Question

5.Suppose that your demand schedule for compact discs is as follows: Price Quantity demanded, income 10 000 rub. Quantity demanded, income 12 000 rub. 8 40 60 10 36 42 12 24 30 14 16 20 16 6 10 a. Calculate your price elasticity of demand as the price of compact discs increases from 8 to 10 if your income is 10 000, and your income is 12 000. b. Calculate your income elasticity of demand as your income increases from 10 000 to 12 000 if the price is 12, and the price is16. 6.The price for a good A has risen from 175 rub. to 210 rub. The demand for a good B has increased from 5400 units to 7100 units. Calculate the cross- price elasticity of demand?

Answer 1

Solution:

Question 5:

a.). Calculate your price elasticity of demand as the price of compact discs increases from 8 to 10 if your income is 10 000, and your income is 12 000.

When Income is 10,000:

Price elasticity of demand = $=\frac{\%\;change\; in\; quantity\; demanded}{\%\; change\; in\; price}$

$\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 }$

Q₁ = 32                               P₁ = 8

Q₂ = 40                               P₂ = 10

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

Price elasticity of demand (PEd) = 1

b.). Income elasticity of demand (YEd):

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

When price is 12:

$\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{I_{2} -I_{1}}{(I_{2}+I_{1})/2 }$

Q₁ = 24                               I₁ = 10,000

Q₂ = 30                               I₂ = 12,000

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

Income elasticity of demand (YEd) = 1.22

When the price is 16:

$\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{I_{2} -I_{1}}{(I_{2}+I_{1})/2 }$

Q₁ = 8                                 I₁ = 10,000

Q₂ = 12                               I₂ = 12,000

YEd= $\frac{12 -8}{(12+8)/2 }\div \frac{10,000 -12,000}{(10,000+12,000)/2 } = \frac{4}{10} \div\frac{2,000}{11,000}= \frac{0.4}{0.18} = 2.2$

Income elasticity of demand (YEd) = 2.2

Question 6:

Cross elasticity of demand (XEd) $=\frac{\%\;change\; in\; quantity\; demanded\; for \; Good\; B}{\%\; change\; in\; price\; for \; Good\; A}$

$\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 }$

Q₁ = 5,400                               P₁ = 175

Q₂ = 7,100                               P₂ = 210

PEd= $\frac{7,100 -5,400}{(7,100+5,400)/2 }\div \frac{210 -175}{(210+175)/2 } = \frac{1,700}{6,250} \div\frac{210}{192.5}= \frac{0.27}{0.18} = 1.5$

Cross elasticity of demand (XEd) = 1.5

Good A and Good B are substitutes since XEd is greater than zero