Question

When the price of product A decreased from $2 to $1, the consumer bought 28 units of product B instead of 20. What is the consumer's cross-price elasticity of demand for these two products? What does the calculated elasticity imply about the relationship between product A and product B for this consumer?

Answer 1

Cross price elasticity of demand (XED) measures the changes in the quantity demanded of a particular commodity as a result of change in price of another commodity. It is calculated as;

Cross price elasticity of demand is equal to percentage change in quantity demanded of product A divided by percentage change in price of product B.

Percentage change in quantity of B = $\frac{Q_i-Q_o}{(Q_i+Q_o)/2}\times100$

Percentage change in price of A = $\frac{P_i-P_o}{(P_i+P_o)/2}\times100$

%change in quantity of B = (28-20)/(28+20)/2 = 0.33 X 100 = 33

% change in price of A = (1-2)/(1+2)/2 = -0.66 X 100 = -66

XED = 33/-66 = -0.5

Since the cross price elasticity of demand is negative, A and B are complementary products.