Answer to Question #301765 in Economics of Enterprise for Leonidos

Question

3. After a careful statistical analysis, the Childester Company concludes that the demand function for the product is, Q = 500 - 3P + 2Pr + 0.1I Where Q is the quantity demanded of its product, P is the price of its product, Pr is the price of its rival's product, and I is the per capital disposable income (Rs.). At present, P = Rs. 10, Pr = Rs. 20, and I = Rs. 6,000. (a) What is the price elasticity of demand for firm's product? (b) What is the income elasticity of demand for firm's product? (c) What is the cross elasticity of demand between its product and its rival's product? 

Answer 1

(a) What is the price elasticity of demand for a firm's product?

The own-price elasticity explains how the quantity demanded responds to a variation in the product price

The price elasticity of demand is measured by the following formula:

E_p = $\frac{ΔQ}{ΔP}\times\frac{P}{Q}$

From the given demand function, $\frac{ΔQ}{ΔP}$ = −3, so the price elasticity is:

E_p = $-3\times\frac{10}{1110}$

E_p = - 0.027

The price elasticity is: - 0.027

(b) What is the income elasticity of demand for a firm's product?

The income elasticity measures how much demand changes in response to a change in money income.

The demand elasticity of income is calculated as follows:

E₁ = $\frac{ΔQ}{ΔI}\times\frac{I}{Q}$

From the given demand function, $\frac{ΔQ}{ΔI}$ = 0.1 , so the income elasticity is:

E₁ = 0.1 $\times \frac{6000}{1110}$

E₁ = 0.54

Income elasticity is: 0.54

(c) What is the cross elasticity of demand between its product and its rival's product? 

The cross-price elasticity demonstrates how the quantity demanded of a specific product responds to price changes with its competitors' products. As a result, the cross-price elasticity formula is:

E_pr = $\frac{ΔQ}{ΔP_r}\times\frac{P_r}{Q}$

$\frac{ΔQ}{ΔP_r}$ = 2 is the result of the equation. Where the elasticity of cross-price is:

E_pr = $2\times\frac{20}{1110}$

E_pr = 0.0360

The elasticity of cross-price is: 0.0360