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 = P 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

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 I Graphically 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

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 –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

Compute elasticity of demand at price of 5.75 and quantity of 3. Eta =- 5.75/( ) = Compute elasticity of demand at price of 5.75 and quantity of 3. Eta =- 5.75/( ) =- 1.35

Responsiveness to Other Determinants of Demand Income elasticity Cross-price elasticity Elasticity with respect to advertising expenditures.