Question

1) Given the demand curve for a commodity as Q = 60 - 3P where Q is the quantity demanded and P the price per unit, determine the price elasticity of demand at P = 10.

2) The demand curve for a commodity X is given by Q_X=16 P_X^(-4) where Q_X is the quantity demanded and P_X is the price. What is the price elasticity of demand at P_X = 2 and Q_X = 1.

3) Derive an equation to calculate the income elasticity of demand at any point on the following function: Q = 40 -〖 Y〗^(-3/2) where Q is the quantity demanded and Y is the consumer’s income in Gh₵ ‘000.

4) The demand equation for a consumer is given by Q = 1/P^α . Show that price elasticity of demand is α

Answer 1

1)

$$Q=30$$

$$E=-3\times \frac{10}{30}=-1$$

2)

$$\frac{\varDelta Q}{\varDelta p}=-64p^{-5}$$

$$E=-2\times \frac{2}{1}=-4$$

3)

$$\frac {\varDelta Q}{\varDelta y}=\frac{3}{2}y^{-\frac{5}{2}}$$

$$E=\frac{3}{2}y^{-\frac{5}{2}}\times \frac{y}{40-y^{-\frac{3}{2}}}$$

$$E=\frac {3y^{-\frac{3}{2}}}{80-2y^{-\frac{3}{2}}}$$

4)

$$\frac {\varDelta Q}{\varDelta p}=-\alpha\times p^{-\alpha-1}$$

$$E=-\alpha\times p^{-\alpha-1}\times p\times p^{\alpha}=-\alpha$$