Question

Given the demand function

Pd = 35 − Q2,

and the supply function

Ps = 3 + Q2.

Calculate the producer surplus for the supply function.

Answer 1

At equilibrium

$PD=PS$

$(35-Q^2)=(3+Q^2)\\ 32 =2Q^2\\ Q=4$

Q at equilibrium = 4

The producer surplus is

$4*(3+4^2)-\int(3+Q^2)dQ$

$19*4-(3Q+Q^3/3)$

Since Q=4

$19*4-(3*4+4^3/3)$ =$42.60