Solution
The average profit is
Vx
X
4x - Vi
AP(x)
=4
Vx
thousand dollars per hundred units. To find what happens at a very low level of pro-
duction, we examine the limit of AP(x) as x +0:
4x - Vx
1
4 - 1/Vx becomes negative and
lim
= lim 4 -
grows large in absolute value
x³0 Vx
lim AP(x)
r0
x=0
x
We interpret this limit as saying that as fewer and fewer units are produced, the
average profit derived from producing each unit is actually a huge loss. This makes
sense because when only a few units are produced, fixed start-up costs dominate any
revenue that may be derived from sales.