Q.For the demand function $p=30-2x$ and supply function $p=5+3x$, find the equilibrium point, and then compute the Consumer's Surplus and Producer's Surplus.

Finding where demand equals supply gives the equilibrium point, which is then used in both the CS and PS integral formulas.

Finding the equilibrium point

Setting demand equal to supply: $30-2x=5+3x \Rightarrow 25=5x \Rightarrow x_0=5$. Then $p_0=30-2(5)=20$ (checking against supply: $5+3(5)=20$ ✓, both give the same $p_0$).

Consumer's Surplus

Producer's Surplus

$=100-(25+37.5)=100-62.5=37.5$ …

Subtracting the rectangle from the demand-curve integral in the WRONG order for CS (i.e. computing $x_0p_0-\int_0^{x_0}f(x)dx$ instead of the correct $\int_0^{x …