Question

Suppose market demand is given Q_d=a-bp as and market supply is given as, Q_s=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

Price elasticity of supply at equilibrium

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

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

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

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

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 supply equation $\frac{\Delta Q}{\Delta P }$ is the gradient of the equation

therefore from $Q{s}=(c+ dp)$ 

$d$ is the gradient of the equation

the price elasticity of supply will be

$P{e}=d \times \frac{P}{q}$