Answer to Question #189020 in Microeconomics for Rida Awwal

Question

In the demand function Q=P^-0.4 , calculate price elasticity of demand and identify type of good

Answer 1

Given $Q=P^{-0.4}$

The concept of price elasticity describes how revenue increases as prices change.

Computing the price elasticity of this demand function

Computing the price elasticity of this demand function

$E_d=\frac{P}{Q(P)}\frac{dQ}{dP}$

$Finding \frac{dQ}{dP}=\frac{d}{dP}(P^{-0.4})=-0.4P^{-1.4}$

substituting back in equation

$E_d=\frac{P}{P^{-0.4}}\times -0.4P^{-1.4}$

$E_d=-0.4(P^{0.6} \times P^{-1.4}$

$E_d=-0.4(P^{-0.8})$

The above equation shows that the demand elasticity. Negative sign describes how demand reacts to price changes:

As the price rises, the quantity demanded falls, and as the price falls, the quantity demanded rises.

The fact that it is negative indicates that price p and quantity demanded q is moving in opposite directions.

The above equation generalizes to the fact that Ed will always have a value less than 1.

This indicates good to be price elastic that means many substitute of goods are available.

Therefore it is a type of substitute good.