SupposedemandforinkjetprintersisestimatedtobeQx=1000—5Px +10P— 2Pz+0.1M.Ifownprice(Px)=80,relatedprices,P=50,Pz=150,andincome,M= 20,000; answer the following:
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) =
= 10
Price elasticity of demand (PED) = = 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 =
= -5
Cross-elasticity of demand (PED) =
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 =
= -2
Cross-elasticity of demand (PED) = -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 =
= 0.1
Income elasticity of demand (YED) =
Income elasticity of demand (YED) = 0.62
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