Question

Given the following inverse demand and supply curves
P=8-Qd/2
P=2+Qs
and assuming the price is fixed below the equilibrium price at $5, what is the loss in producer surplus due to the price ceiling

The answer is $3.50
But how did they get to this ? Please explain.

Answer 1

At equilibrium, Qd = Qs

16 - 2P = P-2

3P = 18

6 - equilibrium price (Pe)

Qs = 6-2=4 units

With a price of $ 5 Qs = 5-2 = 3 units

the loss in producer surplus due to the price ceiling - $5 (P)

= (6-5)*3+1/2*((6-5)*(4-3))=1*3+1/2*(1*1)=3+0.5=3.5