Question

The relationship between a consumer’s income and the quantity of X, he consumes is given by the equation M=1000Q²

Calculate his point price income elasticity of demand for X when his income is 64,000.

Answer 1

When his income is 64,000, then:

$1,000Q^2 = 64,000,$

Q = 8 units.

$Q = (M/1000)^{0.5}.$

$Q'(M) = 0.5×1000^{0.5}/M^{0.5}.$

Point price income elasticity of demand for X is:

$Ei = M×Q'(M)/Q = \frac{64,000×0.5×1000^{0.5}}{8×64,000^{0.5}}= 500.$

So, the demand is income-elastic.