Question

The demand and supply for a good are respectively QD = 16 – 2P + 2I and QS = 2P – 4 with QD denoting the quantity demanded, QS the quantity supplied, and P the price for the good. Suppose the consumers’ income is I = 2. 6) Determine the price-elasticity of demand if P = 2. 7) Determine the income-elasticity of demand if P = 2. 8) Determine the price-elasticity of supply if P = 4. 9) Determine consumers’ expenditures at the equilibrium. 10) Determine the consumer surplus at the equilibrium. 11) Determine consumers’ total benefits at the equilibrium. 12) Determine producers’ total revenues at the equilibrium. 13) Determine producers’ total cost (there are no fixed costs) at the equilibrium. 14) Determine the producer surplus at the equilibrium. 15) Determine the total surplus at the equilibrium.

Answer 1

6. Qd when price=2 and income=2

Qd=16-2*2+2*2=16

Price elasticity of demand=dQd/dP*P/Q=(-)2*2/16=(-).25

7. Income elasticity of demand=dQd/dI*I/Q=2*2/16=.25

8.Qs=2*4-4=4

price elasticity of supply=dQs/dP*P/Q=2*4/4=2

9. At equilibrium Qd=Qs

16-2*P+2*2=2*P-4

P=6 (equilibrium price)

Qd=Qs=8(equilibrium quantity)

Consumer expenditure=P*Q=6*8=48

10. When Qd=0 Price=10

Consumer Surplus=1/2*(10-6)*8=16

11.Total Consumer benefit= Area under the demand curve=Consumer surplus+Consumer expenditure=16+48=64

12.Producers revenue=Consumers expenditure=48

13.Producers total cost=Area under the supply curve=1/2*8*6=24

14.Producer Surplus=1/2*8*6=24

15.Total surplus=Consumer Surplus + producer Surplus=16+24=40