Question

Economists in Champaign have been studying the local market for pizza. They've found that the demand for pizza can be described by the following equation: P= 20 - 0.1Q.

What is the price elasticity of demand(using the Midpoint method) when moving from a quantity of 20 to 30?

Answer 1

$P=20-0.1Q\\P=20-0.1(20)\\=20-2\\=18$

When Q=30

$P=20-0.1(30)\\=20-3\\=17$

$\frac{Q_2-Q_1}{\frac{Q_2+Q_1}{2}}\div\frac{P_2-P_1}{\frac{P_2+P_1}{2}}$

$Q_2=30\\Q_1=20\\P_2=17\\P_1=18$

$\frac{30-20}{\frac{30+20}{2}}\div\frac{17-18}{\frac{17+18}{2}}$

$\frac{10}{25}\div\frac{-1}{17.5}$

$0.4\div0.057\\=-7.02$