and MR is negative when TR declines

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Elasticity And Total Revenue

• If you cut prices and make it up in volume,
  this is the TR test.
• EX If your Ep for goods you sell is -1.7 and
  you cut your prices by 5
• Will sales increase enough to increase TR?
• -1.7 DQ/-5
• DQ 8.5 so quantity of goods sold will rise by
  8.5

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Arc Price Elasticity

• Price elasticity between two points on demand
  curve
• Ep Q1-Q2/(P1 -P2) x P1 P2)/2 /(Q1 Q2)/2
• Shows how managers can analyze the impact of a
  price change on a goods sales volume

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Arc Price Elasticity

• If Ep -1.5, then between two points on demand
  curve, a 1 change in price results in a 1.5
  opposite change in quantity demanded.

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Inside Business 3-1

• page 76-77
• Calculating and Using the Arc Elasticity An
  Application to the Housing Market
• How is the arc elasticity different from the own
  price elasticity?

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Alternative Formulation For Point Price Elasticity

• Ep a1 X P/Q
• where a1 is estimated coefficient of P in a
  linear regression equation
• if a1 -1,606 and Q 8,064 and P 7, then Ep
  -1.39

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Price Elasticities of Demand in the Real World

• Tables 3-2 and 3-3, pages 78-80

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Factors Affecting Elasticity

• Available Substitutes
• The more substitutes available for the good, the
  more elastic the demand.
• Time
• Demand tends to be more inelastic in the short
  term than in the long term.
• Time allows consumers to seek out available
  substitutes.
• Expenditure Share
• Goods that comprise a small share of consumers
  budgets tend to be more inelastic than goods for
  which consumers spend a large portion of their
  incomes.

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Cross Price Elasticity of Demand
Substitutes
- Complements

• Exy is responsiveness of demand for good X to a
  change in price of good Y

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Cross-price Elasticity Demand

• if Exy .15, then a 10 increase in price of
  good Y results in a 1.5 increase in demand for
  good X (a substitute)
• Exy gt 0 for substitutes
• Exy lt 0 for complements

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Cross-Price Elasticity Demand

• Exy (Qx2-Qx1)/(Py2- Py1) X (Py2Py1)/(Qx2Qx1)
• a high cross price elasticity of demand is used
  to define an industry since it indicates goods
  are very similar

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Cross-Price Elasticities

• Demonstration Problem 3-1
• If the price of recreation increases by 15 , how
  does this affect your stores sales of generic
  food products?
• 0.15 DQ/15
• DQ 2.25
• Food and recreation are substitutes

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Income Elasticity
Normal Good
- Inferior Good

• Em is measure of responsiveness of demand to a
  change in income
• DQd/ DM
• measures the shift in demand curve at each price
  level

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Income Elasticity Of Demand

• Point income elasticity of demand can be
  rewritten
• Em a3 X M/Q
• where a3 is estimated coefficient of M in linear
  regression
• if Em .20, then a 10 increase in income will
  result in a 2 percent increase in demand for the
  good

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Income Elasticity Of Demand

• This measure is not as precise as price
  elasticity of demand
• What do you use to measure income?
• GDP, national income, personal income, etc)
• Good may be normal or inferior
• Useful for forecasting change in demand under
  different economic conditions

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Income Elasticity

• Selected Income Elasticities, page 85
• Demonstration Problem 3-2
• -1.94 DQ/.10 -19.4

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Other Elasticities

• Advertising Elasticity of Demand DQdX/DAX
• Cross-Advertising Elasticity of Demand
  DQdX/DAY
• Supply elasticities DQs/DP

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Uses of Elasticities

• Pricing
• Managing cash flows
• Impact of changes in competitors prices
• Impact of economic booms and recessions
• Impact of advertising campaigns
• And lots more!

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Example 1 Pricing and Cash Flows

• According to an FTC Report by Michael Ward,
  ATTs own price elasticity of demand for long
  distance services is -8.64.
• ATT needs to boost revenues in order to meet
  its marketing goals.
• To accomplish this goal, should ATT raise or
  lower its price?

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Answer Lower price!

• Since demand is elastic, a reduction in price
  will increase quantity demanded by a greater
  percentage than the price decline, resulting in
  more revenues for ATT.

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Example 2 Quantifying the Change

• If ATT lowered price by 3 percent, what would
  happen to the volume of long distance telephone
  calls routed through ATT?

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Answer

• Calls would increase by 25.92 percent!

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Example 3 Impact of a change in a competitors
price

• According to an FTC Report by Michael Ward,
  ATTs cross price elasticity of demand for long
  distance services is 9.06.
• If MCI and other competitors reduced their prices
  by 4 percent, what would happen to the demand for
  ATT services?

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Answer

• ATTs demand would fall by 36.24 percent!

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Demand Functions

• Mathematical representations of demand curves
• Example
• X and Y are substitutes (coefficient of PY is
  positive)
• X is an inferior good (coefficient of M is
  negative)

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Specific Demand Functions

• Linear Demand

Income Elasticity
Own Price Elasticity
Cross Price Elasticity
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Obtaining Elasticities from Demand Functions

• Regression equation example
• Q1.5 - 3.0Px .8M 2.0Py - .6Ps 1.2A
• Coffee demanded is function of price, income,
  competitive brand of coffee, price of sugar, and
  advertising expenditures

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Elasticities For Nonlinear Demand Functions

• Where managers find that a good's demand is NOT a
  linear function of prices, income, advertising
  and other demand shifters.
• EX If Qd cPb Pb Mb Hb
• If we take the logarithm of this equation, we get
  an equation that is linear in the logarithms of
  the variables

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Log-linear Demand Function

• log Qd bo bxlogPx bylogPy bMlogM bHlogH
• When the demand for Good X is log-linear, the
  elasticities are simply the coefficients of the
  corresponding logarithm

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Log-Linear Demand

• Demand for cereal regression
• Q -7.256 - 1.647log(Pc) 1.071log(M) 0.126
  log(A)
• -1.647 shows that demand for cereal is elastic
• each coefficient is an elasticity
• Demonstration Problem 3-4, page 92

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Example of Linear Demand

• Qd 10 - 2P
• Own-Price Elasticity (-2)P/Q
• If P1, Q8 (since 10 - 2 8)
• Own price elasticity at P1, Q8
• (-2)(1)/8 - 0.25

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Log-Linear Demand
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Example of Log-Linear Demand

• log Qd 10 - 2 log P
• Own Price Elasticity -2

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P
D
D
Q
Log Linear
Linear
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Summary

• Elasticities are tools you can use to quantify
  the impact of changes in prices, income, and
  advertising on sales and revenues.