Question

You are the manager of a firm that receives revenues of $20,000 per year from product X and $70,000 per year from product Y. The own price elasticity of demand for product X is -2, and the cross-price elasticity of demand between product Y and X is -1.5.

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

Solution:-

% rise in Px = 1%

Ex1Px = -2 = % change in Qx / % Change in Px

               -2 =% change in Qx

% change in Qx = -2%

= Cross Elasticity = Ey1Px = -1.5 = % change in Qy/% change in Px

                                                  -1.5 = % change in Qy/1

                              % change in Qy = -1.5%

% Change in Revenue of X = % change in Px + % change in Qx

                                                = 1-2 = -1%

% Change in Revenue of X = % change in Py + % change in Qy

                                               =0-1.5 =1.5%

Now Total Revenue = [ 20000+ 20000(-0.01)] + [70000 +70000(-0.015)]

                                     = (20000-200) + (70000 – 1050)

                                     =19,800 + 68,950

                                     =$88,750

Change in Revenue = 88750 – 90000 = -1250

Thus, the change in revenue from both the products X and Y with a fall in price, is $1250.