Answer to Question #270450 in Economics of Enterprise for Abdi Obsa

Question

Suppose market demand is given Qd=a-bp as and market supply is given as, Qs=c+dp and then find the following

o Equilibrium price

o Equilibrium quantity

o Price elasticity of demand at equilibrium

o Price elasticity of supply at equilibrium

Answer 1

At equilibrium price, the quantity demanded is equal to quantity supplied in the market

$Q{d}=Q{s}$

therefore

$(a- bp)= (c+dp)$

$(a-c) =(dp + bp)$

$(a - c)=p(d +p)$

$p=(a - c)/(b + d)$

$equilibrium price =(a - c)/(b + d)$

Equilibrium quantity is gotten by substituting the equilibrium price into the demand equation

$Qd=a - bp$

$qd =a- b[\frac{ a-c}{b+d}]$

$q=a- [\frac{ab +cb}{b+d}]$

$Q =\frac{(ab+bd)-(ab+cb)}{b+d}$

$Q=\frac{ab -ab+cb+bd}{b+d}$

EQUILLIBRIUM QUANTITY IS GIVEN BY

$Q=\frac{cb + ad}{b + d}$

Price elasticity of demand at equilibrium

$price elasticity=\frac{percentage change in quantity}{percentagechange in price}$

PERCENTAGE CHANGE IN QUANTINTY =$\frac {\Delta Q}{Q}$

PERCENTAGE CHANGE IN PRICE=$\frac {\Delta P}{P}$

change in quantity$\Delta Q =Q{1}- Q$

change in price$\Delta Q =P{1}- P$

PRICE ELASTICITY =$\frac{\Delta Q}{ Q} \times \frac{P}{\Delta P}$

PRICE ELASTICITY =$\frac{\Delta Q}{\Delta P } \times \frac{P}{Q}$

but from the demand equation $\frac{\Delta Q}{\Delta P }$ is the gradient of the equation

therefore from $Q{s}=(a- bp)$ $-b$ is the gradient of the equation

the price elasticity of demand will be

$P{e}=-b \times \frac{P}{q}$