Answer to Question #323154 in Microeconomics for Eugjeanne

Question

A market consists of two individuals . Their demand equations are:

P= 4 - 0.25Q₁ and P = 10 - 0.5Q₂

a) What is the market demand equation?

b) At a price of $2, what is the point price elasticity for each person and for the market?

Answer 1

$P_1=4-0.25Q_1$

$P_2=10-0.5Q_2$

A) The market demand, Q, is given as the total of all individual demands:

$Q_1=16-4P_1$

At P=$2, Q₁=8

$Q_2=20-2P_2$

At P=$2, Q₂= 16

$\therefore Q=36-6P$

B) $\epsilon=\frac{{d}{Q}}{{d}{P}}×\frac{P}{Q}$

Point elasticity of the market at Q=24 and P=2

$\epsilon_m=-6×\frac{2}{24}$

$\epsilon_m=-0.17$

$\epsilon_{P{_{1}}}=-4×\frac{2}{8}$

$\epsilon_{P_{1}}=-1$

$\epsilon_{P_{2}}=-2×\frac{2}{16}$

$\epsilon_{P_{2}}=-0.25$