Applications to Economics: Consumer and Producer Surplus

The demand function $p = D(q)$ records the maximum price a buyer will pay for the $q$-th unit. At the market price $P^* = D(Q^*)$, buyers who would have paid more than $P^*$ gain a surplus equal to the gap between their willingness to pay and the actual price. Summing these gaps via a Riemann sum and taking the limit gives consumer surplus $= \int_0^{Q^*}[D(q) - P^*]\,dq$ — a single integral of the area-between-curves type from Areas Between Curves. The mirror image, producer surplus, measures the gain to sellers. Together they are the foundation for welfare analysis: optimal policies maximise total surplus, and taxes or price controls create deadweight losses (areas of destroyed surplus) that appear as gaps in the integral.

Learning objectives. By the end of this note you should be able to: