Question

When the price of a good x falls from £5 to £3, the demand for good y increases from 14 units to 18 units. Use the mid-point approach to calculate the cross price elasticity of demand and identify whether the goods are complements or substitutes. (4 marks)

Answer 1

$\%$ change in quantity $=\frac{Q_{2}-Q_{1}}{(Q_{2}+Q_{1})\div 2}\times 100\%=\frac{(18-14)}{(18+14)\div 2}\times 100=4/16\times100=25\%$

$\%$ change in price $=\frac{(P_{2}-P_{2})}{(P_{2}+P_{1})\div 2}\times 100=\frac{(3-5)}{(3+5)\div 2}\times 100=-2/4\times100=-50\%$

cross price elasticity of demand$=\%$ change in quantity$/\%$ change in price$=25/-50=-0.5$

Because the cross-price elasticity is negative, good x and good y are complementary goods.