Question

You are the manager of a firm that receive revenue of Rs.30000 per year from pproduct X and Rs.70000 per year from product Y. The own price elastacity of demand for product X is -2.5 and the cross price elastacity of demand between product Y and X is 1.1. How much will you firm's total revenue ( revenue from both products) change if you increase the price of good X by 1 present

Answer 1

It is given that the firm earns revenue from the sale of two commodities, that is, commodity-X and commodity-Y

Firm earns Rs.30,000 from sale of commodity-X and Rs.70,000 from sale of commodity-Y.

The own price-elasticity demand of commodity-X is -2.5

It implies if there is 1% increase (decrease) in price, the quantity demanded will decrease (increase) by 2.5%

Similarly, the cross price-elasticity of demand between commodity-X and commodity-Y is 1.1

It implies that the commodities are perfect substitutes to each other. A 1% increase (decrease) in price of one commodity leads to 1.1% increase (decrease) in quantity demanded of other commodity.

Following is the formula to calculate the change in revenue due to change in the price of the commodity-X:

$ΔR = [R_X(1+E_{Q_X, P_X})+R_Y(E_{Q_Y, P_X})](\% ΔP_X) \;\;(1)$

ΔR is the revenue earned from sale of commodity-X

$E_{Q_X, P_X}$ is the own price-elasticity of demand

$R_Y$ is the revenue earned from sale of commodity-Y

$E_{Q_Y, P_X}$ is the cross price elasticity of demand

$\% ΔP_X$ is the percentage change in price of commodity-X

The values of the above variables are as follows:

$R_X=30000 \\ E_{Q_X, P_X} = -2.5 \\ R_Y = 70000 \\ E_{Q_Y, P_X} = 1.1 \\ \% ΔP_X = 1 \% \; or \;0.01$

Substituting these values into equation (1), the change in revenue is as follows:

$ΔR = [R_X(1+E_{Q_X, P_X})+R_Y(E_{Q_Y, P_X})](\% ΔP_X) \\ = [30000(1+(-2.5))+(70000)(1.1)](0.01) \\ = (-45000+77000)(0.01) \\ = 320$

Answer: Rs.320