Answer to Question #222181 in Microeconomics for Afaq

Question

The accompanying table shows the price and yearly quantity sold of souvenir T-shirts in the town of Crystal Lake according to the average income of the tourists visiting.

Price of T-shirt



Quantity of T-shirts demanded when average tourist income is $20,000

Quantity of T-shirts demanded when average tourist income is $30,000

$4

3,000

5,000

5

2,400

4,200

6

1,600

3,000

7

800

1,800

a. Using the midpoint method, calculate the price elasticity of demand when the price of a T-shirt rises from $5 to $6 and the average tourist income is $20,000. Also calculate it when the average tourist income is $30,000.

b. Using the midpoint method, calculate the income elasticity of demand when the price of a T-shirt is $4 and the average tourist income increases from $20,000 to $30,000. Also calculate it when the price is $7.

Answer 1

a) Price elasticity of demand

For average tourist income $\$20000$ average quantity demanded is

$\frac{2400+1600}{2}=2000$

$\%$ change in the quantity demanded$=2400-1600=800$

$=\frac{800}{2000}×100=40\%$

Percentage change in price

$=\frac{5+6}{2}=5.5$

$change=\frac{6-5}{5.5}=0.18×100=18\%$

Price elasticity$=\frac{40}{18}=2.22$

For average tourist income $\$30000$ average quantity demanded is

$\frac{4200+3000}{2}=3600$

$\%change inquantitydemanded=\frac{1200}{3600}×100=33.33\%$

Percentage change in price

$=\frac{5+6}{2}=5.5$ change

$=\frac{6-5}{5.5}=0.18×100=18\%$

Price elasticity$=\frac{33.33}{18}=1.85$

b) Income elasticity of demand

When the price of T-shirt is $4.% change in quantity demanded is

$\frac{5000-3000}{(5000+3000)÷2}×100=\frac{2000}{4000}×100=50\%$

and the %change in income is

$\frac{30000-20000}{(30000+20000)÷2} ×100=\frac{10000}{25000}×100=40\%$

The income elasticity of demand therefore is

$\frac{50\%}{40\%}=1.25$

When the price of T-shirt is $7,%change in quantity demanded is

$\frac{1800-800}{(1800+800)÷2}×100=\frac{1000}{1300}×100=76.9\%$

%change in income is as before

$\frac{30000-20000}{(30000+20000)÷2}×100=\frac{10000}{25000}×100=40\%$

The income elasticity of demand therefore is

$\frac{76.9\%}{40\%}=1.9$