Elasticity and Its Applications

Economics 230

J.F. O’Connor

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.

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

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.

Factors Affecting Quantity Demanded

• Own price

• Price of substitutes

• Price of complements

• Income of consumers

• Preferences of consumers

• Advertising

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

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

Equation:

P= 7 - .5Q

Equation:

P= 7 - .5Q

A Linear Demand Curve

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Pric

e

Quantity

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

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

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

• Measure price elasticity of demand at P=5.5

• (1/Slope) = - 14/7

• Quantity = 3

• Elasticity = - (14/7)5.5/3 = -11/ 3 = -3.7

• Price elasticity of demand at P=1.5

• Quantity = 11

• Elasticity = -(14/7)1.5/11 = - 3/11

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. Let’s try it!

At p=5.5

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

At p=5.5

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

A Linear Demand Curve

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Price

Quantity

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

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

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

What Determines the Elasticity of Demand?

• Availability of Substitutes– demand for apples more elastic than demand for

fruit

• Importance in the Consumer’s Budget• demand for housing more elastic than demand

for salt

• Time– response increases with time

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

Demand for Plones

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8 9 10

Price

Quantity

Compute elasticity of demand at price of 5.75 and quantity of 3.

Eta =- 5.75/(10-5.75)

=- 1.35

Compute elasticity of demand at price of 5.75 and quantity of 3.

Eta =- 5.75/(10-5.75)

=- 1.35

Responsiveness to Other Determinants of Demand

• Income elasticity

• Cross-price elasticity

• Elasticity with respect to advertising expenditures.