Allocating Fixed Costs
A firm has a product line .
The total cost of production is
If we equate MR and MC for each product, revenue and variable costs are as given in columns 4 and 5 of the following table.
(See below for solution.)
product | Revenue | Variable | Cost | Allocated Fixed cost | Accounting Profit | ||
1 | 6 | 14 | 84 | 48 | 0.4 | 68 | -32 |
2 | 12 | 18 | 216 | 72 | 0.6 | 102 | 42 |
Total | 300 | 120 | 1.0 | 170 | 10 |
Table 1: Allocating Fixed Costs
One way an accountant might allocate fixed costs is to use the variable cost share. Since the total variable cost is 120 and the variable cost for product 1 is 48, the cost share is 48/120 = 0.4.
Based on this rule, product 1 should be eliminated from the product line. Table 1 becomes
product | Revenue | Variable | Cost | Allocated Fixed cost | Accounting Profit | ||
2 | 12 | 18 | 216 | 72 | 1.0 | 170 | -26 |
Total | 216 | 72 | 1.0 | 170 | -26 |
Table : </span></p> <p class="MsoNormal"><span style="font-size:14.0pt">Since the profit is zero the form shuts down.</span></p> <p class="MsoNormal"><span style="font-size:14.0pt"> </span></p> <p class="MsoNormal"><span style="font-size:14.0pt">An alternative Accounting Rule is to allocate costs according to the revenue share.</span></p> <p class="MsoNormal"><span style="font-size:14.0pt"> </span></p> <p class="MsoNormal"><span style="font-size:14.0pt"> </span></p> <table border="1" cellspacing="0" cellpadding="0" style="border-collapse:collapse;border:none"> <tr> <td width="71" valign="top" style="width:53.6pt;border:solid windowtext .5pt;padding:0pt 5.4pt 0pt 5.4pt"> <p class="MsoNormal"><span style="font-size:14.0pt">product</span></p> </td> <td width="33" valign="top" style="width:24.8pt;border:solid windowtext .5pt;border-left:none;padding:0pt 5.4pt 0pt 5.4pt"> <p class="MsoNormal"><span style="font-size:14.0pt"><script> MPSetEqnAttrs('eq0011','',3,[[9,11,4,-1,-1],[13,15,5,-1,-1],[14,19,7,-1,-1],[14,17,7,-1,-1],[19,22,8,-1,-1],[25,28,11,-2,-2],[40,47,17,-3,-3]]); MPEquation();
Revenue
Variable
Cost
Revenue
share
Allocated
Fixed cost
Accounting
Profit
1
6
14
84
48
0.28
47.60
-11.60
2
12
18
216
72
0.72
122.40
21.60
Total
300
120
1.0
170
10
Table 2: Allocating Fixed Costs under alternative accounting rule
Thus under this rule product 1 is again unprofitable and is eliminated.
What should the firm do?
How should it do its accounting?
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Solving for profit maximizing quantities (ignoring the fixed cost.)
&nbsp; </span></p> <p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:14.0pt">&nbsp;</span></p> <p class="MsoNormal"><span style="font-size:14.0pt">Then to maximize the profit from product 1 <script> MPSetEqnAttrs('eq0015','',3,[[39,18,4,-1,-1],[53,24,5,-1,-1],[65,30,7,-1,-1],[59,27,7,-1,-1],[78,35,8,-1,-1],[99,44,11,-2,-2],[165,74,17,-3,-3]]); MPEquation();.</span></p> <p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:14.0pt"> </span></p> <p class="MsoNormal"><span style="font-size:14.0pt">Product 2 is analyzed in identical fashion.<br> <br> </span></p> <p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:14.0pt"><script> MPSetEqnAttrs('eq0016','',3,[[357,18,4,-1,-1],[477,24,5,-1,-1],[598,29,7,-1,-1],[538,27,7,-1,-1],[716,34,8,-1,-1],[897,43,11,-2,-2],[1494,73,17,-3,-3]]); MPEquation();
&nbsp; </span></p> <p class="MsoNormal" style="text-indent:36.0pt"><span style="font-size:14.0pt">&nbsp;</span></p> <p class="MsoNormal"><span style="font-size:14.0pt">Then to maximize the profit from product 2,&nbsp; <script> MPSetEqnAttrs('eq0018','',3,[[47,18,4,-1,-1],[65,24,5,-1,-1],[79,30,7,-1,-1],[72,27,7,-1,-1],[96,35,8,-1,-1],[120,44,11,-2,-2],[201,74,17,-3,-3]]); MPEquation();.</span></p> <p class="MsoNormal"><span style="font-size:14.0pt"> </span></p> </div> </body> </html>