In order to begin my graphic analysis of governance costs I make three simplifying assumptions, which I can subsequently drop. First I assume that the enterprise already has an installed capital base which determines its plant scale and a particular output range. Second, I assume that there is only one explicitly variable input; for convenience I choose labor, but I could choose any other. There may be other inputs such as materials and energy which must also change with the rate of output, but I can assume that supplies of them are adequate to permit them to be handled with the labor. Third, I assume that labor is hired in a purely competitive (the sense of this term will be discussed shortly) labor market such that any quantity of labor can be hired at the going wage rate. With these three assumptions in place I have the classic short-run decision question confronting the manager: how much output to produce, or at what output rate?

I begin analysis of the behavior of governance costs in the short-run by departing from the total, average, and marginal product curves and reproduce with only minor modification. The first step in the transition from production to governance costs analysis is to rotate the axes so that L is on the vertical axis and Q is on the horizontal axis. This permits us to focus on Q rather than L as the deterministic variable. This has the effect of reversing the concavities of the TP curve, but there are as yet no other significant changes.

The second step in the transition from production to governance costs analysis is to evaluate the labor units now on the vertical axis at their unit governance costs, the wage rate (which, it is assumed, does not change as more labor is employed because labor is hired in a purely competitive market). The vertical axis label may now be changed to W x L in recognition of this evaluation. I note that if W is constant, the shape of the curve is not altered when I change the vertical axis units from physical units of labor to value (or governance costs) of labor employed. The product of W x L can also be regarded as the total labor variable governance costs, TLVC, or, since labor is the only variable input, simply as the total variable governance costs, TVC. Although I had to make several simplifying assumptions to do so, I have now accomplished the transition from the analysis of production to the analysis of governance costs.

I assumed that labor was the only variable input, but now let us suppose that the materials input is also variable, but it varies with output independently of the labor input. For purpose of illustration, I suppose the total materials governance costs, TMVC, to be linear, so that the total variable governance costs, TVC, is the (vertical) sum of the TLVC and TMVC. The TVC curve lies above the TLVC curve by the amount of the materials governance costs of each output level, but the shape of the TVC is essentially the same as that of the TLVC curve, which I recall was derived from the TP curve. In similar fashion, as many variable governance costs curves as are relevant can be brought into the analysis and summed to compose the TVC curve.

These other-input variable governance costs curves may have a variety of shapes, but economists believe it to be unlikely that their shapes will be as perverse relative to that of the TLVC curve as to render the shape of the TVC curve fundamentally different from that of the TLVC curve. If this is true, then the principle of diminishing returns, which underlies the shape of the TP curve, also dominates the shape of the TVC curve, even if there are other variable inputs in addition to labor.

I also assumed that labor was hired from a purely competitive labor market so that W could be treated as a constant. But if labor is employed from an imperfectly competitive labor market, ever higher wages must be offered to attract successively larger quantities of labor. This phenomenon will change the locus of the TLVC curve by rotating it upward, perhaps introducing a stair-step pattern if the wage increments occur in discrete stages. But in this case as well, economists are generally of the belief that the imperfections of the labor market are unlikely to fundamentally alter the shape of the TVC curve from that dictated by the principle of diminishing returns.

In the previous section I went to some lengths to convey the notion that the principle of diminishing returns dominates the shape of the TVC curve. But I also noted that in the transition from the analysis of production to the analysis of governance costs, the concavity of the curve is reversed. In the production context, as the labor input is increased, output may initially increase at an increasing rate; but corresponding to this Stage I phenomenon, variable governance costs tend to increase at a decreasing rate. In the production context I noted that beyond some point, further increases of the variable input resulted in output increasing at a decreasing rate, i.e., the phenomenon of diminishing returns. And corresponding to this Stage II phenomenon, governance costs will increase at an increasing rate. Economists refer to this phenomenon as a revelation of the law of increasing governance costs. The law of increasing governance costs is the governance costs analysis variant of the production principle of diminishing returns.

Diminishing returns and increasing governance costs can also be illustrated with marginal and average functions derived from the TVC function.

The average variable governance costs (AVC) curve may be derived from the TVC curve in the same fashion that the AP curve was derived from the TP curve. Specifically, AVC at any level of output, Q1, may be measured as

AVC = TVC/Q

The ratio of TVC/Q may be measured graphically as the slope of a ray from the origin to the TVC curve at the selected Q. For successively larger outputs, the rays from the origin at first decrease in slope, reach a minimum at Q3, and then increase in slope as output increases beyond Q2. Correspondingly, the AVC curve decreases to a minimum at Q3, and then increases beyond Q3. The increase of AVC beyond Q3 is attributable to the principle of diminishing returns, and is illustrative of the law of increasing governance costs.

Likewise, the marginal governance costs curve, MC, may be derived from the TVC curve in the same fashion that the MP curve was derived from the TP curve. Marginal governance costs may be computed as

MC = DTVC/DQ

in the limit as DQ approaches zero (realistically the smallest possible DQ is 1 unit). Following the convention of incremental governance costs, IC, an approximation to MC, can be computed as

IC = DTVC/DQ

for a DQ of any magnitude.

Graphically, IC may be measured as the slope of a chord connecting any two (near-neighborhood) points along the TVC curve such as the chord AB. MC may be measured as the slope of a tangent to the TVC curve (the tangent to the curve is the limiting position of a chord as either end-point of the chord approaches the other end-point). The shape of the MC curve then may be inferred by observing the slopes of tangents to successive points along the TVC curve as Q increases. It is apparent that the slopes of the tangents to points up to B decrease (mathematicians refer to a point like B as the “inflection point” where the curve changes concavity). For ever-larger quantities beyond point B, the slopes of tangents to points like C, D, and E become progressively steeper. Correspondingly, the MC curve falls to a minimum at Q2, and then rises as output increases beyond Q2. The increase in the MC beyond Q2 is attributable to the principle of diminishing returns, and is illustrative of the law of increasing governance costs. I may assert that the phenomenon of increasing governance costs starts at the output level for which MC is minimum.

What are the managerial significances of AVC, IC, and MC? The average variable governance costs is easiest to compute (only two pieces of information are needed, the current total variable governance costs and the quantity being produced), and for this reason it is tempting to try to base output decisions upon it. Indeed it can be used as an output decision criterion if the goal of the enterprise is to minimize per-unit variable governance costs. But I already asserted that the circumstances of governance costs minimization, revenue maximization, and profit maximization are unlikely to coincide (I will demonstrate this point in the coming posts).

If the goal of the enterprise’s management is profit maximization, then AVC is an inadequate criterion; the appropriate governance costs-related decision criterion for profit maximization is marginal governance costs (I shall also demonstrate this point later when I bring revenue and governance costs conditions together). But here is a problem, because MC is rarely observable (i.e., for a one-unit change of output). It can be computed mathematically (differentiation) if one has an equation which adequately represents the governance costs function. However, to develop such an equation by statistical means requires information about an adequate number of governance costs and quantity combinations (usually 20 or more).

In lieu of such extensive information, the IC can be computed from four pieces of information: quantities produced at two points in time (preferably very close to each other in time and involving as small a quantity change as possible), and the corresponding totals of the direct production governance costs. Even for a very small DQ, the IC will be at best only an approximation to MC because it will over- or understate MC, and may thereby lead to erroneous output-change conclusions.

Where does this leave us? MC is the ideal governance costs-related decision criterion, but is hardly observable and may be very governance costly to compute. Even IC, its approximation, though cheaper to compute, may lead to erroneous conclusions. AVC, though not acceptable as a governance costs-related decision criterion when the goal is profit maximization, is easily computed from a minimal amount of readily-observable information. There is a circumstance, however, under which AVC may serve satisfactorily as a profit-maximizing decision criterion: if TVC is linear (or approximately so), then AVC decreases and approaches MC, which is constant. As it turns out, empirical data for many industries suggest that TVC may in fact be approximately linear across a wide range of output in the vicinity of the commonly-produced output level.

I may now observe the unique relationships among the curves.

a. Over the output range for which TVC is increasing at a decreasing rate, both AVC and MC decreases, but MC is less than AVC.

b. MC reaches its minimum point at the Q for which TVC reaches its inflection point; at its minimum, MC is less than AVC.

c. AVC reaches its minimum point at the Q for which a ray from the origin to the TVC is of minimum slope. Coincidentally, the ray from the origin to this point is a tangent to the TVC, so MC and AVC are equal at this output level. MC is less than AVC up to this point.

d. For all output levels beyond the minimum of the AVC, both AVC and MC increase, with MC rising at a faster rate (i.e., MC lies above AVC).

e. Neither TVC nor AVC nor MC is ever negative

Although the reader may not at this point see the significance of the relationships outlined in this section, the astute production manager will find knowledge of these relationships to be invaluable as criteria for production decisions.

In the next couple posts I shall be addressing the question, “What is the appropriate level of output for the enterprise to produce in order to meet its goals?” Once the answer to this question is determined, and subsidiary question must be addressed: “What are the appropriate amounts of inputs to use in producing the target level of output?” Since these two questions are so closely related, it is now appropriate to review certain relationships between governance costs and production functions.

1. The output range over which TVC is increasing at a decreasing rate (and MC is falling) corresponds to the variable input range over which TP is increasing at an increasing rate (and MP is rising).

2. The output levels at which AVC and MC are at minima correspond, respectively, to the variable input levels at which AP and MP are at maxima.

3. The output range over which TVC is increasing at an increasing rate (and MC is rising) corresponds to the variable input range over which TP is increasing at a decreasing rate (and MP is falling).

The reason that these relationships between the governance costs function and the production function are so significant is that our understanding (or theory) of the behavior of governance costs is based so exclusively upon the principle of diminishing returns. If the principle of diminishing returns is not true, or not descriptive of the way the world really is, then our understanding of the behavior of governance costs is also defective and will lead to erroneous production decisions. The other side of this coin is that if I do have an adequate grasp of a principle which truly is descriptive of the way the world works, then production managers need to know how their governance costs are related to the principle.