Solution to Oinkle Sam's Problem



We have the following 4 equations to solve for the 4 unknowns m, b, q', and p':

p' = mq' + b (1)
(2)
(3)
(4)


Performing the integration in equation (4) gives

(5)

Substituting equation (2) into equation (5) yields

and solving for q' yields

q'   =   660

Then by equation (2)

Substituting equation (1) into equation (3) yields

-m(q')2   =   66,000

and solving for m, using q', gives

Substituting the m, q', and p' we have found into equation (1) gives

b   =   p'   -   mq'   =   400


So the final answers are that the equilibrium point is at

(q', p')   =   (660, 300)

and that the equation for the linear demand curve is