Section 3 Elasticity

Presented by

MOHAMED ABD-ELMOHSEN Assistant lecture

Economic departmentFaculty of commerce Suez canal university

(PED) Definition

The price elasticity of demand (PED)is a units-free measure of the responsiveness of the quantity demanded of a good to a change in its price when all other influences on buyers’ plans remain the same.

• Calculating ElasticityThe price elasticity of demand is calculated by using the formula:

Percentage change in quantity demanded

Percentage change in price

• If the quantity demanded doesn’t change when the price changes, the price elasticity of demand is zero and the good as a perfectly inelastic demand.

• If the percentage change in the quantity demanded equals the percentage change in price, the price elasticity of demand equals 1 and the good has unit elastic demand.

• Between the two previous cases, the percentage change in the quantity demanded is smaller than the percentage change in price so that the price elasticity of demand is less than 1 and the good has inelastic demand.

• If the percentage change in the quantity demanded is infinitely large when the price barely changes, the price elasticity of demand is infinite and the good has

• perfectly elastic demand• If the percentage change in the quantity demanded is

greater than the percentage change in price, the price elasticity of demand is greater than 1 and the good has elastic demand.

• If demand is elastic, a 1 percent price cut increases the quantity sold by more than 1 percent, and total revenue

• increases.

• If demand is inelastic, a 1 percent price cut decreases the quantity sold by more than 1 percent, and

• total revenues decreases.• If demand is unitary elastic, a 1 percent price cut increases

the quantity sold by 1 percent, and total revenue • remains unchanged.• If a price cut increases total revenue, demand is • elastic• If a price cut decreases total revenue, demand is • inelastic.• If a price cut leaves total revenue unchanged, demand is• unit elastic

Types of price Elasticity Demand(PED)Elastic >1 Unit elastic = 1 Inelastic <1 Zero elastic =0 Perfectly

elastic= ∞p p p p P

∆Q > ∆p ∆Q = ∆p ∆Q < ∆p ∆Q not change

∆p not change

Total Revenue =

P × QD

Total Revenue =

P × QD

(not change)

Total Revenue =

P × QD

Total Revenue =

P × QD

Total Revenue =

P × QD

1- Calculate the Price elasticity of demand when:

a. The price fall from $25 to15.

B. The price fall from $15 to 10.

C. The price fall from $10 to 0.

D. Interpret your results in a, b, and c.

Original point New point

Price 25 15

QD 0 20

A)Fall from 25 - 15 B) fall from 15 to 10

PED= ( %∆ Q) / (% ∆ p) (%∆ Q)= (QD(N) – QD(O) ) / QD(avreg)

∆ Q = (20-0 ) ∕ 10 =2(% ∆ p)= (P(N) –p(o) ) / Op = (15- 25) / 20 = - 0.5PED= (2∕- 0.5) =- 4 When the price increase about 1% the demand fall about 4 % (Elastic)& indirect relation between price & QD

Original point New point

Price 25 15

QD 0 20

PED= ( %∆ Q) / (% ∆ p)∆ Q= (QD(N) – QD(O) ) / QD(avereg)

%∆ Q= (30-20)/25 = 0.4∆ p= (10-15)/ 12.5= -0.4PED=(0.4 / -0.4 )PED= -1When the price increase 1% the demand fall 1% (unit Elastic)

Original point New point

Price 15 10

QD 20 30

C- The price fall from $10 to 0.

PED= ( %∆ Q) / (% ∆ p)%∆ Q= (QD(N) – QD(O) ) / QD(avreg)

%∆ Q= (50-30)/40 = 0.5 %∆p =( p(n) - p(o) ) p(avredge)

∆p = (0 -10 ) /5 = -2PED= (0.5/ -2) = - 0.25When the price rise about 1% the quantity fall about 0.25%(inelastic)

Original point New point

Price 10 0

QD 30 50

When the price rise about 1% the quantity fall about 0.25%

(inelastic)

2)The price elasticity of demand is defined as the magnitude of

A)The change in quantity demanded divided by the change in priceB)The change in price divided by the change in quantity demanded C)The percentage change in quantity demanded divided by the percentage change in priceD)The percentage change in price divided by the percentage change in quantity demanded

3) If a 20 percent increase in the price of a used car results in a 10 percent decrease in the quantity of used cars demanded, then the price elasticity of demand equals

A) 0.5. B) 1.0. C) 2.0. D) 10.0.

4) The demand schedule for hotel rooms is:Price

(dollars per night)QD

(millions of rooms per night)200 100

250 80

400 50

500 40

800 25

1000 20

A- What happens to total revenue if the price falls from $400 to $250?

B- What happens to total revenue if the price falls from $250 to $200?

C- At what price is the total revenue at a maximum? Explain and interpret your answer?

D- Is the demand for hotel room’s elastic, unit elastic, or inelastic?

A- if the price falls from $400 to $250? ( nothing change in Total revenue )

b- price falls from $250 to $200? (nothing change)

c- Total Revenue is constant at all points

Price QD Total Revenue

(dollars per night) (millions of rooms per night) P * QD200 100 20000250 80 20000400 50 20000500 40 20000800 25 20000

1000 20 20000

• Because, The percentage change in quantity demanded = the percentage change in price

• D- the demand for hotel room’s is unit elastic

5) Consider the market of CDs

Qd= 120 – 10 p

A- Find the equilibrium price and equilibrium quantity.

B- Find the Price Elasticity of Demand (PED) at equilibrium.

C- Find the Price Elasticity of Supply (PES) at equilibrium.

Qs= 30p

• Equilibrium price=3, Equilibrium Q= 90

PED= ( %∆ Q) / (% ∆ p)

( %∆ Q)= (QD(n)- QD(o) )/ QD(avre)

= (80- 100) /90 = -0.2222

(%∆ p)= (P(n) – p(o) )/ p (avre)

= (4-2 )/3 = 0.66666667 PED= (-0. 22/ 0.66) = -0.33

price QD=120-10p Qs=30p1 110 302 100 603 90 904 80 1205 70 150

PES = ( %∆ QS) / (% ∆ p)( %∆ QS)= QS(n)- QS(o) )/ QS (avre)

= (120-60)/ 90= 0.666666667

(% ∆ p)= (P(n) – p(o) )/ p (avre) = (4- 2)/ 3 = 0.66666667 PES= (0.666/ 0.666) = 1