Answer to Question #247330 in Microeconomics for tstrain

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

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

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

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

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

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

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