Answer to Question #271893 in Microeconomics for kalehiwot

Question

1.     Find the price elasticity of supply at price of Birr 8 if the supply function is:

Q = 25 – 4P + P²

What is elasticity at Birr 4 and at Birr 5? Interpret the result.

Answer 1

$Q=25-4P+P^2$

Elasticity of supply:

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

$=\frac{P}{25-4P+P^2}(-4+2P)$

$=\frac{-4P+2P^2}{25-4P+P^2}$

At P= Birr 8,

$=\frac{-4(8)+2(8^2)}{25-4(8)+8^2}=1.88$

Price elasticity of supply being 1.88 implies that supply is elastic.

At P=Birr 4,

Elasticity of supply:

$=\frac{-4(4)+2(4^2)}{25-4(4)+4^2}=0.64$

Elasticity of supply being 0.64 implies that supply is inelastic.

At P=Birr 5,

Elasticity of supply:

$=\frac{-4(5)+2(5^2)}{25-4(5)+5^2}=1$

Elasticity of supply being 1 implies that supply is unit elastic.