Elasticity and Its Applications

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Elasticity and Its Applications

• Economics 230
• J.F. OConnor

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Questions

• Are consumers spending more on gasoline now
  (1.40/gal.) than three months ago (1.10/gal) ?
  (Yes!)
• Price of airline tickets has increased in the
  past 3 months. Are consumers spending more on
  airline travel? (No!)
• Why the difference? Answer lies in responsiveness
  to price.

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Measuring Responsiveness of One Variable to
Another

• Two Methods
• Rate of change
• Elasticity
• Rate of Change in y with respect to x is the
  change in y divided by the change in x, ceteris
  paribus
• Elasticity of y w.r.t. to x is the percentage
  change in y divided by the percentage change in
  x, ceteris paribus

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Comments

• Rate of change is measured geometrically by
  slope.
• Advantage of elasticity is that, in contrast to
  rate, it does not depend on the units of
  measurement.
• Elasticity can be measured geometrically, from a
  table, or from an equation.

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Factors Affecting Quantity Demanded

• Own price
• Price of substitutes
• Price of complements
• Income of consumers
• Preferences of consumers
• Advertising

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Demand Curve

• Relationship between quantity demanded of the
  good and its price when other factors affecting
  demand are held constant.
• Then the demand curve is Q 14 - 2P
• The convention in graphing demand curves is to
  put price on the vertical axis

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Demand Curve (contd.)

• The equation is then P 7 - .5Q
• Law of Demand (empirical generalization)
• A change in price, ceteris paribus, will result
  in a change in quantity demanded in the opposite
  direction
• Demand curve has negative slope

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Equation P 7 - .5Q
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Responsiveness of Quantity Demanded to Price

• Two Measures
• Rate of change in quantity wrt to price or
  (change in quantity)/ (change in price) inverse
  of the slope
• Elasticity Percentage change in quantity
  divided by percentage change in price

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What is wrong with rate of change?

• It is an adequate measure of responsiveness but
  its value depends on the units of measurement.
  Hard to compare the sensitivity of demand for
  airline tickets with that of the demand for food.
• Elasticity is independent of units of
  measurements. Thus, comparisons across goods are
  possible

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Measuring Elasticity IGraphically

• By definition elasticity is
  (1/slope)(price/quantity)
• Measure elasticity at Price 3.5 in prior
  example
• (1/Slope) - 14/7
• Quantity 7
• Elasticity - (14/7)3.5/7 -1

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• Measure price elasticity of demand at P5.5
• (1/Slope) - 14/7
• Quantity 3
• Elasticity - (14/7)5.5/3 -11/ 3 -3.7
• Price elasticity of demand at P1.5
• Quantity 11
• Elasticity -(14/7)1.5/11 - 3/11

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Observations

• Elasticity varies along the linear demand curves
  while slope is constant
• Simple way to measure price elasticity - take the
  price on the vertical axis and divide it by the
  distance from price to the intercept or maximum
  price. Put a negative sign in front. Lets try
  it!

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At p5.5 eta -5.5/(7-5.5) -11/3 At P
3.5, eta -3.5/(7-3.5) -1 At P
1.5, eta -1.5/(7-1.5) -11/3
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Classifying Direct Price Elasticity of Demand

• Perfectly inelastic ( eta 0 )
• Inelastic ( eta between 0 and -1)
• Unitary elastic ( eta -1 )
• Elastic ( eta less than negative one or
  numerically greater than 1 )
• Perfectly elastic ( eta negative infinity )
• Note Mankiw drops negative sign

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What Happens to the Amount Spent on a Good when
its Price Increases?

• It all depends on the direct price elasticity of
  demand !
• Key relationship
• Change in expenditure change in price
  change in quantity

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The Effect of an Increase in Price on Expenditure

• Demand
• Perfectly inelastic
• inelastic
• unitary elasticity
• elastic
• perfectly elastic
• Repeat for a decrease in price

• Expenditure
• increase
• increase
• no change
• decrease
• decrease to zero

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What Determines the Elasticity of Demand?

• Availability of Substitutes
• demand for apples more elastic than demand for
  fruit
• Importance in the Consumers Budget
• demand for housing more elastic than demand for
  salt
• Time
• response increases with time

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Measuring Elasticity for a Non-linear Demand Curve

• Can still use the graphical technique
• Draw tangent at price at which elasticity is to
  be evaluated
• Compute negative of price divided by the
  difference between the intercept of the tangent
  and the price

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Compute elasticity of demand at price of 5.75 and
quantity of 3. Eta - 5.75/(10-5.75) -
1.35
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Responsiveness to Other Determinants of Demand

• Income elasticity
• Cross-price elasticity
• Elasticity with respect to advertising
  expenditures.