Answer to Question #228543 in Microeconomics for Zion

Question #228543
In the demand function Q=p‒0.4, calculate price elasticity of demand and identify type of goods
1
Expert's answer
2021-08-23T13:18:07-0400

Given Q=P0.4Q=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

Ed=PQ(P)dQdPE_d=\frac{P}{Q(P)}\frac{dQ}{dP}


FindingdQdP=ddP(P0.4)=0.4P1.4Finding \frac{dQ}{dP}=\frac{d}{dP}(P^{-0.4})=-0.4P^{-1.4}


substituting back in equation

Ed=PP0.4×0.4P1.4E_d=\frac{P}{P^{-0.4}}\times -0.4P^{-1.4}


Ed=0.4(P0.6×P1.4E_d=-0.4(P^{0.6} \times P^{-1.4}


Ed=0.4(P0.8)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.


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