# E LASTICITY IMBA NCCU Managerial Economics Jack Wu.

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E LASTICITY IMBA NCCU Managerial Economics Jack Wu

C ASE : N EW Y ORK C ITY T RANSIT A UTHORITY 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. We can use the concept of elasticity to address these questions.

O WN -P RICE E LASTICITY : E=Q%/P% Definition: percentage change in quantity demanded resulting from 1% increase in price of the item. Alternatively,

O WN - PRICE ELASTICITY : C ALCULATION

C ALCULATING E LASTICITY 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

C ALCULATING E LASTICITY Point approach: Elasticity={[Q1-Q2]/Q2}/{[P1-P2]/P2} % change in qty = (1.5-1.44)/1.44= 4.16% % change in price = (1-1.10)/1.10=-9.09 % Elasticity=4.16%/-9.09%=-0.45

C ALCULATING E LASTICITY Arc Approach (midpoint method): 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

O WN -P RICE E LASTICITY |E|=0, perfectly inelastic 0<|E|<1, inelastic |E|=1, unit elastic |E|>1, elastic |E|=infinity, perfectly elastic

O WN - PRICE ELASTICITY : S LOPE Steeper demand curve means demand less elastic But slope not same as elasticity

0 Quantity Price DEMAND CURVES perfectly elastic demand perfectly inelastic demand

E LASTICITY ON L INEAR D EMAND C URVE Vertical intercept: perfectly elastic Upper segment: elastic Middle: Unit elastic Lower segment: inelastic Horizontal intercept: perfectly inelastic

O WN -P RICE E LASTICITIES

O WN -P RICE E LASTICITY : D ETERMINANTS availability of direct or indirect substitutes Narrowly defined or Broadly defined market cost / benefit of economizing (searching for better price) buyer ’ s prior commitments separation of buyer and payee

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

AA DVANTAGE 1981: 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?

F ORECASTING Forecasting quantity demanded Change in quantity demanded = price elasticity of demand x change in price

F ORECASTING : P RICE 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

I NCOME E LASTICITY, I=Q%/Y% Definition: percentage change in quantity demanded resulting from 1% increase in income. Alternatively,

I NCOME E LASTICITY I >0, Normal good I <0, Inferior good Among normal goods: 01, luxury

INCOME ELASTICITY

C ROSS -P RICE E LASTICITY : C=Q%/P O % 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)

C ROSS -P RICE E LASTICITY C>0, Substitutes C<0, complements C=0, independent

CROSS-PRICE ELASTICITIES

A DVERTISING E LASTICITY : A =Q%/A% Definition: percentage change in quantity demanded resulting from 1% increase in advertising expenditure.

A DVERTISING ELASTICITY : E STIMATES ItemMarketElasticity BeerU.S.0 WineU.S.0.08 CigarettesU.S.0.04 If advertising elasticities are so low, why do manufacturers of beer, wine, cigarettes advertise so heavily?

A DVERTISING direct effect: raises demand indirect effect: makes demand less sensitive to price Own price elasticity for antihypertensive drugs Without advertising: -2.05 With advertising:-1.6

F ORECASTING D EMAND Q%=E*P%+I*Y%+C*Po%+a*A%

F ORECASTING D EMAND Effect on cigarette demand of 10% higher income 5% less advertising changeelas.effect income10%0.11% advert. -5%0.04-0.2% net+0.8%

A DJUSTMENT T IME 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

A DJUSTMENT T IME 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 1.51.61.75 long-run demand short-run demand Quantity (Million units a month) Price (\$ per unit) NON-DURABLE: SHORT/LONG-RUN DEMAND

SHORT/LONG-RUN ELASTICITIES

S TATISTICAL E STIMATION : D ATA 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

M ULTIPLE R EGRESSION 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 (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.