When the price of a bicycle falls from $220 to $180 and other things remain the same, I. the quantity of bicycles demanded increases from 150 to 250 an hour.
II. the quantity of skateboards demanded decreases from 125 to 75 an hour.
III. the quantity of bicycle helmets demanded increases from 170 to 230 an hour.
Bicycle helmets and bicycles are ________ because a fall in the price of a bicycle brings ________ in the quantity demanded of bicycle helmets. The cross elasticity of demand for bicycle helmets with respect to bicycles is ________.
A)complements; an increase; -1.5
B)substitutes; a decrease; 1.5
C)substitutes; an increase; -0.67
D)complements; a decrease; 0.67
E)complements; an increase; 1.5

Question

Quizplus · Accepted Answer

Bicycle helmets and bicycles are complements because a fall in the price of a bicycle brings an increase in the quantity demanded of bicycle helmets (from 170 to 230). The cross elasticity of demand for bicycle helmets with respect to bicycles is negative because they are complements. The formula for cross elasticity of demand is (% change in quantity demanded of bicycle helmets)/(% change in price of bicycles). Using the values given in the question, we get:

% change in quantity demanded of bicycle helmets = [(230-170)/((170+230)/2)]*100% = 35% increase

% change in price of bicycles = [(180-220)/((180+220)/2)]*100% = 18.2% decrease

Therefore, the cross elasticity of demand for bicycle helmets with respect to bicycles is:

(-35%)/(18.2%) = -1.92 ≈ -1.5

So, the best choice is A) complements; an increase; -1.5.

When the Price of a Bicycle Falls from $220 to $180