Law of DemandOther things equal, the quantity demanded of

a good falls when the price of good rises .Elasticity

A measure of the responsiveness of quantity demanded or quantity supplied to one of its determinants.

Price Elasticity of DemandA measure of how much the quantity demanded of a good responds to a change in the price of that good, computed as the percentage change in quantity demanded divided by the percentage change in price.

QuestionSuppose that your demand schedule for compact discs is as follows:

PriceQUANTITY

DEMANDEDQUANTITY

DEMANDED

$ (INCOME = $10,000) (INCOME = $12,000)

8 40 50

10 32 45

12 24 30

14 16 20

16 8 12

a. Use the midpoint method to calculate your price elasticity of demand as the price of compact discs increases from $8 to $10 if (i) your income

is $10000 and (ii) your income is $ 12000.

b. Calculate your income elasticity of demand as your income increases from $10,000 to $12000 if (i) the price is $12 (ii) the price is $16.

Solutiona(i). The price of compact discs increase

from $8 to $10, (i) if our income is $10,000;

According to the midpoint method, (Q2 - Q1)/[( Q2 + Q1)/2]

Price elasticity of demand = (P2 - P1)/[( P2 + P1)/2]

P1 = 8 Q1 = 40P2 = 10 Q2 = 32

PriceQUANTITY

DEMANDED

QUANTITY DEMANDE

D

$(INCOME = $10,000)

(INCOME = $12,000)

8 40 50

10 32 45

So, (32 -40)/ [ (32+ 40/2]

Price elasticity of demand = (10 - 8)/[( 10 + 8)/2]

-8/ 72/2 -8/36 -2/9

Price elasticity of demand = = = 2/18/2 2/9

2/9

Price elasticity of demand = -1

Our price elasticity of demand is equal 1So, our price elasticity of demand is unit elastic

demand.

Price

Quantity

q2

q1

p2

p1

P1 = 8 , Q1 = 40 – total revenue = p1 x Q1 = 8x40 = 320P2= 10,Q2 = 32 – total revenue = P2 x Q2 = 10x32 = 320

-in unit elastic demand(Ed=1) , a change in the price does not affect total revenue.

Demand curve

a(ii). The price of compact discs increase from $8 to $10, (ii) if our income is $12,000;

According to the midpoint method, (Q2 - Q1)/[( Q2 + Q1)/2]

Price elasticity of demand = (P2 - P1)/[( P2 + P1)/2]

P1 = 8 Q1 = 50P2 = 10 Q2 = 45

PriceQUANTITY DEMANDE

D

QUANTITY DEMANDE

D

$(INCOME = $10,000)

(INCOME = $12,000)

8 40 50

10 32 45

So, (45 -50)/ ( 45+ 50/2]

Price elasticity of demand = (10 - 8)/[( 10 + 8)/2]

-5/ 95/2 -5x 2/95 -2/19 2 9

Price elasticity of demand = = = = x 2/18/2 2/9 2/9 19 2

Price elasticity of demand = 9/19 = 0.47

Our price elasticity of demand is smaller than 1So, Our price elasticity of demand is inelastic

demand.

Price

Quantity

q2

q1

p2

p1

P1 = 8 , Q1 = 50 – total revenue = p1 x Q1 = 8x50 = 400P2= 10,Q2 = 45 – total revenue = P2 x Q2 = 10x32 = 450

-in inelastic demand (Ed < 1) , a price increase rises total revenue and a price decrease reduces total revenue.

Demand curve

b. Calculate your income elasticity of demand as your income increases from $10,000 to $12000 if (i) the price is $12 (ii) the price is $16.

i. Our income elasticity of demand is as our income increases from $ 10,000 to $ 12000 if (i) the price is $ 12

According to the equation Percentage change in

quantity demandedIncome elasticity of demanded =

Percentage change in incomePrice

QUANTITY DEMANDED

QUANTITY DEMANDED

$ (INCOME = $10,000) (INCOME = $12,000)

12 24 30

Point A: Income = 10,000 Quantity Demanded = 24 Point B: Income = 12,000 Quantity Demanded = 30

Going to Point A to Point B, the income rises by 20 percent because 12000-10000/10000 x 100 = 20

andthe quantity demanded also rise 25 percent because 30-24/24 x 100 = 25

25 5Income elasticity of demanded = = = 1.25

20 4

As our income increases from $ 10,000 to $ 12000 if (i) the price is $ 12 , our income elasticity of demand is 1.25 and so it is positive income elasticity and we conclude that is normal good.

ii. Our income elasticity of demand is as our income increases from $ 10,000 to $ 12000 if (ii) the price is $ 16

According to the equation

Percentage change in quantity demanded

Income elasticity of demanded = Percentage change in

income

PriceQUANTITY

DEMANDEDQUANTITY

DEMANDED

$ (INCOME = $10,000)

(INCOME = $12,000)

16 8 12

Point A: Income = 10,000 Quantity Demanded = 8 Point B: Income = 12,000 Quantity Demanded = 12

Going to Point A to Point B, the income rises by 20 percent because 12000-10000/10000 x 100 = 20

andthe quantity demanded also rise 50 percent because 12-8/12 x 100 = 33

50 10Income elasticity of demanded = = = 2.5

20 4

As our income increases from $ 10,000 to $ 12000 if (ii) the price is $ 16 , our income elasticity of demand is 2.5 and so it is positive income elasticity and we conclude that is normal good.