Question #281234


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


1
Expert's answer
2021-12-19T13:43:00-0500

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) = QP×PQ\frac{\triangle Q}{\triangle P} \times \frac{P}{Q}

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

Price elasticity of demand (PED) = 10×503,25010\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 = QPx×PxQ\frac{\triangle Q}{\triangle P_{x} } \times \frac{P_{x} }{Q}

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

Cross-elasticity of demand (PED) = 5×803,250=0.12-5\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 = QPz×PzQ\frac{\triangle Q}{\triangle P_{z} } \times \frac{P_{z} }{Q}

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

Cross-elasticity of demand (PED) =2×1503,250=0.09-2\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 = QM×MQ\frac{\triangle Q}{\triangle M} \times \frac{M}{Q}

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

Income elasticity of demand (YED) = 0.1×20,0003,250=3,250=0.620.1\times \frac{20,000}{3,250} =3,250 = 0.62

Income elasticity of demand (YED) = 0.62

 


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