Question

1.     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

Solution:

a.). At equilibrium: Qd = Qs

a – bp = c + dp

p = $c - \frac{a}{b} + d$

Equilibrium price = $c - \frac{a}{b} + d$

 

b.). Equilibrium quantity:

Plug price into the demand function to derive the equilibrium quantity:

Qd = a – bp

Qd = a – b($c - \frac{a}{b} + d$ )

Qd = $2ab + ad - \frac{cb}{b} + d$

Equilibrium quantity: $2ab + ad - \frac{cb}{b} + d$

c.). Price elasticity of demand at equilibrium:

Price elasticity of demand (PED) = $\frac{\triangle Qd}{P} \times \frac{P}{Qd}$

$\frac{\triangle Qd}{P} = -b$

PED = $-b \times \frac{c-a}{b+d} \div \frac{2ab+ad-cb}{b+d}$

PED = $-b\frac{c-a}{2ab+ad-cb}$

 

d.). Price elasticity of supply at equilibrium:

Price elasticity of supply (PES) = $\frac{\triangle Qs}{P} \times \frac{P}{Qs}$

$\frac{\triangle Qs}{P} = d$

PES = $d \times \frac{c-a}{b+d} \div \frac{cb+2cd-da}{b+d}$

 

PES =$\frac{d(c-a)}{cb+2cd - da}$