Question

Suppose that the demand curve for wheat is Q=100−10p and the supply curve is Q=10p. The government imposes a price ceiling of p=3

i) Describe how the equilibrium changes. ii) What effect does this price ceiling have on consumer surplus, producer surplus, and deadweight loss?

Answer 1

i)
Qs=100-10p and Qd=10p
At equilibrium Qs=Qd
100-10p=10p
20p=100
p=5
Q=10(5)=50
If there is a price ceiling of $3 then
Qs=10(3)=30 and
Qd=100-10(3)=70
Thus, there will be a shortage of 70-30=40 units
ii)
Initially
if Qd=0 p=10
CS=0.5*(10-5)*(50)=125
if Qs=0 thenp=0
PS=0.5*(5-0)*(50)=125

After ceiling
CS=(0.5*(10-7)*(30))+ (30*(7-3))=165
PS=0.5*(3-0)(30)=45
DWL=0.5*(7-3)*(50-30)=40

The price ceiling leads to a deadweight loss,decreases producer surplus and increases consumer surplus.