Question

Consumer buys 10 units of Good A when the price of Good B is $5. When the price of Good B rises to $6 (the price of Good A remaining unchanged) the consumer buys 14 units of Good A.

Part A:

Using an appropriate formula, calculate this Consumer’s cross Elasticity of demand for Good A. Show your working.

Part B:

Is Good A, a substitute for, or a complement to, Good B? Explain your reasoning.

Answer 1

Cross Elasticity of demand for Good A = $\frac{\%\;change\; in\; quantity\; demanded\; for\; Good\; A}{\%\; change\; in\; price\; of\; Good\; B}$

$=\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \div \frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 }$

Where: Q₁ = 10, Q₂ = 14, P₁ = 5, P₂ = 6

$= \frac{14 -10}{(14+10)/2 }\div \frac{6 - 5}{(6+5)/2 }$

$=\frac{4}{12} \div \frac{1}{5.5} = \frac{0.33}{0.18} = 1.83$

Cross Elasticity of demand for Good A = 1.83

Part B:

Good A is a substitute to good B.

Explanation; Since the cross price elasticity of demand is positive this clearly shows that the two products are substitutes to each other.