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.

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