Please help with this!?

Question

The demand equation for a certain type of printer is given by
D=-200p+35,000
The supply equation is predicted to be
S=-p^2+400p-20,000
Find the equilibrium price.

Answer 1

We need to solve both the equations and find p. At equilibrium, supply and demand match, that means the two equations will be equal.

S = D

-p^2 + 400p - 20000 = -200p + 35000

Rearranging the two equations, we can rewrite

p^2 - 600p + 55000 = 0

This is a quadratic equation in p of the form ax^2 + bx + c = 0 which has the roots,

x1 = [-b + sqrt(b^2 - 4ac)] / 2a and x2 = [-b - sqrt(b^2 - 4ac)] / 2a

So, we can write:

p1 = [600 + sqrt(600 x 600 + 4 x 55000)] / 2

p2 need not be considered since it will be a negative quantity and has no real significance (price can't be negative)

p1 = [600 + sqrt(360000 + 220000)] / 2

= (600 + 505.96) / 2 = 552.98 or 553 approx.

Note that the quadratic equation does not have integer factors.

An alternative method of solving such problems is to plot the equations graphically and see the point of intersection.