Question

Economists in Champaign have been studying the local market for Truly. They've found that the demand for Truly can be described by the following equation: P = 40 - 0.15Q What is the price elasticity of demand(using the Midpoint methodwhen moving from a quantity of 150 to 160? (input your answer in absolute value, and round it to include 2 decimal places.)

Answer 1

Given that $P=40-0.15Q$

When Q=150 , P=17.5

When Q=160 , P=16

$(Q_1,P_1)=(150,17.5)$

$(Q_2,P_2)=(160,16)$

The midpoint price elasticity of demand is given as:

$PED=\frac{\frac{Q_2-Q_1}{(Q_2+Q_1)/2}×100}{\frac{P_2-P_1}{(P_2+P_1)/2}×100}$

$PED=\frac{\frac{160-150}{(160+150)/2}×100}{\frac{17.5-16}{(17.5+16)/2}×100}$

$PED=\frac{\frac{10}{310/2}×100}{\frac{-1.5}{33.5/2}×100}$

$PED=0.72$