Question

The price elasticity of bananas is -0.8 and the cross price elasticity of bananas with respect to
the price of berries is 0.5. If the price of bananas increases by 10 % and the price of berries
falls by 4 %, what will happen to banana demand?
a. A 10 percent increase
b. A 10 percent decrease
c. A 16 percent increase
d. A 5 percent increase
e. None of the above

Answer 1

Price elasticity of demand is given by the following formula:

Price elasticity of demand = % change in quantity demanded / % change in prices

On the other hand, Cross price elasticity of demand is given as:

Cross price elasticity = % change in quantity demanded Product A/ % change in the price of product B

Given that, Cross price elasticity of demand = 0.5 to berries.

Thus, 0.5 = % change in quantity demanded of banana / % change in price of berries

or 0.5 = % change in quantity demanded for banana / (-0.04)

or % change in quantity demanded for banana = -0.02 or 2% decrease in quantity demanded

Now, also given that price elasticity of banana = -0.8

Price elasticity = % change in quantity demanded / % change in prices

or (-0.8) = % change in quantity demanded / 0.1

or % change in quantity demanded = -0.08 or 8% decrease in quantity demanded

Thus, total change in quantity demanded for banana = -10%

or a 10% decrease in quantity demanded

Thus, Option B is the correct answer.