Answer to Question #305200 in Macroeconomics for Xeniya

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:

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

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

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

$PED=0.72$