Answer to Question #166112 in Microeconomics for Sixtus george

Question

1. Suppose we have the following demand curve P=100-Q/2 calculate the elasticity of demand at point A(P=50) and B(P=80)

Answer 1

The elasticity of demand is equal to:'

$E_d=\dfrac{d Q}{d P}\times \dfrac{P}{Q}$

The demand equation is P=100-Q/2. Therefore:

$dP=-\dfrac{1}{2}dQ\\[0.3cm] \dfrac{dQ}{dP}=-2$

At P=50, the quantity demanded is:

$50=100-Q/2\\[0.3cm] Q=100$

Therefore, the elasticity of demand is:

$E_d=-2\times\dfrac{50}{100}\\ E_d=\boxed{-1}$

At P=80, the quantity demanded is:

$80=100-Q/2\\[0.3cm] Q=40$

Therefore, the price elasticity of demand is:

$E_d=-2\times \dfrac{80}{40}\\ E_d=\boxed{-4}$