elasticity and its applications economics 230 j.f. o’connor
TRANSCRIPT
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.