Question

Suppose that your demand schedule for DVDs
is as follows:
Quantity Demanded Quantity Demanded
Price (income = $10,000) (income = $12,000)
$ 8 40 DVDs 50 DVDs
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
DVDs increases from $8 to $10 if (i) your
income is $10,000 and (ii) your income is
$12,000.
b. Calculate your income elasticity of demand
as your income increases from $10,000 to
$12,000 if (i) the price is $12 and (ii) the price
is $16.

Answer 1

Solution:

a.). Price elasticity of demand (PEd) = $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

Using mid-point formula = $\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 }$

When income is 10,000:

Q₂ = 32                  P₂ = 10

Q₁ = 40                  P₁ = 8

PEd = $\frac{32 -40}{(32+40)/2 } \div \frac{10 -8}{(10+8)/2 } = \frac{ -8}{36 }\div \frac{ 2}{9 } = \frac{ -0.22}{0.22 } = -1$

PEd = 1, which is unit elastic.

When income is 12,000:

Q₂ = 45                  P₂ = 10

Q₁ = 50                  P₁ = 8

PEd = $\frac{45 -50}{(45+50)/2 } \div \frac{10 -8}{(10+8)/2 } = \frac{ -5}{47.5 }\div \frac{ 2}{9 } = \frac{ -0.11}{0.22 } = -0.48$

PEd = 0.48, which is unit inelastic.

b.). Income elasticity of demand (YEd) = $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; Income}$

Using mid-point formula = $\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{I_{2} -I_{1}}{(I_{2}+I_{1})/2 }$

When Price is 12:

Q₂ = 30                  I₂ = 12,000

Q₁ = 24                  I₁ = 10,000

YEd = $\frac{30 -24}{(30+24)/2 } \div \frac{12,000 -10,000}{(12,000+10,000)/2 } = \frac{ 6}{27 }\div \frac{ 2000}{11,000 } = \frac{ 0.22}{0.18 } = 1.22$

Income elasticity of demand (YEd) = 1.22, which means that DVDs are income elastic. They are normal products and a luxury.

 

When Price is 16:

Q₂ = 12                  I₂ = 12,000

Q₁ = 8                    I₁ = 10,000

YEd = $\frac{12 -8}{(12+8)/2 } \div \frac{12,000 -10,000}{(12,000+10,000)/2 } = \frac{ 4}{27 }\div \frac{ 2000}{11,000 } = \frac{ 0.4}{0.18 } = 2.22$

Income elasticity of demand (YEd) = 2.22, which means that DVDs are highly income elastic. They are normal products and a luxury. As income increases, so is their demand.