Answer to Question #281234 in Microeconomics for Esayas

Question

SupposedemandforinkjetprintersisestimatedtobeQx=1000—5Px +10P— 2Pz+0.1M.Ifownprice(Px)=80,relatedprices,P=50,Pz=150,andincome,M= 20,000; answer the following:

Answer 1

Solution:

a.). What is the price elasticity of demand?

First, derive Qx:

Qx = 1000 – 5(50) + 10(80) – 2(150) + 0.1(20,000) = 1000 – 250 + 800 – 300 + 2000 = 3,250

Qx = 3,250

Price elasticity of demand (PED) = $\frac{\triangle Q}{\triangle P} \times \frac{P}{Q}$

$\frac{\triangle Q}{\triangle P}$ = 10

Price elasticity of demand (PED) = $10\times \frac{50}{3,250}$ = 0.15

Price elasticity of demand (PED) = 0.15

 

b.). What is the cross-elasticity of demand with respect to commodity X?

Cross-elasticity of demand = $\frac{\triangle Q}{\triangle P_{x} } \times \frac{P_{x} }{Q}$

$\frac{\triangle Q}{\triangle P_{x} }$ = -5

Cross-elasticity of demand (PED) = $-5\times \frac{80}{3,250} = -0.12$

Cross-elasticity of demand (PED) = 0.12

Commodity X is a complementary good since it has a negative cross-elasticity of demand. That is, as the price of one good increases, the demand for the second good decreases.

 

c.). What is the cross-elasticity of demand with respect to commodity Z?

Cross-elasticity of demand = $\frac{\triangle Q}{\triangle P_{z} } \times \frac{P_{z} }{Q}$

$\frac{\triangle Q}{\triangle P_{z} }$ = -2

Cross-elasticity of demand (PED) =$-2\times \frac{150}{3,250} = -0.09$ -2 x 150/3,250 = -0.09

Cross-elasticity of demand (PED) = 0.09

Commodity Z is a complementary good since it has a negative cross-elasticity of demand. That is, as the price of one good increases, the demand for the second good decreases.

d.). What is the income elasticity of demand?

M = Income

Income elasticity of demand = $\frac{\triangle Q}{\triangle M} \times \frac{M}{Q}$

$\frac{\triangle Q}{\triangle M}$ = 0.1

Income elasticity of demand (YED) = $0.1\times \frac{20,000}{3,250} =3,250 = 0.62$

Income elasticity of demand (YED) = 0.62