Unformatted text preview: mercial Price $800 $800 $800 Total Revenue $190,584 $181,584 $212,285 Total Expenses $231,513 $229,925 $233,723 Net Income (Loss) $(41,472) $(40,341) $(21,438) If this trend continues, PDS will eventually breakeven (provided of course nothing else changes). This begs the question:
what is the breakeven number of commercial hours? For PDS this is a cumbersome calculation because it has two types
of customers: commercial and intercompany. Before doing breakeven calculations for two “divisions” let’s do it for one
“division” (the standard approach shown in most accounting and finance courses).
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ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Let us solve this problem by first assuming PDS only serves commercial customers (not commercial and intercompany
customers), has a linear cost function, and has ample capacity. In this case profits are: By definition: Substitute this back in: ( ) ) is known as the contribution margin (what an additional unit of output contributes to profits). At
The term (
the breakeven output profits are zero so that:
(
If the cost function is linear then ) is a constant so that:
( Notice that if
then
and if (
the
number canbe negative (if ) ) then
. It’s conceivable that in the formula above
) To accommodate this possibility:
( ) This formula assumes that the company has ample capacity. With a finite capacity, the breakeven output will be (make
sure you understand this):
( ( ) ) _____________________________________________________________________________________ _____________
Example: Suppose a company has the following cost function (notice it’s linear, so that the company has constant
returns): Observe that
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ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Currently, . What is the breakeven quantity? From above: Now suppose the cost function becomes: Fixed cost has increased by $1,000. Now, the breakeven quantity is: Since price and were constant, the company has to sell more units to cover the higher fixed costs. __________________________________________________________________________________________________
Let us now compute the PDS’s commercial breakeven quantity: Breakeven Output Requires:
() () With constant returns we can solve for breakeven output analytically: By definition:
⏟ ⏟
{ } To accommodate the possibility that this number can be negative and that there may be a finite capacity, the formula
becomes:
( { ( ) } ) 35
ECO 204 Chapter 13: The Short Run Cost Minimization Problem (this version 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. From the case recall that intercompany revenue is capped at $82,000/month and that intercompany data services price
is
/hour, intercompany hours are capped at an average of:
hours per month
Comme...
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 Fall '09
 AJAZHUSSAIN
 Economics, Microeconomics, Economics of production, Sayed Ajaz Hussain

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