Question

You are the manager of a firm that receives revenues of $40,000 per year from product X and $90,000 per year from product Y. The own price elasticity of demand for product X is -1.5, and the cross-price elasticity of demand between product Y and X is -1.8.

How much will your firm's total revenues (revenues from both products) change if you increase the price of good X by 2 percent?

Instructions: Enter your response rounded to the nearest dollar. Use a negative sign (-) if applicable.

$

Answer 1

Price elasticity of demand of X = % change in Quantity demand of X/ % change in its own price = -1.5

Now suppose, % change in its own price = 2%

=> % change in Quantity demand /2 = -1.5

Hence Quantity demand of X will decrease by 3%

Cross Price elasticity of demand of Y = % change in Quantity demand of Y / % change price of X = -1.8

Now suppose, % change Price of X = 2%

=> % change in Quantity demand of Y/2 = -1.8

Hence Quantity demand of Y will decrease by 3.6%

Total Revenue (TR) = Price *Quantity = PQ

Formula:

% change in (UV) = % change in U + % change in V

TR = PQ

% change in TR from X = % change in P + % change in Q = 2 - 3 = -1%

Hence Revenue from X will decrease by 1% => Revenue will decrease by (1/100)*40,000 = $400

Now Price of Y is same hence % change in Price of Y = 0.

Now,

% change in TR from Y = % change in P + % change in Q = 0 - 3.6 = -3.6%

Hence Revenue from Y will decrease by 3.6% => Revenue will decrease by (3.6/100)*90,000 = $3240

Hence Total Revenue will change by -400 -3240 = -$3640