The demand function is $p = 30 - x^{2}$ and the supply function is $p = 2 x^{2} + 3$. What is the producer surplus at equilibrium?

Explanation

1. 01

   The market clears at $x_0 = 3$, $p_0 = 21$.

2. 02

   $PS = 21 \times 3 - \int_0^{3} (2 x^{2} + 3)\,dx = 63 - 27 = 36$.