Question

Suppose that the demand function for good x is given by x = 10 - 2p_x + p_y + 0.5M, where M=10 is income and p_x = 2 and p_y = 5.

(a) Calculate the own price elasticity of demand.

(b) Calculate the cross price elasticity of demand. Are the goods substitutes or complements?

(c) Is the good normal or inferior? Calculate the income elasticity of demand.

(d) Is the good a necessity or a luxury?

Answer 1

a) To calculate own Ped, increase price of X keeping others constant, formula = %change in Q/%change in Px

X	Px	Py	M		%change in Qx	%change in Px	Ped
16	2	5	10
14	3	5	10		-0.125	0.5	-0.25

b)

X	Px	Py	M		%change in Qx	%change in Py	Ped
16	2	5	10
17	2	6	10		0.0625	0.2	0.3125

Since elasticity is positive, the goods are substitute

c)

X	Px	Py	M		%change in Qx	%change in Px	Ped
16	2	5	10
16.5	2	5	11		0.03125	0.1	0.3125

with the increase in income quantity demanded increases and hence it is nomrla good

d) It is a necessity as own price elasticity is negative