Economic - Demand Elasticity Final

7/29/2019 Economic - Demand Elasticity Final

http://slidepdf.com/reader/full/economic-demand-elasticity-final 1/40

Budi Yulianto, ST, MSc, PhDFakultas Teknik - Universitas Sebelas Maret Surakarta - Indonesia



PENDAHULUAN Fungsi demand mengasumsikan tingkat dan distribusi

tertentu dari income, populasi, dan karakteristik sosialekonomi tertentu.

Demand dipengaruhi oleh: harga/tarif; harga barang/jasapengganti, selera atau kebiasaan yg berubah; perubahantingkat pendapatan dan distribusinya; jumlah danperubahan struktur penduduk.

Secara umum, demand perjalanan pada berbagai tingkatharga untuk kondisi linier bisa digambarkan dalampersamaan:

q = jumlah permintaan perjalanan p = harga

, = parameter permintaan (konstan)



ELASTISITAS DEMAND Elastisitas demand (ed) menggambarkan tingkat

sensitivitas demand yg diakibatkan oleh perubahanharga.

ed = persentase perubahan jumlah demand perjalanan

akibat perubahan harga sebesar 1%

ed = δq/q = δq x pδp/p δp q

δq adalah perubahan jumlah perjalanan akibat perubahan

harga δp



Arc Formula for Elasticity Although the exact formula for calculating an elasticity is

useful for theory, in practice economists usually calculate

an approximation called the Arc Elasticity.

You are really approximating the elasticity between twopoints.

Need two points to perform the calculation.



Arc price elasticity: ed = δq/q = δq x p

δp/p δp q

= Q1 – Q0 (P1 + P0)/2

P1 – P0 (Q1 + Q0)/2

where:

Q1 and Q0 represent the quantity of travel demanded

corresponding to price P0 and P1, respectively.

For a linear demand function, the elasticity with respect toprice can be determined by:

ed = 1 - α /q



Example 1 An aggregate demand function is represented by:

q = 200 – 10p

Where:

q is the number of trip,

p is the price per trip

Find: the price elasticity of demand whenq = 0, 50, 100, 150, 200 trips

corresponding to

p = 20, 15, 10, 5, 0 cents



Solution 1Eq: ed = 1 - α /q where: α = 200

ed = 1 - 200/200 = 0 ed = 1 - 200/150 = -0.133

ed = 1 - 200/100 = -1 ed = 1 - 200/50 = -3

ed = 1 - 200/0 = -~

200 Volume (q)150100500

5

10

15

20

P r i c e

( p )

q = 200 -10p

200 Volume (q)

(e=-~)

150100500

5

10

15

20

P r i c e

( p )

− 3

− 1

− 0.133

0

q = 200 -10p

When the price/trip is 20 cents, no tripare made.

When nothing is charged/trip, 200 trips

are made.

Price elasticity for this transportationsystem varies from 0 to ~, with unitelasticity when p = 10



ELASTISITAS DEMAND

FUNGSI LINIER

0 α /2 α

α/β

H

a r g a

( p )

Volume (q)

Elastis sempurna (e=-~)

Titik elastis (e=-1)

Tak elastis sempurna (e=0)

Daerah elastis

Daerah tak elastis

Fungsi demand: q = α – β.p

Meaning the resulting % change in quantity of trip makingwill be larger than the % change in price.

In this case, demand is relatively sensitive to price change.



Kemiringan garis konstan, tetapi elastis berubah dari ~hingga 0.

Makin kearah bawah kurva, makin tidak elastis.

Besar elastisitas pada suatu titik tertentu disepanjangkurva, besarnya adalah panjang segmen kurva dibawahtitik tersebut dibagi dengan panjang segmen diatasnya.



Elastic Economic Relations When an elasticity is large (greater than 1 in absolute

value), we call the relation that it describes Elastic.

Elastic demand means that the quantity demanded issensitive to the price. Elastic supply means that the quantity supplied is

sensitive to the price.

Demand elastic: jika total revenue (hasil/pendapatan)dengan perubahan harga/faktor ygmempengaruhi permintaan, dan e>1. Misal: Keperluantidak mendesak, banyak pengganti yg sejenis, barangtahan lama dan dapat diperbaiki, mempunyai beragam

kegunaan.



Inelastic Economic Relations When an elasticity is small (between 0 and 1 in absolute

value), we call the relation that it describes Inelastic.

Inelastic demand means that the quantity demanded isnot very sensitive to the price.

Inelastic supply means that the quantity supplied is notvery sensitive to the price.

Demand inelastic: jika total revenue (hasil/pendapatan)bergerak dengan perubahan harga/faktor ygmempengaruhi permintaan, maka e<1. Misal: Substitusiyang baik tidak tersedia, sangat diperlukan sekali,

barang/jasa merupakan komplementer (co: beli mobil perlubensin).



Demand elastisitas unitair: total revenue tidak terpengaruholeh perubahan harga/faktor. Merupakan borderline caseantara demand elastis dan demand tak elastis. Naik-turunnya harga/faktor diimbangi oleh perubahan kwantitassecara proporsional, sehingga revenue total tidak berubah.

Unit Elastic



Size of Price Elasticities

0 1 2 3 4 5 6

Unit elastic

Inelastic Elastic

Elastic: own price elasticity greater than 1

Unit elastic: own price elasticity equal to 1

Inelastic: own price elasticity less than 1



Using Demand Elasticity: Total

Expenditures Do the total expenditures on a product go up or down when

the price increases?

The price increase means more spent for each unit.

But, quantity demanded declines as price rises.

So, we must measure the measure the price elasticity of demand to answer the question.



Bridge Toll Example 2a Current toll for the George Washington Bridge is $2.00/trip.

Suppose the quantity demanded at $2.00/trip is 100,000trips/hour.

If the price elasticity of demand for bridge trips is 2.0.

What is the effect of a 10% toll increase?



Bridge Toll: Elastic Demand Price elasticity of demand = 2.0

Toll increase of 10% implies a 20% decline in the quantitydemanded.

Trips fall to 80,000/hour (=100,000-20,000).

Total expenditure falls to $176,000/hour (=80,000 x$2.20).

$176,000 < $200,000, the revenue from a $2.00 toll.



Bridge Toll Example 2b

Now suppose the elasticity of demand for bridge trips is0.5.

How would the number of trips and the expenditure ontolls be affected by a 10% increase in the toll?



Bridge Toll: Inelastic Demand

Price elasticity of demand = 0.5

Toll increase of 10% implies a 5% decline in the quantitydemanded.

Trips fall to 95,000/hour (=100,000-5,000).

Total expenditure rises to $209,000/hour (= 95,000x$2.20).

$209,000 > $200,000, the revenue from a $2.00 toll.



Elasticity and TotalExpenditure (Graph)

Price

Quantity

M

Elasticity = 1: Total

expenditure is at amaximum

Elasticity > 1: Price reduction

increases total expenditure; price

increase reduces it.

Elasticity < 1:

Price reduction

reduces total

expenditure;

price increase

increases it.

At the point M, thedemand curve is unitelastic. M is the midpoint

of this linear demandcurve Above M, demand is

elastic, so totalexpenditure falls as theprice rises

Below M, demand isinelastic. so totalexpenditure falls as pricefalls.

Total expenditure ismaximized at the point M,where the elasticity = 1.



Change in ExpenditureComponents

Price

Quantity

E

F G

P*

P

Q Q*

Demand

Old (price, quantity) is(P,Q).

New (price, quantity) is(P*,Q*).

Expenditures increase if G isbigger than E.

Since the point (P,Q) is

above the midpoint of thelinear demand curve, weknow that totalexpenditures will increaseat the lower price (P*,Q*).So, E must be smaller thanG.



Some Technical Definitions ForExtreme Elasticity Values

Economists use the terms “perfectly elastic (elastissempurna)” and “perfectly inelastic (elastis tak sempurna)”

” to describe extreme values of price elasticities.

Perfectly elastic means the quantity (demanded orsupplied) is as price sensitive as possible.

Perfectly inelastic means that the quantity (demanded orsupplied) has no price sensitivity at all.



Perfectly Elastic Demand

Price

Quantity

Perfectly Elastic Demand (elasticity = ∞)

We say that

demand isperfectly elasticwhen a 1%change in theprice would result

in an infinitechange in quantitydemanded.



Perfectly Inelastic Demand

Price

Quantity

Perfectly

Inelastic

Demand

(elasticity = 0)

We say thatdemand is

perfectly inelasticwhen a 1%change in theprice would result

in no change inquantitydemanded.



Perfectly Elastic Supply

Price

Quantity

Perfectly Elastic Supply (elasticity = ∞)

We say thatsupply isperfectly elasticwhen a 1%change in theprice would result

in an infinitechange inquantity supplied.



Perfectly Inelastic Supply

Price

Quantity

Perfectly

Inelastic

Supply

(elasticity = 0)

We say thatsupply is

perfectly inelasticwhen a 1%change in theprice would resultin no change inquantity supplied.



Example 3

When bus ticket price was $5, the number of bus passenger

was 20 persons per day.

Since the price has risen to $6, the demand has fallen to 16persons per day.

What is the elasticity of demand over this range of prices?



Solution 3

Arc price elasticity ed = Q1 – Q0 (P1 + P0)/2

P1 – P0 (Q1 + Q0)/2

= (16 – 20) (6 + 5)/2 = -4 (5.5) = -1.22

(6 – 5) (16 + 20)/2 1 (18)

(elastic)



FAKTOR-FAKTOR YG BERPENGARUHPADA ELASTISITAS DEMAND

ei = (% perubahan jumlah permintaan)

(% perubahan pendapatan)

Barang normal (ei>0), permintaan meningkat seiring denganpeningkatan pendapatan konsumen.

Barang superior (ei>1), permintaan meningkat seiring

dengan peningkatan pendapatan konsumen serta alokasiincome untuk barang tsb juga meningkat. Barang inferior, permintaan menurun ketika pendapatan

konsumen meningkat.Mobil merupakan barang superior, sedangkan membeli tiket

kendaraan umum untuk bepergian merupakan baranginferior.



In general, consumers by more than otherwise good when

the price goes down and buy less than otherwise when theprice goes up.Some factors that affect price elasticity as follows:

If a consumer spends a substantial % of income on

transportation, the more willing will he or she be to searchhard for a substitute if the price of transportation goes up.

[Semakin besar alokasi pendapatan untuk suatu barang,maka kecenderungan untuk mencari barang substitusi

makin besar].



The narrower the definition of a good, the more substitutesthe good is likely to have, and thus the more elastic its

demand will be. For example, the demand for BMW is moreelastic than demand for automobiles, and the demand forautomobiles is more elastic than the demand fortransportation.

[Semakin terbatas definisi suatu barang , semakin banyak barang sebagai penggantinya, maka permintaan semakinelastis] (BMW > Mobil > Transportasi)



If consumers find out that the price and availability of substitutes are easy, the more elastic the demand will be.

Advertising plays an important role in making availablesubstitutes to consumers. In the same context, the moretime consumers have to finds substitutes, the more elasticdemand becomes.

[Semakin besar pengetahuan pasar seorang konsumenatas suatu barang, maka permintaan akan lebih elastis].



Those goods that consumers consider to be necessitiesusually have inelastic demands, whereas goods considered

by consumers to be luxurious usually have elasticdemands. Eyeglass for a consumer are a necessary good,with few substitutes, whereas vacation trip to UK is aluxury good with several substitutes.

[Barang yang merupakan kebutuhan utama, biasanyapermintaannya tidak elastis].



Besar ) bilaterjadi perubahan harga pada unit barang adalah:

e = (% perubahan jumlah permintaan)

(% perubahan harga)

e>1, hubungan harga dgn revenue adalah negatif (demandelastic) H naik – R turun, H turun – R naik.

e<1, hubungan harga dan revenue adalah positif (demandinelastic) H naik – R naik, H turun – R turun.

e=1, total pendapatan tetap, meskipun harga naik turun.



Example 4

A bus company’s linear demand curve is P = 10 – 0.05Q,where P is the price of a one-way ticket, and Q is the number

of tickets sold per hour.

Determine the total revenue along the curve.



Solution 4P = 10 – 0.05Q

R = QP

= Q(10 – 0.05Q)

= 10Q – 0.05Q2

dR/dQ = 10 – (0.05 x 2)Q

And this is = 0 when R is maximum

Therefore:

Q = 100 when R is $500 (maximum)

P = 10 – 0.05Q

Q (Tickets)

P

( $ )

$10

0 200

R = 10Q – 0.05Q2

2000

T o t a l

R e v e n u e

P = 10 – 0.05Q

Q (Tickets)

P

( $ )

$10

0 200

R = 10Q – 0.05Q2

2000

$500

T o t a l

R e v e n u e

100

Starting from a price of $10 at near 0 ticket sold and decreasing theprice eventually to half ($5), the revenue steadily increases to amaximum of $500/hrs (over the elastic portion).

After that, the revenue decreases as the price further decreases andfinally approaches near 0, when the demand approaches 200 (over

the inelastic portion)



Kraft Demand Model

The demand function for situation where the elasticity of demand for travel with respect to its price is essentially

Constant:

Q = α(p)β

Where α and β are constant parameters of the demandfunction.



Example 5

The elasticity of transit demand with respect to price hasbeen found to be equal to -2.75, which means that a 1%

increase in transit fare will result in a 2.75 decrease numberof passengers using the system.

A transit line on this system carries 12,500 passengers perday, charging 50 cents per ride. The management wants to

raise the fare to 70 cents per ride.

What advice would you offer to management?



Solution 5

Q = α(P)β 12,500 = α(50)-2.75 α = 12,500 x (50) 2.75 = 5.876 x 108

Q = 5.876 x 108 x P-2.75

An increase in fare from 50 to 70 cents will attract a demand of

Q = 5.876 x 108 x (70)-2.75 = 4,955

Therefore to increase in fare from 50 to 70 cents (a 40% increase) is likely to reducethe patronage on this line from 12,500 passengers per day to 4,955 (a decrease

60.36%).

In terms of revenue, the results are as follows:

50 cents/rider x 12,500 passengers = $6,250

70 cents/rider x 4,955 passengers = $3,468.5

Loss in revenue = $2,781



Discussion:

In general, it has been observed that when the price is Elastic (-2.75),

raising the unit price will result in Loss, but lowering price will result intotal Gain.

The converse is always true; if the price is Inelastic, raising the unit pricewill result in total Gain, whereas lowering the unit price will result in totalLoss.

Old Fare ($ cent) Old Demand (Qo) New fare ($ cent) New Demand (Qn) Old Fare ($) New Fare ($) Loss or Gain Revenue

70 4,955 $6,250 $3,469 $2,781

60 7,571 $6,250 $4,543 $1,707

50 12,500 $6,250 $6,250 $0

40 23,090 $6,250 $9,236 -$2,986

30 50,933 $6,250 $15,280 -$9,030

20 155,328 $6,250 $31,066 -$24,816

10 1,044,917 $6,250 $104,492 -$98,242

50 12,500

Revenue

Economic - Demand Elasticity Final

Documents

Transcript of Economic - Demand Elasticity Final