Question

For this question, consider the market for oranges. Oranges are sold in dozens and the price is in dollars/dozen. The market is defined by the following:

QD= 4000 – 150P

QS= 3600 = 120P

1. Calculate the price, the quantity demanded, and the quantity supplied of oranges when the market is at equilibrium.
2. Calculate the price elasticity of demand for oranges at equilibrium.
3. Calculate the price elasticity of supply at equilibrium.

Answer 1

a)In equilibrium Qd=Qs

i.e 4000-150P=3600+120P

400=270P

P=40/27

P=Dollar /dozen 1.48

Qd=4000-150*(1.48)

Qd= 3778(dozens)

Qs=3600+120*(1.48)=3778(dozens)

b) Price Elasticity of Demand for oranges

Qd=4000-150P

dQd/dP=-150

Price elasticity of demand at equilibrium= dQd*P/dP*Q

P/Q= 0.000392

where P=$1.48/dozen and Qd=3778 (dozens) in equilibrium

Price elasticity of demand at equilibrium=[-150*0.000392] = -0.05882

c) Price elasticity of supply in equilibrium

Qs=3600+120P

dQs/dP=120

Price elasticity of supply at equilibrium= dQs*P/dP*Qs

P/Q= 0.000392

where P=$1.48/dozen and Qd=3778 (dozens) in equilibrium

Price elasticity of supply in equilibrium = 120* 0.000392=0.047056