Question

A market consists of two individuals. Their demand equation are 

Q1 = 16 - 4P and Q2 = 20 – 2P, respectively. 

= a) What is the market demand equation?

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

Answer 1

a) Market demand = Sum of individual demand

$MD = Q_1 + Q_2 \\ = 16 -4P + 20 -2P \\ = 36 -6P$

b) At P = $2

Point price elasticity:

$PPE = \frac{dMD}{dp} \times \frac{p}{MD} \\ PPE_{market} = \frac{d(36-6p)}{dp} \times \frac{2}{36-6p} \\ = -6 \times \frac{2}{36 – 6 \times 2} \\ = \frac{-12}{24} \\ = -0.5 \\ PPE_{individ.1} = \frac{d(16-4p)}{dp} \times \frac{2}{16-4p} \\ = -4 \times \frac{2}{16-4 \times 2} \\ = \frac{-8}{8} \\ = -1 \\ PPE_{individ.2} = \frac{d(20-2p)}{dp} \times \frac{2}{20-2p} \\ = -2 \times \frac{2}{20-2\times 2} \\ = \frac{-4}{16} \\ = \frac{-1}{4} \\ = -0.25$