# Solution Set Up

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

Known Determine
Producer's surplus = 132,000

Consumer's surplus = 132,000/4
= 33,000

Demand curve, D(q), is linear.

1) Equilibrium point

2) Demand Curve
Equation

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

 D(q) = p = mq + b

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

 D(q') = p' = mq' + b (1)

where m is the slope and b is the y-intercept of the line. Also observe that
 D(0) = b

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

 (2)

The consumer's surplus (33,000) is the area of the triangle shown shaded in the graph below

and since the area of a triangle is (base x height)/2, then the equation which results is

 (3)

The producer's surplus of 132,000 is the area shown shaded in the graph below

which results in the equation

 (4)

Note: Slide your mouse over the terms in equation (4) to see what each term represents in the graph above.

Now you are ready to solve Oinkle Sam's problem. Equations (1) through (4) give you 4 equations in the 4 unknowns m, b, q', and p'. After you have solved this system of equations, the equation of the linear demand curve is specified by the m and b, and the equilibrium point is specified by the q' and p'.

Next: After trying to solve it yourself, see "The Solution" to Oinkle Sam's problem.