The supply function is $p = 2 + x^{2}$, and 4 units are sold at the market price. What is the producer surplus?

Explanation

1. 01

   At $x_0 = 4$ the price is $p_0 = 2 + 16 = 18$, so producers receive $18 \times 4 = 72$.

2. 02

   $PS = 72 - \int_{0}^{4} (2 + x^{2})\,dx = 72 - \left(8 + \frac{64}{3}\right) = \frac{128}{3}$ rupees, about ₹42.67.