You are the manager of a firm that receives revenues of 5000

You are the manager of a firm that receives revenues of $50,000 per year from product X and $80,000 per year from product Y. The own price elasticity of demand for product X is -3, 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.

Solution

The firm receives $50,000 annually as revenues from product X and $80,000 as revenues from product Y. The own price elasticity of demand for product X is given by ed = -3, and the cross-price elasticity of demand between product Y and X is given by ec = 1.8. This value is positive which implies that X and Y are substitutes. This is because cross price elasticity is positive. A rise in price of X will increase the demand for Y

If you increase the price of good X by 2 percent, according to the own price elasticity of X, the reduction in the quantity demanded of X will be

ed = % change in QD of X/% change in price of X

-3 = % fall in Qty of X / 2%

Hence quantity demanded of X falls by 6%.

Revenue = Price x Quantity

% change in revenue = % change in price + % change in Qd

We see that when price of X rises by 2%, its quantity demanded falls by 6% so that revenue will decrease by (2 - 6) = 4%

New revenue from X will be 50000*(1 - 4%) = $48000.

Similarly, we have

ec = % change in QD of Y/% change in price of X

1.8 = % fall in Qty of Y / 2%

Hence quantity demanded of Y will rise by 3.6%. Revenue from Y will directly increase by 3.6% since there are no changes in price of Y. Hence revenue from Y will be 80000*(1 + 3.6%) = $82880.

Old revenue was $50000 + $80000 = $130,000. New revenue is $48000 + $82880 = $130,880. Hence your firm\'s total revenues (revenues from both products) will increase by $880.