The demand function is $p = 40 - x^{2}$ and the supply function is $p = 3x^{2} + 4$. What is the producer surplus at equilibrium?

Explanation

1. 01

   Equilibrium: $x_0 = 3$, $p_0 = 31$, so producers receive $31 \times 3 = 93$.

2. 02

   $PS = 93 - \int_{0}^{3} (3x^{2} + 4)\,dx = 93 - (27 + 12) = 54$ rupees.