Explain why the cross elasticity of demand for substitute goods is positive and the cross elasticity of demand for complements is negative

What will be an ideal response?

The equation for the cross elasticity of demand is the percentage change in quantity demanded of product A divided by the percentage change in price of another product, B. Consider the case in which A and B are substitutes. In this case, when the price of B falls, the quantity of A demanded decreases and when the price of B rises, the quantity of A demanded increases. Because the quantity demanded of product A is in the numerator, then the decrease in the quantity of A demanded when the price of the other product falls means, that the cross elasticity will be positive. (There is a negative number in the numerator and also a negative number in the denominator, so the fraction, the cross elasticity, is positive.) For a price increase, there are positive numbers in both the numerator and denominator, so again the fraction is positive. In either case, the result will be a positive number, that is, the cross elasticity of demand is positive.
Next, consider the case in which A and B are complements. In this case, an increase in the price of B decreases the quantity demanded of A and a decrease in the price of B increases the quantity demanded of A. Here, the change in quantity in the numerator always has the opposite sign from the change in the price in the denominator, so the resulting cross elasticity of demand will be negative.