Price Elasticity of DemandOverheads

How much would your roommate payto watch a live fight?How does Showtime decide howmuch to charge for a live fight?

What about Hank and Sons Concrete?How much should they charge per square foot?Can ISU raise parking revenue by raising parking fees?Or will the increase in price drive demanddown so far that revenue falls?

All of these pricing issues revolve around the issue of how responsive the quantity demanded is to price.Elasticity is a measure of how responsiveone variable is to changes in another variable?

The Law of DemandThe law of demand states that whenthe price of a good rises,and everything else remains the same, the quantity of the good demanded will fall.The real issue is how far it will fall.

The demand function is given byQD = quantity demandedP = price of the goodZD = other factors that affect demand

The inverse demand function is given byTo obtain the inverse demand function wejust solve the demand function for Pas a function of Q

Examples QD = 20 - 2P2P + QD = 202P = 20 - QDP = 10 - 1/2 QDSlope = - 1/2

Examples QD = 60 - 3P3P + QD = 603P = 60 - QDP = 20 - 1/3 QDSlope = - 1/3

The slope of a demand curve is given by thechange in Q divided by the change in POne measure of responsiveness is slopeFor demand

The slope of an inverse demand curve is given bythe change in P divided by the change in QFor inverse demand

QD = 60 - 3PExamplesSlope = - 1/3Slope = - 3P = 20 - 1/3 QD

QD = 20 - 2PExamplesSlope = - 1/2Slope = - 2P = 10 - 1/2 QD

We can also find slope from tabular dataQP01029486786105

QP01019.52938.54857.56776.58695.5105114.5124133.5143152.5162171.5181190.5200Demand for Handballs

QP01019.52938.54857.56776.58695.5105114.5124133.5143152.5162171.5181190.5200

Demand for Handballs012345678910110246810121416182022QuantityPrice

QP01019.52938.54857.56776.58695.5105114.5124133.5143152.5162171.5181190.5200

Demand for Handballs012345678910110246810121416182022QuantityPriceQ = 2 - 4 = -2P = 9 - 8 = 1

Problems with slope as a measure of responsivenessSlope depends on the units of measurementThe same slope can be associated withvery different percentage changes

Examples QD = 200 - 2P2P + QD = 2002P = 200 - QDP = 100 - 1/2 QD

QP0100199.5299398.5498597.5697796.5896995.510951194.512941393.51493Consider data on racquetsLet P change from 95 to 96 P = 96 - 95 = 1 Q = 8 - 10 = -2A $1.00 price change when P = $95.00 is tiny

Graphically for racquetsDemand for Racquets889092949698100102024681012141618QuantityPriceLarge % change in QSmall % change in PSlope = - 1/2

Graphically for hand ballsLarge % change in QLarge % change in PSlope = - 1/2Demand for Handballs012345678910110246810121416182022QuantityPriceP P = 7 - 6 = 1 Q = 6 - 8 = -2

So slope is not such a good measureof responsivenessInstead of slope we use percentage changesThe ratio of the percentage change in one variableto the percentage change in another variableis called elasticity

The Own Price Elasticity of Demandis given byThere are a number of ways to computepercentage changes

Initial point method for computingThe Own Price Elasticity of Demand

Price Elasticity of Demand (Initial Point Method)P Q6 85.5 95 104.5 114 12

Final point method for computingThe Own Price Elasticity of Demand

Price Elasticity of Demand (Final Point Method)P Q6 85.5 95 104.5 114 12

The answer is very differentdepending on the choice of the base pointSo we usually useThe midpoint method for computingThe Own Price Elasticity of Demand

Elasticity of Demand Using the Mid-PointFor QD we use the midpoint of the Qs

Similarly for pricesFor P we use the midpoint of the Ps

Price Elasticity of Demand (Mid-Point Method)QP8695.5105114.5124

Classification of the elasticity of demandInelastic demandWhen the numerical value of the elasticity of demand is between 0 and -1.0, we say that demand is inelastic.

Classification of the elasticity of demandElastic demandWhen the numerical value of the elasticity of demand is less than -1.0, we say that demand is elastic.

Classification of the elasticity of demandUnitary elastic demandWhen the numerical value of the elasticity of demand is equal to -1.0, we say that demand is unitary elastic.

Classification of the elasticity of demandPerfectly elastic - D = - Perfectly inelastic - D = 0horizontalvertical

Elasticity of demand with linear demandConsider a linear inverse demand functionThe slope is (-B) for all values of P and QFor example, The slope is -0.5 = - 1/2

PQ12011.5111210.531049.55968.57887.597106.5116125.5135144.5154163.517318Demand for Diskettes0123456789101112130246810121416182022QuantityPrice

The slope is constant but the elasticity of demand will varyPQ12011.5111210.531049.55968.57887.597106.5116125.5135144.5154163.517318

The slope is constant but the elasticity of demand will varyPQ12011.5111210.531049.55968.57887.597106.5116125.5135144.5154163.517318

The slope is constant but the elasticity of demand will varyA linear demand curve becomes more inelasticas we lower price and increase quantityThe elasticity gets closer to zero

QPElasticityExpenditure0120211-23.000022410-7.00004069-3.80005488-2.428664107-1.666770126-1.181872145-0.846270164-0.600064183-0.411854202-0.263240221-0.142922240-0.04350The slope is constant but the elasticity of demand will vary

QPElasticityExpenditure0120211-23.000022410-7.00004069-3.80005488-2.428664107-1.666770126-1.181872145-0.846270164-0.600064183-0.411854202-0.263240221-0.142922240-0.04350The slope is constant but the elasticity of demand will vary

NoteWe do not say that demand is elasticor inelastic ..We say that demand is elastic or inelastic at a given point

Example

The Own Price Elasticity of Demandand Total Expenditure on an ItemHow do changes in an items price affectexpenditure on the item?If I lower the price of a product, will the increasedsales make up for the lower price per unit?

Expenditure for the consumeris equal to revenue for the firmRevenue = R = price x quantity = PQExpenditure = E = price x quantity = PQ

P = change in priceModeling changes in price and quantityQ = change in quantityThe Law of Demand says thatas P increases Q will decreaseP Q

P = initial priceP = change in priceSoP + P = final priceQ = initial quantityQ = change in quantityQ + Q = final quantity

Initial Revenue = PQSoP + P = final price = P Q + P Q + P Q + P QQ + Q = final quantityFinal Revenue = (P + P) (Q + Q)

Now find the change in revenueR = final revenue - initial revenue = P Q + P Q + P Q + P Q - P Q = P Q + P Q + P Q%R = R / R = R / P Q

We can rewrite this expression as follows

Classification of the elasticity of demandInelastic demand% Q and % P are of opposite sign so%R has the same sign as %P +-

Classification of the elasticity of demandInelastic demand% Q and % P are of opposite sign so%R has the same sign as %P -+Lower price lower revenue Higher price higher revenue

Classification of the elasticity of demandElastic demand% Q and % P are of opposite sign so%R has the opposite sign as %P Higher price lower revenue Lower price higher revenue +-

Classification of the elasticity of demandUnitary elastic demand% Q and % P are of opposite sign so theireffects will cancel out and %R = 0.+-

QPElasticityRevenue0120211-23.000022410-7.00004069-3.80005488-2.428664107-1.666770126-1.181872145-0.846270164-0.600064183-0.411854202-0.263240221-0.142922240-0.04350Tabular data

0120 211-23.000022 410-7.000040 69-3.800054 88-2.428664107-1.666770126-1.181872145-0.846270164-0.600064183-0.411854202-0.263240221-0.142922240-0.04350Graphical analysisQPElasticityRevenueDemand for Diskettes0123456789101112130246810121416182022QuantityPriceLose B, gain A, revenue rises

0120 211-23.000022 410-7.000040 69-3.800054 88-2.428664107-1.666770126-1.181872145-0.846270164-0.600064183-0.411854202-0.263240221-0.142922240-0.04350Graphical analysisQPElasticityRevenueDemand for Diskettes0123456789101112130246810121416182022QuantityPriceLose A, gain B, revenue falls

Factors affecting the elasticity of demandAvailability of substitutesImportance of item in the buyers budget

Availability of substitutesThe easier it is to substitute for a good,the more elastic the demandWith many substitutes, individuals willmove away from a good whose price increases

Examples of goods with easy substitutionGasoline at different storesSoft drinksDetergentAirline ticketsLocal telephone service

Narrow definition of productThe more narrowly we define an item,the more elastic the demandWith a narrow definition, there will lots ofsubstitutes

Examples of narrowly defined goodsLemon-lime drinksCorn at a specific farmers marketVanilla ice creamFoodTransportation

Necessities tend to have inelastic demandNecessities tend to have few substitutes

Examples of necessitiesSaltInsulinFoodTrips to HawaiiSailboats

Demand is more elastic in the long-runThere is more time to adjust in the long run

Examples of short and long run elasticityPostal ratesGasolineSweeteners

Factors affecting the elasticity of demandImportance of item in the buyers budgetThe more of their total budget consumersspend on an item,the more elastic the demand for the goodThe elasticity is larger because the item hasa large budget impact

Big ticket items and elasticityHousingBig summer vacationsTable saltCollege tuition

The End