Answer to Question #225407 in Microeconomics for gikovi

Question

Q1)

P_a | Qd_a | Qd_b | I

----------|------------ |------------|-------------

6.0 | 100 | 20 | 2000

| | |

6.5 | 90 | 30 | 1800

| | |

7.0 | 70 | 50 | 1600

| | |

7.5 | 40 | 70 | 1400

| | |

8.0 | 10 | 85 | 1200

where, P_a = Price of A

Qd_a = Quantity demand for A

Qd_b = Quantity demand for B

I = Income

On the basis of the above data, answer the following questions: -

(i) If income increases from $ 1000 to $ 2000, from the above table estimate the elasticity of demand.

(ii) Compute the income elasticity of demand for A & B when income of consumer increases from $ 1400 to $ 1800. Also interpret the result and explain the result by the method of a diagram.

Q2) If quantity demand for chicken increases by 20% when price of beef increases from 0.4 penny to 0.5 penny, then compute the cross price elasticity from chicken to beef.

Answer 1

1)

(i)

$e_{p}=\frac{\frac{Q_2-Q_1}{(Q_1+Q_2)/2}}{\frac{P_2-P_1}{(P_2+P_1)/2}}$

e_p=price elasticity

Q=quantity of the demanded good

P=price of the demanded good

$e_{p}=\frac{\frac{5-10}{(5+10)/2}}{\frac{8.5-8}{(8.5+2)/2}}$

$e_{p}=\frac{\frac{-5}{7.5}}{\frac{0.5}{8.25}}\\=\frac{0.667}{0.061}\\=-10.93$

The price elasticity of demand is less than one hence it is inelastic.

(ii)

income elasticity of demand(e_d) $=\frac{\frac{Q_2-Q_1}{(Q_1+Q_2)/2}}{\frac{I_2-I_1}{(I_2+I_1)/2}}$

e_d=income elasticity of demand

Q= quantity demanded

I=change in income

$e_{d} \space of \space A=\frac{\frac{90-40}{(90+40)/2}}{\frac{1800-1400}{(1800+1400)/2}}$

$e_{d}=\frac{\frac{50}{65}}{\frac{400}{1600}}\\=\frac{0.769}{0.25}\\=3.076$

 A is a normal good because it has a positive income elasticity of demand.

Increase in income leads to a rise in demand.

$e_{d} \space of \space B=\frac{\frac{30-70}{(30+70)/2}}{\frac{1800-1400}{(1800+1400)/2}}$

$e_{d}=\frac{\frac{-40}{50}}{\frac{400}{1600}}\\=\frac{0.8}{0.25}\\=-3.2$

B is a inferior good because it has a negative income elasticity of demand.

Increase in income leads to a fall in demand.

2)

cross price elasticity $\frac{\frac{Qc_2-Qc_1}{(Qc_1+Qc_2)/2}}{\frac{Pb_2-Pb_1}{(Pb_2+Pb_1)/2}}$

Qc= quantity of chicken demanded

pb=price of beef

$=\frac{20}{\frac{0.5-0.4}{(0.5+0.4)/2}}$

$=\frac{20}{\frac{0.9}{0.45}}\\=\frac{20}{20}\\=1$