Question

Consider the following market. Demand is given by QD = 5 − P where QD is the quantity demand and P is the price. Supply is given by QS = P/2 where QS is the quantity supplied.

a. What is the market equilibrium quantity and price?

b. Calculate consumer, producer, and total surplus. Depict your answer in a graph.

c. Suppose the government imposes a price floor of P = 4. Calculate the consumer surplus, producer surplus, and deadweight loss. Depict your answer in a graph.

Answer 1

a)

Demand is given by

QD=5-P

Supply is given by

QS=P/2

In equilibrium, set QD=QS

5-P=P/2

5=1.5P

P=3.3333

Q=P/2=3.3333/2=1.6667

b)

Consumer surplus is the area below demand curve and above equilibrium price. This triangular area is shown by blue lines.

Consumer surplus=1/2*Base*height=(1/2)*(5-3.33)*1.67=1.39445

Producer surplus is the area above supply curve and below equilibrium price. This triangular area is shown by red lines.

Producer Surplus=1/2*Base*height=1/2*3.33*1.67=2.78055

Total surplus=Consumer surplus+ Producer surplus=1.39445+2.78055=4.175

c)

Consumer surplus is the area below demand curve and above price floor. This triangular area is shown by blue lines.

Consumer surplus=1/2*Base*height=(1/2)*(5-4)*1 =0.50

Producer surplus is the area above supply curve and below price floor. This area is shown by red lines.

Producer surplus=(4-2)*1+1/2*(2-0)*1=3

Deadweigth loss is a triangular area shown by green lines.

Deadweight loss=Total surplus in equilibrium condition-Producer surplus-Consumer surplus

Deadweight loss=4.175-3-0.5=0.675