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I have a math question.Can you please help?

Posted August 26th, 2007 by Anonymous
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Suppose a consumer will demand 40 units of a product when the price is $12.75 and 25 units when the price is $18.75 each.What is the demand equation and what is the price per unit when 37 units are demanded?

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solution

On August 26th, 2007 Isoscel says:

p = price
q = quantity

We suppose we have a linear demand equation p = aq + b

$ 12.75 = a40 + b $ (Eq1)
$ 18.75 = a25 + b $ (Eq2)

we subtract the second equation from the first (Eq1 - Eq2 ):
$ 12.75 - 18.75 = a(40 - 25) + b-b $
$ -6 = a15 $
$ a = -\frac{6}{15} = - \frac{2}{5} = -0.4 $

We replace this into the first equation (Eq1):
$ 12.75 = -\frac{2}{5}40 + b $
$ b = 12.75 + \frac{2\cdot40}{5} = 12.75 + 16 = 28.75 $

So a = -0.4 and b = 28.75

So the demand equation
$ p = aq + b $
is now:
$ p = -0.4q + 28.75 $

The price per unit when 37 units are demanded is:
$ P = -0.4\cdot37 + 28.75 = -14.8 + 28.75 = 13.95 $

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