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

a) Equilibrium price;

At equilibrium; $Q_{d}=Q_{s}$

$a-bp=c+dp$

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

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

b)Equilibrium quantity;

$Q_{e}=a-b(\frac{a-c}{b+d})$

$=\frac{ad+ac}{b+d}$

c) Price elasticity of demand at equilibrium; we will use point elasticity of demand formula

Point Elasticity of demand; =$(\frac{-1}{slope})(\frac{P_{e}}{Q_{e}})$

$\frac{P_{e}}{Q_{e}}=\frac{a-c}{b+d}\cdot\frac{b+d}{ad+ac}=\frac{a-c}{ad+ac}$

The demand equation will be rewritten as;

$Q_{d}=a-bp$

$bp=a-Q_{d}$

$p=\frac{a}{b}-(\frac{1}{b})Q_{d}$

Price elasticity of demand$=(-1.-b)\cdot\frac{a-c}{ad+ac}=\frac{ab-ac}{ad+ac}$

d) Price elasticity of supply at equilibrium; we will use point elasticity of supply formula

Point Elasticity of demand; =$(\frac{-1}{slope})(\frac{P_{e}}{Q_{e}})$

$\frac{P_{e}}{Q_{e}}=\frac{a-c}{b+d}\cdot\frac{b+d}{ad+ac}=\frac{a-c}{ad+ac}$

The supply equation will be rewritten as;

$Q_{d}=c+dp$

$dp=Q_{s}-c$

$p=(\frac{1}{d})Q_{s}-\frac{c}{d}$

Price elasticity of supply$=(1.d)\cdot\frac{a-c}{ad+ac}=\frac{ad-cd}{ad+ac}$