Fixed, VariabIe, and Total
Costs per Unit

The preceding data don’t show costs per set produced, and you probably think of business output in terms of cost and selling price per unit. You may already have divided the total-cost figures by the number of stereo sets produced to see what the cost per set is at different levels of output. If you haven’t, it’s a sensible thing to do. The result is shown in Table 22-2. These are, of course, just hypothetical figures. But their general character is important, because in some ways they are typi- cal of all such cost data.

Fixed cost per unit will always be a steadily decreasing series, because the constant total-fixed- cost figure (here $1,000) is divided by a steadily rising volume of output. This is what is commonly known as “spreading the overhead.” The drop in fixed cost per unit is very rapid at first, but as volume grows the additional cost reduction per unit steadily decreases in importance.

Variable cost per unit will generally fall at the outset, then flatten out somewhat, and then rise again as plant “capacity” is approached. To produce one set, the company has to have labor and materials of all the types needed for the set.

On the labor side, it will clearly be inefficient to try to call each type of skilled labor in just long enough to work on one set. If we try to use two or three jacks-of-all-trades, we get less efficient work than by dividing the work up among experts on the various parts of the job. Similarly, it may be cheaper to buy materials in larger quantities than to buy just enough to produce one set per month. It’s not efficient to produce only one or two sets a month.

At the other extreme, once the “capacity” for which the plant was planned has been reached, costs are likely to shoot up rapidly if we try to produce still more sets per month. “Capacity” is seldom an absolute limit in a plant. For example, steel plants may operate above 100 per cent of capacity; rated capacity allows for an average amount of shut-down time for maintenance and repairs, which can be postponed temporarily. But expansion of output beyond plant “capacity” of- ten means expensive overtime work, hiring of lower-skilled workers, more spoilage under pres- sure of speed-up, and a variety of other such factors.

Thus, without going into details at the mo- ment, it seems reasonable that with any given plant (which we have assumed) variable costs per —~ unit will rise rapidly at some point beyond “ca- pacity” output. Just when this point is reached depends, of course, on the individual firm. In many industries, variable costs per unit are ap- parently flat over wide ranges of output. In others, where small-scale operations are advantageous, in- crease in output beyond low levels may lead quickly to rising unit costs.

Total cost per unit is simply the sum of fixed cost per unit and variable cost per unit. Or it can be obtained by dividing total cost by the number of units produced. The decreasing fixed cost per unit will always pull down on total unit cost as output rises. At first, as long as both fixed and variable costs per unit are declining, clearly the total cost per unit is declining. But at some point total unit costs will begin to rise, often after a long flat area in which the fixed cost per unit declines slightly and the variable cost per unit is substan- tially constant or slightly rising. The rise in total unit cost will begin when variable cost per unit turns up more than enough to offset the down- ward pull of declining fixed unit costs. This point is at the sixth unit in our hi-fl plant. Total unit cost is relatively stable over the output range of three to six units, with the minimum cost per unit at an output of five sets per month.

This simple example should warn you against one common fallacy—the idea that each firm has a cost of production for its product. In every firm, cost of production per unit varies with output. This is certain at the extremes of very low and above-capacity output. It often also occurs over the range of normal variation in operations.

A good many firms now use what they call “standard costs” in pricing their products and in keeping control over their production processes. A “standard cost” for our hi-fl set would be an esti- mate by our accountant and production man of how much it should cost to produce one set at a normal, or typical, rate of output. If we think of 4 sets monthly as about normal operation, our standard-cost figure would be $1,250 per set.

Such standard-cost estimates play a useful role in modem industry. Many firms use them as a basis for setting prices, and we will meet them again in the chapters ahead. It is important, how- ever, to remember that “standard cost” is only an estimate of unit cost at some selected level of out- put, not necessarily the minimum unit-cost level.

UNIT-COST CURVES

All these per unit cost data can readily be plotted on graphs as cost curves. Figure 22-2 shows the per unit cost data for our hi-fl firm. The shape of the curves corresponds, of course, to the data. Fixed cost per unit falls steadily as the constant total cost is spread over more and more units. Variable cost per unit and total cost per unit are both U-shaped, for the reasons suggested above. In most firms, the TUC (total-unit-cost) curve is probably flatter than in this hypothetical case. That is, there is a wider range of output over which total cost per unit is substantially constant, between the low-output inefficiencies shown at the left of the graph and the above-capacity inef- ficiencies at the right. (For a large, real-world plant producing many units, the cost curves would be smooth and continuous, without the corners shown in the curves for our very small firm.)

FIG. 22-2 Unit-cost curves are derived by dividing the
corresponding total-cost curves by total output. Here fIxed
unit cost slopes downward continuously os the constant
total fixed cost is spread over more units of output. Other
curves are U-shaped.

Be sure you know just what the graph means. For example, at an output of five sets next month, the fixed cost per set will be $200 and the variable cost per unit $1,000, for a total of $1,200. This happens to be the lowest point on the total-unit- cost curve. It is called the “least-cost combina- tion.” It is the lowest cost at which these hi-fl sets can be made, given the existing plant and the firm’s other commitments for the month ahead.