Q.For the demand function $p=40-x$ and supply function $p=10+2x$, find the equilibrium point, and then compute the Consumer's Surplus and Producer's Surplus.

The equilibrium point found by equating demand and supply feeds into both surplus formulas, exactly as in the earlier worked example.

Finding the equilibrium point

$40-x=10+2x \Rightarrow 30=3x \Rightarrow x_0=10$. Then $p_0=40-10=30$ (checking against supply: $10+2(10)=30$ ✓).

Consumer's Surplus

Producer's Surplus

$=300-(100+100)=300-200=100$ …

Using the WRONG equilibrium quantity in the rectangle term (e.g. using $p_0$ alone instead of $x_0p_0$) — the rectangle representing 'amount actually spent/received' a …