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

Solution:

PART A:

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 for Good B. This is because the Cross Elasticity of demand is positive since the demand for one good (Good A) increases when the price for the substitute good (Good B) increases.