# Consumer and producer surplus

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##### Intros
###### Lessons
1. Consumer and Producer Surplus Overview:
2. Review of Consumer and Producer Surplus
3. Evaluating Surplus with Integrals
##### Examples
###### Lessons
1. Calculating Producer and Consumer Surplus

The demand curve for cakes is given by $D(q) = 36 - 2q^{2}$ and the supply curve is given by $S(q) = 8q + 12$.

i)Find the producer surplus

ii)Find the consumer surplus

1. The demand curve for cakes is given by $D(q) = \frac{12}{q + 2}$ and the supply curve is given by $S(q) = q + 3$.

i)Find the producer surplus

ii)Find the consumer surplus

###### Topic Notes

Let $S(q)$ and $D(q)$ be supply and demand curves in terms of $q$, where $q$ is the quantity.

Then we calculate the producer and consumer surplus by using the following formulas:

$PS$ (producer surplus) = $\int_{0}^{\overline q} [\overline p - S(q)] dq$

$CS$ (consumer surplus) = $\int_{0}^{\overline q} [D(q) - \overline p] dq$

Where $\overline p$ and $\overline q$ are equilibrium prices and quantity.