Area Between Two Curves
Recall that the area under a curve and above the x-axis can be computed by the definite integral. If we have two curves
y = f(x) and y = g(x)
Find the area between the curves
= 1/3 - 1/4 = 1/12.
Let y = f(x) be the demand function for a product and y = g(x) be the supply function. Then we define the equilibrium point to be the intersection of the two curves. The consumer surplus is defined by the area above the equilibrium value and below the demand curve, while the producer surplus is defined by the area below the equilibrium value and above the supply curve.
f(x) = 1,000 - 0.4x2
We first find the equilibrium point: