Question

Suppose demand for inkjet printers is estimated to be Q_X = 1000 – 5P_X + 10P_Y – 2P_Z + 0.1_M. If own price (P_X) = 80, related prices, P_Y = 50, P_Z = 150, and income, M = 20,000; answer the following:

A.   Calculate own price elasticity of demand and interpret your result

B.    Calculate cross price elasticity of demand between X and Y and interpret your result

C.    Calculate cross price elasticity of demand between X and Z and interpret your result

D.   Calculate Income elasticity of demand and interpret your result

Answer 1

P_X = 80

P_Y = 50

P_Z = 150

M = 20,000

$Q_X=1000-5P_X+10P_Y-2P_Z+0.1M$

$Q_X=1000-(5\times80)+(10\times50)-(2\times150)+(0.1\times20000)$

$Q_X=1000-400+500-300+2000$

$Q_X=2800$

A.  Own price elasticity of demand (E_P); 

$E_P=\frac{\Delta Q_X}{\Delta P_X}\frac{P_X}{Q_X}=-5\frac{80}{2800}=-0.143$

Negative price elasticity of demand means an increases in price will lead to decrease in demand or decrease in price will lead to increase in demand.

B. Cross price elasticity of demand between X and Y:

$E_c=\frac{\Delta Q_X}{\Delta P_Y}\frac{P_Y}{Q_X}=10\times\frac{50}{2800}=0.179$

Cross price elasticity of demand is positive that means X and Y are substitutes.

C. Cross price elasticity of demand between X and Z:

$E_c=\frac{\Delta Q_X}{\Delta P_Z}\frac{P_Z}{Q_X}=-2\times\frac{150}{2800}=-0.107$

Cross price elasticity of demand is negative that means X and Z are complements.

D. Income elasticity of demand (E_M):

$E_M=\frac{\Delta Q_X}{\Delta Y}\frac{Y}{Q_X}=0.1\times\frac{20000}{2800}=0.714$

Income elasticity of demand is less than 1 but positive. This means an increase in income will lead to rise in demand of inkjet printers. It can also say that inkjet printers is a normal good.