Question

Given by the equations

                             (1)         Qd = 4 - P

                             (2)         Qs = -2+P           

a)    What is the price elasticity of the demand curve at the point of equilibrium?

b)    What is the price elasticity of the supply curve at the point of equilibrium?

Answer 1

At equilibrium

$Qd=Qs\\4-P=-2+P\\4+2=P+P\\6=2P\\P=\frac{6}{2}\\P=3$

$Qd=4-P\\=4-3=1\\Qs=-2+P\\=-2+3=1$

At equilibrium:

P=3

Q=1

a)

Price elasticity of demand at equilibrium

$Ped=\frac{\Delta Q}{\Delta P}\times\frac{P}{Q}$

$\frac{\Delta Q}{\delta P}=-1$

$Ped=-1\times\frac{3}{1}$

$Ped=-3$

b)

Price elasticity of supply at equilibrium

$Es=\frac{\Delta Q}{\Delta P}\times \frac{P}{Q}\\$

$\frac{\Delta Q}{\delta P}=1$

$Es=1\times \frac{3}{1}$

$Es=3$