Question

Suppose a firm produces x and y, the firm earns revenues from x=$50000 and revenues from y equal to $ 30000. the own price elasticity of demand for x is -2 and the cross price elasticity of demand between x and y is -0.6. if the firm lowers the price of product x by 1%, the change in the total revenues will be $?

Answer 1

Answer:

If the firm lowers the price of product x by 1%, the change in the total revenues will be $680.

Explanation:

Own price elasticity of demand of a commodity is the degree of responsiveness of quantity demanded of the commodity to a change in its own price. This is given as -2 for commodity x in the question.

The cross price elasticity of demand between any two commodities is the degree of responsiveness of quantity demanded of the first commodity to a change in the price of the second commodity. This is given as -0.6 for between commodity x and y in the question.

Given the information in the question, the change in the total revenues if the firm lowers the price of product x by 1% can be calculated using the following formula:

ΔTR = [(rx * (1 + ex)) + (ry * cexy)] * Δpx ..................... (1)

ΔTR = Change in the total revenues = ?

rx = revenues from x = $50,000

ex = own price elasticity of demand for x is = -2

ry = revenues from y = $30,000

cexy = cross price elasticity of demand between x and y = -0.6

Δp = Change in the price of product x = -1%

Substituting the values into equation (1), we have:

ΔTR = [(50,000 * (1 + (-2))) + (30,000 * (-0.6)] * (-1%)

ΔTR = [(50,000 - 100,000) - 18,000] * (-1%)

ΔTR = [-50,000 - 18,000] * (-1%)

ΔTR = -68,000 * (-1%)

ΔTR = $680

Therefore, if the firm lowers the price of product x by 1%, the change in the total revenues will be $680.