Science:Math Exam Resources/Courses/MATH101 C/April 2024/Question 18 (c)/Hint 1

A formula for the total surplus when ${\tilde {q}}_{e}$ units are sold over the entire market is

$${\begin{aligned}\int _{0}^{{\tilde {q}}_{e}}D(q)-S(q)\;\mathrm {d} q.\end{aligned}}$$

To intuitively remember this formula, and to understand why it is true, recall that each additional unit sold provides a surplus because the producer sells it for more than they are willing to sell it for, and the customer buys it for less than they are willing to spend it on, until the equilibrium is reached. This integral is the result of adding up those surpluses over all the units sold.