Skip to content

Business Mathematics and Statistics · Ch 3 — Integral Calculus – II (Area under curves; Application of Integration in Economics and Commerce)

Consumer's Surplus and Producer's Surplus

3

Consumer's Surplus and Producer's Surplus

Figure 2 — Demand and Supply Curves Meeting at Equilibrium (5, 20)
Figure 2 — Demand and Supply Curves Meeting at Equilibrium (5, 20)

Equilibrium

Given a demand function p=f(x)p=f(x) (price falls as quantity xx rises) and a supply function p=g(x)p=g(x) (price rises as quantity rises), the equilibrium point (x0,p0)(x_0,p_0) is where they meet: f(x0)=g(x0)=p0f(x_0)=g(x_0)=p_0.

Consumer's Surplus

Consumer's Surplus (CS) measures the extra amount consumers WOULD have been willing to pay, above what they actually paid at the equilibrium price, for every unit up to x0x_0:

CS=∫0x0f(x) dx−x0p0CS=\int_0^{x_0}f(x)\,dx-x_0p_0

Producer's Surplus

Producer's Surplus (PS) measures the extra amount producers actually RECEIVED, above the minimum they would have accepted, for every unit up to x0x_0:

PS=x0p0−∫0x0g(x) dxPS=x_0p_0-\int_0^{x_0}g(x)\,dx

Note

CS uses (area under demand) minus (rectangle); PS uses (rectangle) minus (area under supply) — never the other way round …

Definition 1Consumer's Surplus

CS=∫0x0f(x) dx−x0p0CS=\int_0^{x_0}f(x)\,dx-x_0p_0, where p=f(x)p=f(x) is the demand function and (x0,p0)(x_0,p_0) is the m …

Definition 2Producer's Surplus

PS=x0p0−∫0x0g(x) dxPS=x_0p_0-\int_0^{x_0}g(x)\,dx, where p=g(x)p=g(x) is the supply function and (x0,p0)(x_0,p_0) is the m …

Start your 14-day free trial to unlock the full solution →
← Previous · 2Cost and Revenue Functions from Marginal FunctionsNext →Q7 — Find the area bounded by the curve y=4x-x² and the x-axis (i.e. betwee…