Question

A firm derives revenue from two sources: goods X and Y. Annual revenues from good X and Y are $10,000 and $20,000, respectively.

If the price elasticity of demand for good X is -4.0 and the cross-price elasticity of demand between Y and X is 2.0, then a 2 percent decrease in the price of X will _______.

Answer 1

X demand would rise by 8% ; Y demand would fall by 4%

Step-by-step explanation:

Price Elasticity of Demand is the responsiveness in demand quantity, due to change in good's price

P.Ed = % change in demand / % change in own price

Cross Price Elasticity is the responsiveness in a good's demand quantity, due to change in other good's price

C.Ed = % change in demand (Y) / % change in other good's price (X)

Given {Good X Elasticities} : P.Ed = (-) 4 ; C.Ed = 2

Price of X decrease = 2%

P.Ed = 4 = % change in demand / 2

% change in demand of X = 2 x 4 = 8%

P.Ed absolute value ignoring negative has been taken due to law of demand price - demand inverse relationship already depicting it. So, 2% fall in price of X increases it's quantity demanded by 8%

C.Ed = 2 = % change in Y demand / 2

% change in Y demand = 2 x 2 = 4%

Cross Price Elasticity of demand is positive in case of substitute goods. These goods can be interchange-ably used to satisfy a particular want. Substitutes price & demand are directly related;- as price fall of a good makes it relatively cheap, increases its demand, decreases other good's demand. So, 2% decrease in good X price decreases good Y demand by 4%