Question

Determine the producer surplus when equilibrium price is Pe=5. Given the supply function of p=S(q)= q + 2

Answer 1

At equilibrium point

$5=q+2 \\ q =3$

The producer surplus is

$PS= pq - \int^q_0 s(q)dq \\ PS = 5 \times 3 -\int^3_0 (q+2)dq \\ PS = 15 -[\frac{q^2}{2} + 2q]^3_0 \\ PS = 15 -((4.5+6) -(0)) = 15 -10.5 = 4.5$