Solution Set-Up

The following table lists what we know and what we want to determine:

Producer's surplus
Consumer's surplus

Supply curve

Demand curve, D(q), is linear.

1) Equilibrium point

2) Demand Curve Equation





Since the demand curve is linear, then it has the form


and because this linear curve will be true for all q and p, then it will, in particular, hold for the point (q', p'):



where m is the slope and b is the y-intercept of the line.

Since the supply curve S(q) is known for all q, we have




The consumer's surplus (21,780) is the area of the triangle shown shaded in the graph below

Since the area of a triangle is (base x height)/2, we obtain




The producer's surplus of 108,900 is the area shown shaded in the graph below

and it results in the equation




Now we are ready to solve Sam's problem. Equations (1) through (4) give you 4 equations in the 4 unknowns m, b, p' and q'. After we have solved this system of equations, the equation of the linear demand curve can be determined using the values for m and b. In addition the equilibrium point will be specified by (q', p').

Brief Review Finding the Solution