Question

A cross price elasticity of demand of -1.5 for Good X and Good Y suggests that if the price of of Good X increases by 5.0 percent, then the quantity demanded of Good Y will?

A) increases by 7.5 percent and the goods are complements

B) decreases by 7.5 percent and the goods are complements

C) decreases by 7.5 percent and the goods as substitutes

D) increases by 7.5 percent and the goods are substitutes

Answer 1

Cross-price elasticity of demand= % change in the quantity demand/ % change in the price

When the cross-price elasticity demand sign is positive, then both goods will be substitute goods.

The price of substitute goods and demand for its substitute goods are positively related.

When the cross-price elasticity demand sign is negative, then both goods will be complementary goods

The price of complement goods and demand for its complement goods are negatively related.

Since the given cross-price elasticity of demand is -1.5, so good x and y are complementary goods.

Cross-price elasticity of good X and Y= -1.5

% change in quantity demand of good Y/ %change in the price of good X

= -1.5

% change in quantity demand of good Y/ 5%= -1.5

% change in quantity demand of good Y=-1.5*5%

=-7.5%

The negative sign shows that the quantity demanded of good Y will decrease.

Hence it can be said that if the price of of Good X increases by 5.0 percent, then the quantity demanded of Good Y will decreases by 7.5 percent and the goods are complements.

Hence option B is the correct answer.