Question

6. You áre the manager of a firm that receives revenues of $30,000 per year from product Xand $70,000 per year from product Y. The own price elasticity of demand for product Xis -2.5, and the cross-price elasticity of demand between product Yand Xis 1.1. How much will your firm's total revenues (revenues from both products) change if you increase the price of good Xby 1 percent?

Answer 1

6) We know the formula for own price elasticity of X is

% change in quantity demanded of X/% change in price of X

Note putting the values of the terms in the question,

Ie % change in price of X= 1%

Price elasticity of demand for X= -2.5

we get

% change in quantity demanded= -2.5(1)= -2.5

So when price increases by 1%, the quantity demanded of X reduces by 2.5%. so net change in revenue is

(-2.5)(1)%= -2.5% of $ 30,000 =$(-) 750

Similarly the cross price elasticity is given of goods X and Y, the formula being

% change in quantity demanded of Y/ % change in price of X = E_{px,qy ⁽}ie cross price elasticity of X and Y)

% change in price is 1%

Cross price elasticity= 1.1

% change in quantity demanded of Y = 1.1(1)=1.1

Total change in revenue= % change in price*% change in quantity demanded

= (1.1)(1)% of$70,000

=$ 770

Total change in revenue for both the goods is $770-$750=$ 20

So an increase in 1% of price of good X increases total revenue of both goods by $ 20.

(You can comment for doubts)