ELASTICITYManagerial Economics

Jack Wu

NEW YORK CITY TRANSIT AUTHORITY

May 2003: projected deficit of $1 billion over following two years Raised single-ride fares from $1.50 to $2 Raised discount fares

One-day unlimited pass from $4 to $7 30-day unlimited pass from $63 to $70

Increased pay-per-ride MetroCard discount from 10% bonus for purchase of $15 or more to 20% for purchase of $10 or more.

NY MTA

MTA expected to raise an additional $286 million in revenue.

Management projected that average fares would increase from $1.04 to $1.30, and that total subway ridership would decrease by 2.9%.

MANAGERIAL ECONOMICS QUESTION

Would the MTA forecasts be realized? In order to gauge the effects of the price

increases, the MTA needed to predict how the new fares would impact total subway use, as well as how it would affect subway riders’ use of discount fares.

<Note> We can use the concept of elasticity to address these questions.

OWN-PRICE ELASTICITY: E=Q%/P%

Definition: percentage change in quantity demanded resulting from 1% increase in price of the item.Alternatively,

n_price%_change_i

_demandedn_quantity%_change_i

OWN-PRICE ELASTICITY: CALCULATION

CALCULATING ELASTICITY

Arc Approach:

Elasticity={[Q2-Q1]/avgQ}/{[P2-P1]/avgP

% change in qty = (1.44-1.5)/1.47 = -4.1% % change in price = (1.10-1)/1.05 = 9.5% Elasticity=-4.1%/9.5% =-0.432

CALCULATING ELASTICITY

Point approach: Elasticity={[Q2-Q1]/Q1}/{[P2-P1]/P1}

% change in qty = (1.44-1.5)/1.5= -4%% change in price = (1.10-1)/1= 10%Elasticity=-4%/10%=-0.4

OWN-PRICE ELASTICITY

|E|=0, perfectly inelastic 0<|E|<1, inelastic |E|=1, unit elastic |E|>1, elastic |E|=infinity, perfectly elastic

OWN-PRICE ELASTICITY: SLOPE

Steeper demand curve means demand less elastic

But slope not same as elasticity

0 Quantity

Price

DEMAND CURVES

perfectly elastic demand

perfectly inelastic demand

LINEAR DEMAND CURVE

Vertical intercept: perfectly elastic Upper segment: elastic Middle: Unit elastic Lower segment: inelastic Horizontal intercept: perfectly inelastic

Product Market ElasticityAutomobilesChevette U.S. -3.2Civic U.S. -4Consumer productsmusic CDs Aus -1.83cigarettes U.S. -0.3liquor U.S. -0.2football games U.S. -0.275Utilitieselectricity (residential) Quebec -0.7telephone service Spain -0.1water (residential) U.S. -0.25water (industrial) U.S. -0.85

OWN-PRICE ELASTICITIES

OWN-PRICE ELASTICITY: DETERMINANTS

availability of direct or indirect substitutes

cost / benefit of economizing (searching for better price)

buyer’s prior commitments

separation of buyer and payee

Broadly defined market versus narrowly defined market

AMERICAN AIRLINES

“Extensive research and many years of experience have taught us that business travel demand is quite inelastic… On the other hand, pleasure travel has substantial elasticity.”

Robert L. Crandall, CEO, 1989

AADVANTAGE1981: American Airlines pioneered frequent flyer program buyer commitment business executives fly at the expense of others

FORECASTING:WHEN TO RAISE PRICE

CEO: “Profits are low. We must raise prices.”

Sales Manager: “But my sales would fall!”

Real issue: How sensitive are buyers to price changes?

FORECASTING

Forecasting quantity demanded Change in quantity demanded = price elasticity

of demand x change in price

FORECASTING:PRICE INCREASE

If demand elastic, price increase leads to proportionately greater reduction in purchases lower expenditure

If demand inelastic, price increase leads to proportionately smaller reduction in purchases higher expenditure

INCOME ELASTICITY, I=Q%/Y%

Definition: percentage change in quantity demanded resulting from 1% increase in income.Alternatively,

n_income%_change_i

_demandedn_quantity%_change_i

INCOME ELASTICITY

I >0, Normal good I <0, Inferior good Among normal goods: 0<I<1, necessity I>1, luxury

Item Market ElasticityConsumer productscigarettes U.S. 0.1liquor U.S. 0.2food U.S. 0.8clothing U.S. 1newspapers U.S. 0.9Utilitieselectricity (residential) Quebec 0.1telephone service Spain 0.5

INCOME ELASTICITY

CROSS-PRICE ELASTICITY: C=Q%/PO%

Definition: percentage change in quantity demanded for one item resulting from 1% increase in the price of another item.

(%change in quantity demanded for one item) / (% change in price of another item)

CROSS-PRICE ELASTICITY

C>0, Substitutes C<0, complements C=0, independent

Item Market ElasticityConsumer productsclothing/food U.S. 0.1gasoline (competing stn) Boston, MA 1.2Utilitieselectricity/gas (residential) Quebec 0.1electricity/oil (residential) Quebec 0bus/subway London 0.25

CROSS-PRICE ELASTICITIES

ADVERTISING ELASTICITY: A=Q%/A%

Definition: percentage change in quantity demanded resulting from 1% increase in advertising expenditure.

ADVERTISING ELASTICITY: ESTIMATES

Item Market Elasticity

Beer U.S. 0Wine U.S. 0.08Cigarettes U.S. 0.04

If advertising elasticities are so low, why do manufacturers of beer, wine, cigarettes advertise so heavily?

ADVERTISING

direct effect: raises demand indirect effect: makes demand less sensitive

to price

Own price elasticity for antihypertensive drugsWithout advertising: -2.05With advertising: -1.6

FORECASTING DEMAND

Q%=E*P%+I*Y%+C*Po%+a*A%

FORECASTING DEMAND

Effect on cigarette demand of 10% higher income 5% less advertising

change elas. effect

income 10% 0.1 1%

advert. -5% 0.04 -0.2%

net +0.8%

ADJUSTMENT TIME

short run: time horizon within which a buyer cannot adjust at least one item of consumption/usage

long run: time horizon long enough to adjust all items of consumption/usage

ADJUSTMENT TIME

For non-durable items, the longer the time that buyers have to adjust, the bigger will be the response to a price change.

For durable items, a countervailing effect (that is, the replacement frequency effect) leads demand to be relatively more elastic in the short run.

0

4.5

5

1.5 1.6 1.75

long-run demand

short-run demand

Quantity (Million units a month)

Pri

ce (

$ p

er

unit

)

NON-DURABLE: SHORT/LONG-RUN DEMAND

Item Factor Market Short-run Long-runNondurablescigarettes price U.S. -0.3 -3.3liquor price U.S./Canada -0.2 -1.8gaseline price U.S. -0.1 -0.5

income U.S. 0 0.3bus price London -0.8 -1.3subway price London -0.4 -0.7railway price Philadelphia -0.5 -1.8Durablesautomobiles price U.S. -0.2 -0.5

income U.S. 3 1.4

SHORT/LONG-RUN ELASTICITIES

STATISTICAL ESTIMATION: DATA

time series – record of changes over time in one market

cross section -- record of data at one time over several markets

Panel data: cross section over time

MULTIPLE REGRESSION

Statistical technique to estimate the separate effect of each independent variable on the dependent variable dependent variable = variable whose changes are to be explained independent variable = factor affecting the dependent variable

DISCUSSION QUESTION

An Australian telecommunications carrier wants to estimate the own-price elasticity of the demand for international calls to the United States. It has collected annual records of international calls and prices. In each of the following groups, choose the one factor that you would also consider in the regression equation. Explain your reasoning.

 

DISCUSSION QUESTION: CONTINUED

(A)Consumer characteristics: (i) average per capita income, (ii) average age.

(B)Complements: (i) number of telephone lines, (ii) number of mobile telephone subscribers.

(C)Prices of related items: (i) price of electricity, (ii) postage rate from Australia to the United States.