Expert: Paul Klarreich - 9/10/2007

Question
suppose that 10,000 units of a certian item are sold per day by the entire industry at a price of $150 per item, and that 8,000 units can be sold per day by the same industry at a price of $200 per item. Find the demand equation for p, in terms of x, the number of units sold, assuming the demand curve to be a straight line.
so p= ?

Answer
Questioner:   Shannon
Category:  Advanced Math
Private:  No
 
Subject:  help me....i'm stumped!
Question:  suppose that 10,000 units of a certian item are sold per day by the entire industry at a price of $150 per item, and that 8,000 units can be sold per day by the same industry at a price of $200 per item. Find the demand equation for p, in terms of x, the number of units sold, assuming the demand curve to be a straight line.
so p= ?
.................................
Hi, Shannon,

I don't generally like it when people send questions with specialized jargon, such as 'demand equation', which is strictly a business term.  My suggestion:  Try to eliminate the jargon by stating things in strictly mathematical terms -- you may find that your difficulty vanishes.

In this case, I am going to ignore the jargon and just assume that:

1. You have a linear equation in D and p.
2. Two ordered pairs satisfying the equation are  (D=10,p=150) and (D=8,200) -- eliminating the thousands.

In that case, we first find the slope:
    8 - 10
m = ---------
   200 - 150

    -2     -1
m = ---- = ----
    50     25

then we use that, along with either point, in the point-slope form of a straight line:

y - y0 = m(x - x0), or in this case:

D - D0 = m(p - p0), and we can take

D0 = 8,  p0 = 200,  and we have:

D - 8 = -1/25(p - 200)

A little simplifying:

D - 8 = -p/25 + 8

D = -p/25 + 16

and that should do it.