ElasticityElasticity

What would you do?What would you do?

Winged Foot Gold ClubWinged Foot Gold Club Budget shortfallBudget shortfall Out-of-town membership = Out-of-town membership =

$2,500 annual dues$2,500 annual dues Questions:Questions:

Do you raise the dues?Do you raise the dues? If yes, how much?If yes, how much? What will happen?What will happen?

ElasticityElasticity

How much change in quantity How much change in quantity demanded does a change in price demanded does a change in price create?create?

Elastic = big changesElastic = big changes

Unitary Elasticity = equal changesUnitary Elasticity = equal changes

Inelastic = small changesInelastic = small changes

2 Methods2 Methods

Total Revenue MethodTotal Revenue Method

Compare changes in Price to changes in Compare changes in Price to changes in TRTR

Calculation MethodCalculation Method

Calculate point elasticityCalculate point elasticity

Measuring Total RevenueMeasuring Total Revenue

TR = P * QTR = P * Q ElasticElastic

Small Change in Price Small Change in Price Big change in QuantityBig change in Quantity

TR changes in the opposite direction as PriceTR changes in the opposite direction as Price InelasticInelastic

Small change in PSmall change in P Smaller change in QSmaller change in Q

TR Changes in the same direction as PriceTR Changes in the same direction as Price NB Comparing TR with P, NOT QUANTITYNB Comparing TR with P, NOT QUANTITY

Total RevenueTotal Revenue

D

P

Q0

$4

100

RevenueP x Q = $400

Guidelines for TR MethodGuidelines for TR Method

Elastic DemandElastic Demand Opposite direction of movementOpposite direction of movement If Price goes up……….Revenue goes downIf Price goes up……….Revenue goes down If Price goes down……Revenue goes upIf Price goes down……Revenue goes up

Inelastic DemandInelastic Demand Same direction of movementSame direction of movement If Price goes up……….Revenue goes upIf Price goes up……….Revenue goes up If Price goes down……Revenue goes If Price goes down……Revenue goes

downdown

Total Revenue - InelasticTotal Revenue - Inelastic

D

P

Q0

$4

100

Revenue

90

$5

A - Extra Revenue

B - Lo

st R

evenue

Revenue gained from higher price (A) exceeds revenue lost from lower quantity (B).

Price increases from 4 to 5 while TR increases from 400 to 450. When P & TR move in the same direction it is elastic.

A – Revenue gained from raising price

B – Revenue lost from less quantity sold

Total Revenue - ElasticTotal Revenue - Elastic

D

P

Q0

$4

100

Revenue gained

Revenue

Revenue

Lost

Revenue gained from higher price is exceeded by revenue lost from the lower quantity.

Price increases from 4 to 5 while TR decreases from 400 to 350. When P & TR move in opposite direction it is elastic.

$5

70

A – Revenue gained from raising price

B – Revenue lost from less quantity sold

Point ElasticityPoint Elasticity

Measures small changes on curveMeasures small changes on curve

= % change in Q / % change in P= % change in Q / % change in P

= <(Q= <(Q00-Q-Q11)/Q)/Q00>/<(P>/<(P00-P-P11)/P)/P00>>

ElasticityElasticity

ElasticElastic >1 to infinity>1 to infinity

Unitary elasticityUnitary elasticity =1=1

InelasticInelastic 0 to <10 to <1

ElasticityElasticity

Elasticity changes with Elasticity changes with location on curvelocation on curve

Marginal UtilityMarginal Utility Slopes at ends changeSlopes at ends change Elasticity & Slope not Elasticity & Slope not

the samethe same Large change in high Large change in high

prices = small change prices = small change in quantityin quantity

Small changes at low Small changes at low prices = large change prices = large change in quantityin quantity

Changing ElasticitiesChanging Elasticities

Inelastic – A large change in price…

… leads to a small change in quantity

Elastic – A small change in price…… leads to a large change in quantity

23

10

13

4 5 11 14

Price

Quantity

Elasticity FactorsElasticity Factors

SubstitutesSubstitutes

IncomeIncome

NecessitiesNecessities

TimeTime

Elasticity ExamplesElasticity Examples

ExampleExample

Revenue Table – Slices of PizzaRevenue Table – Slices of Pizza

Price Quantity Revenue = P*QPrice Quantity Revenue = P*Q 0.500.50 300300 150150 1.001.00 250250 250250 1.501.50 200200 300300 2.002.00 150150 300300 2.502.50 100100 250250 3.003.00 50 50 150150

Calculating ElasticityCalculating Elasticity

Consider two examples, the price of a Consider two examples, the price of a slice of pizza changes fromslice of pizza changes from $1.00 to $1.50 $1.00 to $1.50 $2.00 to $2.50$2.00 to $2.50

Use both methods to determine Use both methods to determine elasticityelasticity TRTR CalculationsCalculations

TR MethodTR Method

1.00 to 1.501.00 to 1.50 Price up (1.00 to 1.50)Price up (1.00 to 1.50) Revenue up (250 to 300)Revenue up (250 to 300) Same direction – InelasticSame direction – Inelastic

2.00 to 2.502.00 to 2.50 Price up (2.00 to 2.50)Price up (2.00 to 2.50) Revenue down (300 to 250)Revenue down (300 to 250) Opposite direction – ElasticOpposite direction – Elastic

Calculating Elasticity #1Calculating Elasticity #1

Calculate elasticity as Price increases Calculate elasticity as Price increases from 1.00 to 1.50. Is the elasticity from 1.00 to 1.50. Is the elasticity elastic or inelastic?elastic or inelastic?

=<(200-250)/250>/<(1.50-1.00)/1.00>=<(200-250)/250>/<(1.50-1.00)/1.00> =(-50/250)/(.50/1)=(-50/250)/(.50/1) =-.2/.5=-.2/.5 =-.4=-.4 InelasticInelastic

Calculating Elasticity #2Calculating Elasticity #2

Calculate elasticity as Price increases Calculate elasticity as Price increases from 2.00 to 2.50. Is the elasticity from 2.00 to 2.50. Is the elasticity elastic or inelastic?elastic or inelastic?

=<(100-150)/150>/<(2.50-2.00)/2.00>=<(100-150)/150>/<(2.50-2.00)/2.00> =(-50/150)/(.50/2)=(-50/150)/(.50/2) =-.33/.25=-.33/.25 =-1.33=-1.33 ElasticElastic

Example SummaryExample Summary

Price change from 1.00 to 1.50Price change from 1.00 to 1.50 TR method – InelasticTR method – Inelastic Calculation – InelasticCalculation – Inelastic

Price change from 2.00 to 2.50Price change from 2.00 to 2.50 TR method – ElasticTR method – Elastic Calculation – ElasticCalculation – Elastic

NB Both methods will produce the same NB Both methods will produce the same answeranswer

Arc Elasticity(Midpoint)Arc Elasticity(Midpoint)

Midpoint as opposed to endpointMidpoint as opposed to endpoint More accurate for larger changesMore accurate for larger changes

Winged Foot exampleWinged Foot example

= (Q= (Q22-Q-Q11)/{(Q)/{(Q22+Q+Q11)/2})/2}/(P/(P22-P-P11)/{(P)/{(P22+P+P11)/2})/2}

NB Elasticity changes with position NB Elasticity changes with position on graph.on graph.

Other ElasticitiesOther Elasticities

Income ElasticityIncome Elasticity = % change Q.D./ % change Income= % change Q.D./ % change Income

Cross-Price ElasticityCross-Price Elasticity = % change Q.D. Good #1= % change Q.D. Good #1

/ % change price Good #2/ % change price Good #2 Price Elasticity of SupplyPrice Elasticity of Supply

% change Q.S. / % change Price% change Q.S. / % change Price

Additional PointsAdditional Points

Public GoodsPublic Goods

Surplus & ShortagesSurplus & Shortages

Price CeilingsPrice Ceilings

Price FloorsPrice Floors

RationingRationing