Most of the data for cost analysis will have been compiled by formal accounting systems which may have been designed for tax-reporting rather managerial decision-making purposes. One can of course employ the straight accounting data as reported to estimate what I shall call an “accounting cost” function, but the cost decision maker is urged to recognize and remember when using it for simulation purposes that it over-states some costs and understates other costs. Also, any cost function estimated from historic data will be valid for simulation of future circumstances only if historic patterns persist into the future.
The analyst will have to make adjustments to the accounting cost data to estimate a relevant-cost function. No hard data exist at all about opportunity costs (what the firm is not presently doing but could be doing); only the managerial decision maker can estimate the opportunity costs based upon awareness and perceptions of the foregone alternatives. Needless to say, different managers will have different perceptions and assessments of the available opportunities, and some managers will be more successful than others because of their successful recognition of the pertinent opportunities. The well-designed cost accounting system should recognize temporal cost-output mismatching, but if it does not then some effort must be exerted to allocate certain costs (e.g., repair and maintenance expenses) to the proper time periods.
If the objective is to estimate a short-run cost function, care must be taken to exclude all overhead costs. This may be especially difficult if the cost-accounting system obscures the distinction between some direct and some overhead costs. For example, maintenance and repair expenses often are lumped together (they are typically performed by the same in-house crews or outside contractors), but regular maintenance expenses (presumably at approximately the same expense levels period after period) should be treated as fixed costs. However, repair expenses, to the extent that they are not regular occurrences, should be treated as variable costs. Then there is the problem of matching the repair expense to the appropriate time period since the circumstances culminating in the need for the repair may have spanned several production periods.
Depreciation is an especially knotty problem for the determination of relevant costs. Should it be treated as a variable cost to be included in the estimation of a short-run cost relationship? I have already made reference to the likely divergence between the accounting allowance for decrease in the value of the capital stock and the real phenomenon of capital consumption. Real capital consumption surely does vary with the rate of production, which may be quite uneven from period to period. But since it is not possible to know with certainty in advance what will be the actual physical life of the plant or equipment, it may not be possible to meaningfully impute a cost value to the amount of capital consumption to be allocated as a direct cost to a particular production period.
The accountant handles this problem by selecting a depreciable life (on the basis of past experience, as permitted by the tax authority’s rules, or simply arbitrarily), and designing an allowance schedule which may be straight-line, accelerated, or retarded (again, as permitted by the tax authority’s rules). If a straight-line allocation method (the same proportion of the capital value charged as cost during each period) is used, then a case can be made for excluding depreciation from the list of costs relevant to the short run, because even though it represents a direct cost it does not vary with output. But even if an accelerated or retarded depreciation schedule is used, the proportions of the capital value to be allowed as costs change smoothly, predictably, and monotonically (a mathematical term meaning in one-direction only and hence are unlikely to correspond to real variations in output and the capital consumed in producing it. Given these problems, then, a case can be made for excluding depreciation from the estimation of a short-run cost function, but including repair expenses (properly matched to time periods) as mirroring the real consumption of capital, i.e., the expenditure necessary to restore the real decrease in productive capacity caused by use of the capital.
Another short-run cost estimation problem occurs in time series data if there has been non-trivial variation in the prices of the variable inputs. Short-run costs certainly vary with the prices of inputs, so the analyst must make a methodological choice: either choose to “deflate” each of the TVC components (i.e., TLVC, TMVC, etc.) by a price index appropriate to that cost, or choose to include as other independent variables (i.e., the X1, X2,…, Xn in equation C6-1) the prices of the inputs which are thought to be varying significantly. The regression analysis will reveal which in fact are statistically significant determinants of TVC.
Theoretically, the physical units produced (or some multiple) should be used for Q in the regression model. A problem arises if the firm produces a multiplicity of products, some of which are jointly produced. In this case, Q may have to be the “product mix” normally resulting from the production process. If the market values of the jointly-produced products differ significantly, it may be necessary to use a composite index of the jointly-produced outputs where the weights are the current market prices of the products. Finally, if the objective is to estimate a firm-wide cost curve where the firm is producing multiple products, it may be desirable to use data for value of output evaluated at current market prices. If time series data are employed, both the output and input value data should be deflated by appropriate price indexes.
The alternative heading for this section might be “Getting Enough Useable Data.” In sourcing his data, the analyst is first confronted with a choice between time-series and cross-sectional data. A short-run cost function assumes given technology, managerial capacity, and entrepreneurial abilities. Much recommends the cross-sectional choice for short-run cost estimation since the data are taken across firms or plants, but at a point in time. There is thus no problem of dealing with changes of plant size or of technology, managerial capacity, or entrepreneurial ability. It is perhaps easier to identify the use of the same technology than to find comparable amounts of managerial capacity and entrepreneurial ability in different firms. In this regard, the analyst will simply have to exercise judgment. Alas, there remains a critical problem with cross-sectional data for short-run cost estimation that is difficult to surmount for most firms: data are required from different firms or plants, but competitors often are reluctant to share such sensitive information.
The use of time series data for the firm’s own plant(s) obviates the need to solicit data from competitors. Here the analyst must take care to choose a time span which is not so long that there have occurred changes in technology, management, or entrepreneurship; else data will be for points on different cost functions. This may be a period covering several years, but may be as short as a few months. Then the analyst must divide the period into an adequate number of data collection intervals to yield enough observations for estimation of a statistically-significant cost function. Usually twenty to thirty observations are adequate for this purpose. The duration of the data-collection period may then dictate daily, weekly, or monthly observation intervals. A new short-run cost function must be estimated every time that technology, management, or entrepreneurial ability changes.
In the estimation of a long-run cost function, all costs should be included. It may not be feasible, however, to use a time-series approach since the intervals should be long enough to permit variation in plant size (but still no changes in management or entrepreneurship). In order to get enough long-interval observations, the duration of data collection may have to span several years. Alterations in management or entrepreneurship during the data-collection period will result in points on different long-run cost functions. These conditions may be heroic at best. The use of cross-sectional data, if they can be obtained from other firms and plants, may accommodate requisite variations in plant size, but care must be taken in selection of subjects to avoid different technologies, managerial capacities, or entrepreneurial abilities. Again, these may be heroic conditions.
Whether the analyst is attempting to estimate short- or long-run cost functions, the necessary premise is that each plant is being operated efficiently, with no significant waste of any resources, i.e., at an appropriate point on its cost curve. If at any time or in any plant included in the sample there are wasteful conditions, the observed data will be for a points above the locus of the firm’s true cost curve. If this circumstance occurs in more than a few instances, the estimated cost function will lie above its theoretically true (efficient) location, and will yield erroneous conclusions in simulation exercises.
Whether the management of the firm develops cost-function simulation model or not, the cost-related job involves many facets:
(1) In the long run, selecting the most efficient technology for producing the enterprises selected products;
(2) With that technology, selecting the scale of plant with an output range which is most compatible with current and expected future levels of demand for the products;
(3) Given the right scale of plant, selecting the appropriate output level to meet the enterprise’s goals (profit maximization, cost minimization, optimization, etc.);
(4) For the target level of output, selecting the appropriate internal allocation of the enterprise’s resources, i.e., the most efficient combination of inputs, given the available input prices;
(5) Operating efficiently and without waste, i.e., to operate at points on the enterprise’s production function surface (not below it) and on its respective cost curve (not above it).
Furthermore, economists can argue that if the goal of the enterprise is to maximize profits, and if it does so operate to maximize profits without monopolizing its markets or exploiting its resources, it will also meet a desirable social objective of efficiency in the allocation of resources among industries, among firms within the industries, and between products. Assuming that monopolization and exploitation are averted (admittedly a serious problem), this happy circumstance can be expected to emerge even if social well-being and social economic efficiency are not explicitly managerial goals of the enterprise.