Question

The relationship between a consumer’s income and the quantity of X ,he consumes is

given by the equation M=1000 Q squared

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

Answer 1

The price income elasticity of demand can be found as follows:

$$\epsilon=\dfrac{dQ}{dI}\dfrac{I}{Q},$$ $$Q=\dfrac{I^{0.5}}{\sqrt{1000}}, \dfrac{dQ}{dI}=\dfrac{1}{2\sqrt{1000}Q},$$ $$\epsilon=\dfrac{1}{2\sqrt{1000}Q}\cdot\dfrac{64000}{Q}=\dfrac{1012}{Q}.$$