Question

you are the manager of a firm that receives revenues of$20000 per year from product X and $100,000 per year from product Y. The own price elasticity of demand for product X ia -2, and the cross -price elasticity of demand between product Y and X is -1.6.
How much will your firm's total revenues (revenues from both products) change if you increase the price of good X by 1 percent?

Answer 1

• Own price elasticity of demand = -2

%change in price = 1%

Price elasticity of demand of X = %change in quantity demanded of / %change in price of X

-2 = %change in quantity demanded / 1

%change in quantity demanded = -2%

Initial revenue = $20,000

As revenue = Price * Quantity sold at that price

P * Q = 20,000

Price becomes = P + 1% of P = 1.01P

Quantity becomes = Q - 2% of Q = 0.98Q

New revenue becomes: 1.01P * 0.98Q = 20,000

P * Q = $20,206.1

Thus there would be a change of $206.1 when price rises and demand falls.

• Cross price elasticity = -1.6

%change in price of X = 1%

Cross price elasticity = %change in quantity demanded of Y / %change in price of X

-1.6 = %change in quantity demanded of Y / 1%

%change in quantity demanded of Y = -1.6%

P * Q = $100,000

As price of Y does not change while its quantity falls by 1.6% which makes its quantity 0.984Q

P * 0.984Q = $100,000

P * Q = $101,626.01

Its revenue would rise by $1,626.01

Complementary goods have negative cross price elasticity which means that goods X and good Y are complementary goods.