Answer to Question #227084 in Microeconomics for mukit

Question

Monthly demand and supply schedule for t-shirts are given by:

Price

8

7

6

5

4

3

2

1

Quantity Demanded

6

8

10

12

14

16

18

20

Quantity Supplied

18

16

14

12

10

8

6

4

Income

100

150

200

250

300

350

400

450

 

a)              What is the Price Elasticity of Demand for a price change from $7 to $5? Is it elastic or inelastic? (Use the Arc Elasticity Formula)

b)             What is the Price Elasticity of Supply for a price change from $7 to $5? Is it elastic or inelastic? (Use the Arc Elasticity Formula)

c)              Using Total Revenue, is demand elastic or inelastic for a price change from $4 to $3?

d)             What is the Income Elasticity of Demand for t-shirts when income decreases from $300 to $250? (Use the Arc Elasticity Formula)

Answer 1

a.

price elasticity of demand using the arc formula is given by

$=(change in quantity demanded ÷ mid point of quantity) ÷ (change in price÷ midpoint of price)$

change in respective quantities = 12 - 8 =4

midpoint of quantity demanded = 12+ 8

= 20÷ 2 = 10

change in price = 5 - 7 = -2

midpoint of the price = $5 +7 = 12 ÷ 2 = 6$

therefore PED using the arc formula = $(4 ÷ 10)÷ (-2÷6)$

PED = -1.2 This shows the PED is inelastic at the given point.

b.

PES using the arc method is given by

=$(change in quantity supplied÷ mid point of quantity) ÷ (change in price÷ midpoint of price)$

change in respective quantities is 12 - 16 = -4

midpoint of quantity supplied =12+16

= $28 ÷ 2 = 14$

change in price is 5 - 7 = -2

midpoint of the price = 5 +7

=$12 ÷ 2$

= 6

therefore PES = $(-4 ÷ 14) ÷ (-2÷6) = 0.857$

PES= 0.857 This shows that the PES at the given point is elastic.

c.

PED is given by the change in quantity demanded divided by the change in price

change in quantity demanded = 16- 14

= 2

change in price = 3-4 = -1

PED = $2 ÷ -1$

= -2 -This shows that PED is inelastic

d.

income elasticity of demand is given by

= $(change in quantity demanded ÷ mid point of quantity) ÷ (change in income÷ midpoint of income)$

change in quantity demanded = 14 - 12

= 2

mid point of quantity = 14 + 12

= $26÷ 2$

= 13

change in income = 300-250

= 50

midpoint of income = 300+250

= $550÷2$

= 275

Therefore income elasticity of demand

= $(2÷13) ÷ (50÷275)$

= 0.846 - This shows that the income is elastic