You are the manager of a firm that receives revenues of 6000

You are the manager of a firm that receives revenues of $60,000 per year from product X and $100,000 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 2 percent? ps: I got 1752 but it was wrong

Solution

X = % in Qd of x/% in $ of X

-2.5 = % in Qd of x/1%

-2.5% = % in Qd of x

So the Qd of x decreases by 2.5%, which means we are onlyselling 97.5% of our original Q of x:

PQ = $35,000

(1.01)P(.975)Q = (1.01)(.975)$35,000

=$34,466.25

$34,466.25-%35,000 = -$533.75

yx = % in Qd of Y/% in $ of X

1.1 = % in Qd of Y/1%

1.1% = % in Qd of x

PQ = $70,000

P(1.011)Q = (1.011)$70,000

=$70,700

$70,700-$70,000=$770

now add together the loss of revenue from X and the gain fromY:

-$533.75 + $770 = $236.25 total change in revenue