Question

Consider the following market supply and demand information. P=0.5Q P=20-0.5Q (a) What would be the price elasticity at the market equilibrium point? (b) 10% increase in consumer income changed the demand to P=22-0.5Q, Calculate the income elasticity.

Answer 1

a)

Equilibrium is at Qd=Qs

0.5Q=20-0.5Q

Q=20

P=0.5*20=$10

price elasticity of demand =(dQ/dP)*(P/Q)

the inverse demand curve is

P=20-0.5Q

converting to a normal demand curve

0.5Q=20-P

Q=40-2P

dQ/dP=-2 ............ differentiation of demand curve concerning price

price elasticity of demand =(-2)*(10/20)

=-1

the elasticity of demand is -1, it means the demand is unit elastic.

-------------

b)

the new equilibrium at Qd=Qs

0.5Q=22-0.5Q

Q=22

P=0.5*22=$11

%change in quantity=((new quantity-old quantity)/old quantity)*100

%change in quantity=((22-20)/20)*100=10%

income elasticity of demand =%change in quantity/%change in income

=10/10

=1

the income elasticity of demand is 1, and it shows the good is normal because the elasticity is positive.