As we saw in the single-product case, the firm should continue producing
an item only if R VC or, equivalently, P AVC. Exactly the same principle
applies to the multiproduct case. Furthermore, in the long run the firm should
continue in business only if the total profit in Equation 6.6 is nonnegative; oth-
erwise, it should shut down. The firm’s output rule for multiple goods can be
stated in two parts:- Each good should be produced if, and only if, it makes a positive
contribution to the firm’s fixed costs: Ri VCior, equivalently,
Pi AVCi. - In the long run, the firm should continue operations if, and only if, it
makes positive economic profits.
MULTIPLE PRODUCTS: A NUMERICAL EXAMPLE Suppose a firm’s total fixed
cost is $2.4 million per year. For the first good, P 1 $10, AVC 1 $9, and
Q 1 1.2 million; in turn, P 2 $6.50, AVC 2 $4, and Q 2 .6 million. Total
profit is 1.2 1.5 2.4 $.3 million per year. Each product makes a positive
contribution, and total contribution exceeds total fixed cost. Thus, the firm
should stay in business. What if the second good’s price is $5.50? In the short
run, both goods continue to contribute to fixed costs and, therefore, should be
produced. In the long run, total contribution ($2.1 million) falls short of total
fixed cost, so the firm should shut down. Finally, if the second good’s price is
$3.50, then P 2 AVC 2. The firm should halt production of the second good
immediately and cease operations altogether in the long run.
Sizing up relevant costs for production decisions and measuring costs for
accounting purposes are sometimes in conflict. For instance, almost all
accounting systems allocate fixed costs across the firm’s multiple products.
Typically, these allocations are in proportion to the products’ volumes. If a
product accounts for 20 percent of a firm’s output (whether by units, labor
costs, or machine-hours), it is assigned 20 percent of these costs. These allo-
cated costs are added to the product’s direct unit costs to determine its total
cost of production. According to this cost-accounting system, the product is
profitable if, and only if, its total revenues exceed its total costs.
Although cost accounting systems are useful in many respects (especially
for tax purposes), they can be misleading when it comes to economic deci-
sions. For decision-making purposes, costs that are truly fixed (i.e., don’t
vary) with respect to products’ volumes should not be allocated at all. This
is in keeping with the earlier proposition that fixed costs do not matter.
According to Equation 6.6, contribution is the only relevant measure of a
good’s performance. Production should continue if contribution is positive
and should cease if it is negative. Note that the good’s accounting profit
(by including a fixed-cost allocation) understates its contribution.
Consequently, when it comes to product decisions, accounting profit can be
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