# Break-even Analysis Form 1
The total contribution margin is simply (P ! AVC)Q = TR ! TVC.
Q
TFC
P AVC
BE
=
Break-even Analysis
An enterprise, whether or not a profit maximizer, often finds it useful to know what price (or
output level) must be for total revenue just equal total cost. This can be done with a break-
even analysis. Strictly speaking, this analysis is to determine the minimum level of output
that allows the firm to break even, but it could be used for some other tasks.
In this Appendix, we introduce:
- The algebra of break-even analysis
- Break-even diagram
- Operating leverage
I. THE ALGEBRA OF BREAK-EVEN ANALYSIS
Let Q
BE
denote the break-even output level. By definition
TR (at Q
BE
) = TC (at Q
BE
)
or TR (at Q
BE
) = TFC + TVC (at Q
BE
) (1)
The break-even condition (1) holds true for any cost and demand functions.
Hence, in general, when costs and demand are complex, the analysis of this
condition might not be any simpler than the analysis of profit maximization. Yet,
what is widely known in business as break-even analysis is indeed much easier than
profit analysis, although it also starts with the above identity, because it makes a very
important assumption: that price and average variable cost do not change with output level.
Thus, if we assume that price and AVC are constant, (1) can be rewritten as follows
P.Q
BE
= TFC + AVC.Q
BE
which yields:
(2)
K
The difference “P
!
AVC” is often called the
average contribution margin
1
(ACM) because it represents the portion of selling price that "contributes" to paying
the fixed costs.
! Formula (2) can be generalized to deal with the situation where the firm has determined in
target profit
. The output quantity Q* that will yield this profit is implicitly given
Page 1/16