Question

1. Suppose the demand equation can be represent as QD = 100 -2P and the Supply equation can be represented as QS = -10 + P.

   a. Find the equilibrium price and quantity.
   
   b. At a price ceiling of $20, what is the QD and QS. What is the deadweight loss, consumer surplus and producer surplus amount?

Answer 1

a)

Given QD=100-2P

QS=-10+P

Set QD=QS for equilibrium,

100-2P=-10+P

3P=110

P=(110/3)=$36.67 -----(equilibrium price)

QD=100-2*(110/3)=80/3=26.67

QS=-10+(110/3)=80/3=26.67

Equilibrium quantity=80/3=26.67 units

b)

Let there is a price ceiling of $20,

QD=100-2*20=60

QS=-10+20=10

Dead weight loss=DWL=1/2*(110/3-10)*(45-20)=$333.33

Producer Surplus=PS=1/2*(20-10)*(10-0)=$50

Consumer Surplus=CS=1/2*(50-45)*(10-0)+(45-20)*(10-0)=$275