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Cost

Cost

BIBLIOGRAPHY

In economics, the cost of an event is the highest-valued opportunity necessarily forsaken. The usefulness of the concept of cost is a logical implication of choice among available options. Only if no alternatives were possible or if amounts of all resources were available beyond everyone’s desires, so that all goods were free, would the concepts of cost and of choice be irrelevant. If choices are made on anything other than a random, purposeless basis, a criterion of choice is implied. Whatever the criterion, the chosen option will involve a loss of the highest-valued forsaken option. This implies that only if one chooses actions so as to maximize the value realized will cost be covered.

Failure to appreciate the purpose of the concept of cost can lead to confusing the concept of cost with the undesirable attributes of some event. For example, when one builds a swimming pool, the toil and trouble of digging it and the nuisance of noisy, disobedient neighborhood children and uninvited guests who use it are undesirable attributes of the pool. They are not the costs of creating and having a pool. This distinction between (a) undesirable attributes inherent in some event and (b) the highest-valued forsaken option necessary to realize that event is fundamental, for only the latter is cost as the term is used in economics.

We can illustrate. The construction and possession of the pool involve an amalgam of undesirable and desirable attributes. But if, in some sense, the desirable exceed the undesirable, it does not follow that one would choose to have the pool. One might choose something else instead, say having an extra car, and that too would involve desirable and undesirable attributes. The decision maker must choose among events that are amalgams of “goods and bads.” He cannot choose all events whose desirable features more than offset their undesirable ones, given the limited resources at his disposal. A comparison among all the available options (each consisting of an amalgam of good and bad) yields for each option a rank-indicating measure of value. The cost of one amalgam is the best of the forsaken amalgams. It is not necessary that for each event the good and bad attributes be separated and that there be assigned a measure of the undesirable attributes and also a measure of the desirable. Such a procedure would indicate only that many events are desirable on net, and a criterion of choice among these would still be needed.

We can illustrate with the person deciding whether or not to have a swimming pool. He determines that the “good” consequences of a pool are worth what we shall call “100 units,” while the “bad” are equivalent to the loss of “70 units.” The best alternative to having a pool is, let us say, to take action “A,” with “good” attributes valued at 50 and “bads” valued at a loss of 10. The pool has a net value of 30, while event A is worth 40. The cost of the pool is 40 (not 70), while the cost of A is 30 (not 10). What is lost if the pool is selected is the 40 units of value otherwise available by opting for A.

The temptation to think that because events are valued by comparing the good attributes with the bad, cost must be the bad attributes is encouraged by business usage. Businessmen weigh revenues (as good consequences) against expenses or costs. Considering these costs as the bad attributes overlooks the distinction between valuation and costing. The value of a given event is obtained by weighing its good and bad consequences against each other—if one wants to think in terms of good and bad rather than less or more desirable— but the cost of that event is still not revealed. The highest-valued forsaken option must still be ascertained in order to determine the cost. Even in the businessman’s calculation, what his cost really measures, as shown below, is not the bad consequences of an action but the highest-valued forsaken opportunity.

It is sometimes fallaciously thought that if building a pool involved even more pain or other undesirable consequences, its costs surely must be higher. But the costs of the pool are not higher unless the best alternative is affected. More pain in building a pool may or may not affect my alternative opportunities. If an extra hour of work is involved, then my alternatives are changed because I lose another hour of other desirable uses. The definition of cost does not deny that the pain and time and trouble of producing some event are influential in the measure of cost. But it does show that these aspects enter into costs only by affecting the value of the best forsaken opportunities.

This can be seen more clearly if we consider the following situation in which the alternatives are not affected. Suppose that in building the pool, the pain to be suffered during a given time was to be more intense—but not longer-lived. In this case, the increase in intensity of pain (assuming that recovery is immediate upon the cessation of the work) does not affect the alternative opportunities. These stay the same. What this more intense pain does is reduce the value of the pool, not raise its cost.

Another example of an increase in undesirable attribute that does not increase costs is one that increases that attribute uniformly for all opportunities. In this case, the feature cannot be avoided no matter what one does. A uniform reduction in the value of all options reflects the lower level of “utility” now generally available. One could even call this effect a decrease in costs—since the best-valued options are now lower valued. The costs are lower because the values are lower, for that is what cost reflects.

Clarification of the logical role of the concept of cost in order to explicate clearly the distinction between the two ideas—the value of forsaken alternatives and the so-called undesirable attributes —was begun by the Austrian school of economics in the nineteenth century and was further developed by Frank Knight (1924). [SeeEconomic thought.]

Money costs in a society. The preceding is relatively unambiguous for choices or selections of options in a one-person world. But in a society, selection among options involves not only different options for the same person but also different options available to different people. Therefore an interpersonal value measure is necessary. A society in which choices are made in accord with a single dictator’s preferences resembles the one-person world. In a pluralistic (individualist) society, an interpersonal value measure can be based on inter-personal exchange rates. Voluntary market exchanges among individuals reveal the highest values of available options and, hence, their costs in terms of values of forsaken options. These market prices, to which all people can adjust their choices, provide a common measure of the value of increments of one event relative to others.

For example, a market exchange rate of 1 Coca-Cola for 2 ounces of chocolate indicates the relative value of each. The optional event—having 1 more Coke—is compared with the option of having 2 more ounces of chocolate. In an open market— one in which all people have access to all goods— the exchange rate, or price, of Cokes must at least equal the highest-valued alternatives to 1 more Coke. If the price does not equal the highest-valued alternative, those who value a Coke at more than the market exchange price will prefer, and will be able, to enter the market and offer more for a Coke. And this will raise the exchange rate to at least the highest-valued alternative. Rather than expressing the values of alternatives to 1 Coke in terms of the amounts of chocolate, beer, or other individual goods that are as much desired as 1 Coke, convenience dictates agreement on a common measure of value. Since almost all formal contractual exchanges are conducted with the medium of money, all exchange rates typically are measured in units of money—as so many dollars or cents per Coke. The use of money prices does not mean that money is all that counts, or that people love money. It means simply that money is the medium of exchange and therefore is the convenient denominator of interpersonal exchange values of events or options.

In sum, because goods are substitutable sources of utility, and because substitution is facilitated by exchange via money, it is possible to measure the value of a forsaken option in money terms. When goods can be obtained not only by interpersonal trade but also by production, at the “cost” of other things that could have been produced, the costs incurred in production choices will be related to the market prices of interpersonal exchanges if producers have access to markets in which to offer their products.

Market prices and cost. The preceding discussion implies that cost in an exchange economy is based on market-revealed values. If some productive resources are used in ways that yield less than their highest achievable alternative, or “opportunity,” values, these uses will not cover cost. The incentive to increase one’s wealth induces shifts of resources to their higher-valued use until their cost is at least matched by the value of their currently yielded product. As the output of the service now being produced at a higher rate increases, the value of additional increments will fall until there is no further shifting of resources from other uses. By drawing resources from lower-valued to higher-valued uses, the value of a producible good or service influences the allocation of resources and so the rate of output of the good or service itself.

This adjustment or reallocation of resources among various uses is often expressed less rigorously. For example: (a) “Lower cost resources are shifted to their higher valued uses.” (b) “If costs of production are less than potential values of output, low cost resources will be shifted to increasing the output of the higher priced goods, thus indueing a lower price of that good, until ultimately no disparity exists between costs and values of output.” Both of these formulations, while explaining the shift in resource uses, are misleading in that they refer to “lower-cost” resources. The resources are not really lower-cost; rather, they are being used in lower-valued uses. It is only the lower value of their use that makes them appear to be lower-valued or lower-cost resources. Strictly speaking, the cost of the use of any resource is never less than the highest-valued opportunity for its use; it is always equal to the amount bid by the most optimistic (highest) bidders in the market for that resource.

No matter how any particular set of resources is used, the cost of their use will be the same—only the realized value of the output, or event yielded, will be affected. If resources are used in less than their most valuable ways, their cost will not be covered, and the difference will be an economic loss. This suggests the query, Is it possible for resources to yield a value in excess of their cost? The answer is “Yes,” in the sense that the current market values do not reflect the future value of the resources—which depends upon unforeseen events or actions. For example, if the use of a resource is changed so as to expose a preferred result to the market, the market value of the resource will be raised. This increase in value of the resource above the former market value is initially a profit. With the unforeseen revaluation, however, costs will be revised upward. In effect, profits are capitalized by the market into costs of subsequent use of the resources.

We may digress to note that we can now interpret the principles underlying the categories “demand” and “supply” as applied to factors affecting price, allocation, and value. Demand reflects the value of different amounts of available resources in a particular class of use, say to produce A, while supply represents the value of the resources in all other potential uses. The demand function indicates a negative relationship between the rate at which good A is made available and the value of another unit of availability of A; the supply function indicates an increasing value of all other opportunities of use as more and more of them are forsaken in order to increase the amount of resources devoted to the production of A. If another unit of A has a value greater than the highest value of other necessarily forsaken options (costs on the supply function), the output of A will increase, thereby lowering its unit value and increasing the “costs” (value in other uses only) until the two are brought to equality.

The meaning of costs in the demand for and supply of A refers to the value in the second or next best use—not in the over-all best use. As long as the value of resources in other uses is lower than in the production of good A, more resources will be shifted to A until the value of another unit of A falls to a level that is no greater than that of its component resources in the next best other use. At this point the transfer of resources stops and the rate of output of A will not increase further. But this supply schedule reflects costs only in the other uses; it does not reflect cost of resources in the sense of best opportunities for use over all opportunities, including A. The demand-and-supply classification is satisfactory for investigating factors that affect the output of particular goods relative to other goods, but it is not a satisfactory analytical classification for understanding the meaning of the cost concept in its wider range of application and function.

When are costs incurred? Forsaken alternatives to a current choice are not necessarily composed only of present events. A decision to build a pool can involve a commitment to a sacrifice of future events. In general, a sacrifice of present consumption is valued more highly than the sacrifice of an equivalent future good is valued now. The relationship between the present value of two events, identical except in their time of availability, defines a rate of interest. [SeeInterest.] A rate of interest of 10 per cent per year means that a unit of good A, which would be worth $1.00 if available now, will, if it is available only a year hence, have a value now (referring to the time of valuation, not to the time of availability) of $.909. It follows that if an event A involves the sacrifice both of an alternative good available and worth $1.00 now and of a good available in one year and worth $1.00 at that time (but only $.909 now), the present-value cost of the compound event A is $1.909—the sum of the present value of the present item ($1.00) plus the present value ($.909) of the future item. The cost of event A is therefore the present value of the implied chain of sacrificed options, whether they are realizable now or later.

From this it is tempting to try to draw distinctions such as the following: The present event A involves costs that, although incurred now, are not experienced now. That this distinction is not meaningful can be seen by carefully considering the meaning of incurring a cost. The individual incurs a cost by choosing event A in the sense that his choice makes unavoidable the loss of some otherwise available alternatives. Even if these alternatives were otherwise realizable only far in the future, the cost is incurred now if the present choice of the event A eliminates these future possibilities. The cost is incurred now in the sense that the current choice of the event has meant the irretrievable loss of certain alternatives.

Although the cost is incurred now, the consumption loss can be in the future. For example, a person who buys a car now incurs a cost, but by borrowing he can shift the reduction in consumption to the future. There is no necessity for the reduced consumption to be simultaneous with the incurring of the cost. This is especially true for an individual; borrowing from other people will permit him to transfer the consumption loss to any time he wishes within the limits of the borrowing and repayment schedules available to him.

The cost of a decision to perform some event is not always the same as the cost of the event. For example, if I decide to build a swimming pool that will cost $3,000, does my making a commitment to build a pool involve the entire cost? Not if I can change my mind tomorrow. Thus, the cost of the contracting for a swimming pool may be only $500, in that if subsequently I change my mind, I lose only $500. If, then, the cost of the current commitment to build a pool is $500, when are the remaining $2,500 of costs incurred? They are incurred as work progresses and the successive options are irretrievably lost. In sum, the cost of the decision and the completion of a swimming pool is $3,000. At any moment the whole $3,000 cost may not have been incurred, and has not been incurred to the extent that one can still avoid the loss of the subsequent options included in the $3,000 that would have been lost had the work progressed to completion. What is emphasized in this paragraph is the need to avoid ambiguity in the meaning of the events being costed—e.g., the decision is one event and the execution of the project may be a series of subsequent events. Exactly to what event the costs apply should be made unambiguous.

Examples of measures of cost. Principles underlying the measurement of cost as defined above are simple and will now be illustrated, but it must be emphasized that in actual practice the measurement is very imprecise in that it involves estimates of uncertain future events. We shall consider first the cost of purchasing (obtaining and retaining ownership of) a car, and then the cost of using the car. Its purchase price is $3,000. If we retain the car until it becomes worthless (and if we incur no other costs), the cost of ownership for the indefinite future is $3,000. Assume that we could sell the car immediately for $2,500. At the moment of purchase, then, we have incurred a cost of $500, the cost of acquiring ownership. If we retain the car, we will gradually incur the remaining $2,500 of cost; however, since we can always sell the car, the cost of ownership up to any moment is not the $2,500 but only that portion which cannot be recovered by resale. If a month later we can sell the car for $2,300, the cost of acquiring and retaining ownership for one month is $500 plus $200.

Suppose now we plan to keep the car for two years and then sell it (without using it in the meantime) for $2,000. Of course, $2,000 two years hence does not have the same value as $2,000 now. At a 10 per cent rate of interest the present value of $2,000 deferred two years is $1,652. The present-capital-value measure of the cost of owning a car for two years is equal to the purchase price minus the present value of the resale price two years hence: $3,000 – $1,652 = $1,348. The decrease in the value of the car from the $3,000 purchase price to the $2,000 resale value is called depreciation (for expository simplicity we ignore maintenance expenditures, which are assumed to be optimal). If the reduction were greater than expected, the excess would be called obsolescence.

Table 1
 Beginning of year 1Beginning of year 2End of year 2
Purchase price$3,000$ —$ —
Taxes and insurance150150
Resale value(2,500)(2,200)–2,000
 ——————
 $3,150$150–$2,000
10% present-value factor(1.00)(.909)(.826)
Present-value cost: $1,634.35 = $3,150.00 + $136.35 – $1,652.00

Ownership of a car usually involves more than the costs of acquisition of ownership, even though the car is never to be driven. For example, there are the costs of taxes and insurance. If these total $150 yearly, to be paid at the beginning of each year, the cost of ownership for two years is reckoned as shown in Table 1.

The cost of obtaining and retaining (insured) possession for two years is $1,634.35. By rearranging the data we can express this cost as the sum of depreciation (purchase price minus resale price, adjusted to present value) plus the other ownership costs (taxes and insurance), as in Table 2.

Operating the car will involve more costs and a lower resale value, $1,700 rather than $2,000. Suppose outlays for gasoline, maintenance, and such amount to $500 in the first year and $400 in the second year. (Let these outlays be payable at the end of each year.) The costs of ownership and operation are now $2,667.05, compared with the cost of $1,634.35 for ownership only (see Table 3).

Table 2
Purchase price$3,000 
Resale value–1,652(present value of $2,000 deferred two years)
 —— 
Depreciation$1,348 
Taxes and insurance150(first year)
Taxes and insurance136.35(present value of second year’s payment)
 —— 
Present-value cost$1,634.35 

Events are rarely indivisible; instead, the magnitude of the event can be varied. Thus, in the automobile example, we could consider a set of alternative output programs, e.g., running the car zero miles in two years, one mile in two years, two miles in two years, etc., up to, say, 20,000 miles in two years. Suppose that for each of these we can determine the costs. The differences in costs between adjacent alternative programs is the incremental or marginal cost for the mileage increment. That is, the difference in cost between two-year programs of 19,999 miles and 20,000 miles is called the marginal cost of a mile of travel at 20,000 miles: it is the increment in cost for a 20,000-mile program over the cost for a 19,999-mile program. If we computed the cost for one mile of distance, for two miles, etc., up to 20,000 miles, we could compute a series of marginal costs at, or associated with, one mile more than no miles, one mile more than one mile, one more than two, etc. The sum of all these (including the cost of zero miles with two-year ownership) will total to the cost of ownership and 20,000 miles of travel. The concept of marginal cost is relevant for deciding among available programs because it tells by how much the cost of one program differs from that of adjacent available programs.

In the comparison of mileage programs we do not mean that one performs the program of, say 10,000 miles of travel and then, after completing that program, asks how much one more mile would cost. Instead, initially one considers the cost of a proposed 10,000-mile program and the cost of a proposed 10,001-mile program. The difference in cost between the proposed programs is the marginal

Table 3
 Beginning of year 1Beginning of year 2End of year 2
Purchase price$3,000$—$—
Taxes and insurance150150
Gas, oil, and maintenance500400
Resale value–1,700
 ——————
 $3,150$650–$1,300
10% present-value factor(1.00)(.909)(.826)
Present-value cost: $2,667.05 = $3,150.00 + $590.85 – $1,073.80

cost. (To run one more mile as the result of a last-minute decision may involve a higher extra cost than if one had planned for that extra mile from the beginning. In the extreme situation one might have to buy another car in which to do it.)

For any event there are two associated concepts of cost—total and marginal (the latter referring to a comparison between one particular event and another differing by one unit in some dimension of the event). For every alterable dimension there is a marginal cost of increments in that dimension. Two important dimensions in most output programs are the rate or speed of output and the total volume to be produced. We shall confine our subsequent discussion to changes in these rate and volume dimensions.

The present-capital-value measure of total (or of marginal) cost can be converted into a variety of other equivalent measures for expressing that cost. For example, the present capital value can be re-expressed as a future capital value with the future value measure (t units of time in the future) in the ratio (1 + i)t to the present value, where i is the rate of interest. Alternatively, the present capital value can be converted to a rate of costs over some interval. For example, a present-capital-value cost of $1,000 is, at 10 per cent per year, equivalent to a perpetual rate of cost of $100 per year, or to a rate of $263 per year for 5 years.

If the event being costed consists of a group or collection of homogeneous units, e.g., the production of pianos, or the production of miles of service from a car, or the production of bushels of wheat, the cost can be prorated or expressed as an average cost per unit of each item. In the automobile example, the event consisted of owning and driving a car 20,000 miles in two years, the cost of which was $2,667.05. This can be expressed as $2,667.05/20,000 = 13.3 cents per mile of distance. This is the prorated amount that, if received now for each future mile of service, will enable the receipts to cover the cost.

Sometimes the rate at which revenues must be received in order to cover costs is measured not by dividing the capital-value measure of costs by the total volume of output, but instead by dividing an annual rate of costs by an annual rate of performance or output. For example, the present-value measure of cost in the above illustration was $2,667 (for a two-year program of 20,000 miles of travel at the rate of 10,000 miles per year). The $2,667 present value can be re-expressed as an equivalent-valued continuous-flow annuity for two years, at 10 per cent per year compounded continuously. This steady-flow or rate measure is $1,479 per year for two years (and since there are 8,760 hours in a year, this is equivalent to $1,479 per year/8,760 hours per year = 16.9 cents per hour). The speed of service, at the rate of 10,000 miles per year for two years, is equivalent to 10,000 miles per year/8,760 hours per year = 1.14 miles per hour. If we divide one annual (or hourly) rate of costs by the other annual (or hourly) rate of service (i.e., $1,479 per year/10,000 miles per year, or 16.9 cents per hour/1.14 miles per hour), we get 14.8 cents per mile. Therefore, if costs are to be covered by revenues received concurrently with the service performed, the receipts must be 14.8 cents per mile of distance. (This differs from the earlier cost measure of 13.3 cents per mile paid at the beginning of the entire two-year program because the 14.8 cents is paid later and includes interest on the average delay.)

Extreme care must be taken to ensure that rates are divided by rates or that present-capital-value measures are divided by volume measures of the output. Confusion will result if rate (flow) measures of output are divided into capital-value (stock) measures of cost. That would yield cost per unit of speed of output (e.g., miles per year), not per unit of output (e.g., miles). Since outputs are usually sold or priced in units of output or volume, rather than in units of speed of service, it is more useful to consider the covering of costs by receipts per unit of volume of output rather than per unit of speed or of rate of production.

Fixed and variable costs. The preceding discussion distinguished among events being costed according to whether they involved (a) the ownership of some good, (b) the operation of that good to produce some service, or (c) a unit expansion of the event, giving a marginal cost. For some purposes a classification of costs may be useful. It may be relevant to know, for a chosen output program, what costs have been incurred even if we were, at some subsequent moment, to abandon the program. As was seen in the automobile example, at the moment of purchase we have incurred some loss of resale value, e.g., $3,000 – $2,500 = $500. That “cost” is “sunk” or “historical” Once we purchase the car, it cannot be escaped. It should play no role (except as a help in forecasting costs of similar future events) in any subsequent decision, for regardless of what we do, that historical “cost” has been incurred, and is inescapable and unaffected. For any ensuing decision only the escapable, or “variable,” costs are relevant.

Having separated sunk or historical “costs” (which really are no longer costs) from future costs, we can proceed to classify future costs into invariant and variable costs. Suppose a person can choose among a restricted set of output programs but that associated with all those options there is a common set of activities or inputs, the cost of which is therefore common to each option in the subset. The cost of these common activities is sometimes called a “fixed” cost. Regardless of which option in the subset he chooses, he cannot avoid those “fixed” costs. But since the real range of options is greater, he really can escape that “fixed” cost by choosing an option outside that subset. Therefore that “fixed” cost is not a “sunk” cost. Fixed cost is a useful concept, for example, in situations in which there can be delegation of authority to choose within some subset. So long as the selection is to be made within that subset, only the costs other than the “fixed” costs are relevant. But for the larger range of options, the “fixed” costs are not “fixed” and are relevant for comparing options. To avoid the impression that “fixed” costs are fixed upon a person as an inescapable loss, it seems appropriate to use the name “invariant” rather than “fixed,” but this is not yet a generally accepted terminology. (Fixed or invariant costs would be “sunk” if and only if the subset was in fact the entire set of possible options, for then regardless of what one did, one could not avoid the sacrifice of those alternatives.)

Law of costs. So far, we have classified costs according to differences in the event being costed, and also in terms of various ways of expressing the costs of a specified event or output program. The question to which we turn now is whether there are any laws or general propositions that relate the magnitude of costs to the characteristics of output programs. But first it is pertinent to identify the relevant characteristics or dimensions of an output or production program. As suggested earlier, the total volume and the rate or speed of production are two important dimensions of such a program. A third is the timing of the output. We may denote these three variables as follows: V is the volume of output, v(t) is the rate of output at moment t, T0 is the present moment, and Tm is the terminal moment. An increase in v(t) will either increase V or, for fixed V, will decrease Tm (move is closer to T0). Let C denote the capital-value measure of cost of the entire program. Several laws can now be stated in terms of these symbols.

(1) It is a well-recognized and validated law that cost is larger the larger V is (whether V is increased by increasing v(t) or by increasing Tm). Simply put, a bigger output costs more than a smaller one. Symbolically this means ðC/ðV is positive, even for fixed or unchanged v/(t). The expression ðC/ðV is called the marginal cost with respect to volume.

(2) Another proposition is that ðC/ðV is smaller (but always positive) the larger V is (again with the rate of production held constant and with the increased V being obtained by increasing Tm). In symbols, ð2CV2 is negative. This effect is sometimes referred to as the lower costs effect of mass or large-volume production. A larger output can always be produced by replicating the technique for a smaller output. However, sometimes a larger output can be produced at lower cost through the use of different techniques (e.g., metal dies instead of sand casting for forming metal), but this cheaper method cannot be subdivided proportionately for smaller volume. It follows that larger volume will at most involve proportional increases in total cost (by replication of the cheapest methods for small volumes) and may permit utilization of lower-cost methods. Learning and improvement in methods with a larger volume of output are also predictable. Both effects, substitution of cheaper methods for larger volume and learning, contribute to the decrease in increments of total cost for increments in volume.

The two laws relating costs to volume of output imply that (3) the average cost per unit of volume of output decreases, the larger the volume —a widely recognized phenomenon. This lower unit cost with larger volume is manifested in the extensive standardization of products, in contrast with the less common individually styled, custom-built goods, which would be preferable if the costs were no higher. This lower cost with larger volume (along with the gains from specialization in production resulting from the greater heterogeneity of productive resources) is one reason why larger markets and population areas permit lower costs per unit.

(4) A law relating cost to the rate (not volume) of output is that the cost, C, is a positive function of v(t) for any given V; that is, ðC/ðv is positive. The more rapidly a volume of output is produced, the higher its cost.

(5) Another, possibly less general, law is that the marginal cost with respect to rate, ðC/ðv, while always positive, increases for larger v (that is, ð2C/ðv2 is positive). This law is possibly less general because the evidence is contradictory for “very low” rates of output, at which it is sometimes claimed that increases in the rate might lead to decreasing increases in total cost. Nevertheless, a general and universally valid law is that for every volume of output there exists an output rate beyond which the marginal cost with respect to rate always increases. This is commonly called the law of increasing marginal costs and reflects the well-known law of diminishing marginal returns with respect to rate of output. If expressed in terms of average costs per unit of volume of output, the effect of higher rates of production of that volume is persistently to raise the average cost—after a possible initial fall in average cost for very low output rates.

(6) Instead of increasing the rate at which some constant volume is produced, output programs can be different in that both the rate and the volume are proportionally larger over a specified interval of time. Joint proportional increases in both the rate and the volume (over the given interval of production) will of course raise total costs. The effect on the cost per unit of product is not predictable except for “high” rates of output. Unlike proposition (3), concerning per-unit cost, proposition (6) involves an increase in the rate of output as well as in the volume. These two work in opposite directions on the per-unit cost, with the higher rate increasing unit costs while the larger volume decreases them. The rate effect ultimately will dominate as programs with higher rates are considered. For production programs arrayed according to the rate and volume of output (both varying strictly in proportion to each other) it follows that the average cost per unit of volume of output can be decreasing for small outputs. But as larger outputs are considered, the average cost will, beyond some output rate, begin to rise persistently and with increasing rapidity until a limiting rate of production is realized—at which all the resources of the world are devoted to this one program over that given time interval.

Short-run and long-run costs. We are now in position to examine another classification—short-run and long-run. Although it is common to see references to the short-run and long-run costs of some production program, there is in fact only one cost for any program. The short-run-long-run cost distinction rests on two concepts that are sometimes confounded with each other. A short-run cost is sometimes used to refer to a short, as contrasted with a long, program of production. At other times it is used to refer to the cost of doing something more quickly rather than less quickly. Yet in each case the shorter output and the quicker output both involve higher per-unit costs than do the longer output and the later output. Sometimes the higher per-unit short-run cost (no matter in which of the two different senses) is attributed to an alleged fixity in some of the productive units. In fact, of course, no producer is stuck with literally fixed inputs (except in the sense that momentarily it is hardly possible to increase anything). What is true is that it is more expensive to vary some inputs in any given interval than to vary others. That differential cost of adjusting various inputs is often oversimplified into an extreme bipolar classification of fixed and variable inputs.

The purpose of the long-run-short-run distinction is to note the differences in cost between different output programs, those achieved in the more immediate future in contrast with those undertaken later, when one can get the advantage of less expensive, less hasty adjustments. For example, if the demand for some good increases, producers will be able to respond immediately, but at a higher cost than for less hasty revisions of output. Although the “same” good is being produced (except, of course, for the important difference in the time of its availability), the cost is lower for the later output. To trace the impact of a demand change on output and prices, one will want to recognize the difference in the output and price with the passage of time. Instead of tracing out a continuous history or sequence of subsequent developments, it is convenient to divide the history arbitrarily into two episodes: the relatively immediate response (the short-run) and the limiting ultimate response (the long-run). The difference between these two “runs” indicates the path and direction of effects subsequent to the initial event.

While the long-run-short-run distinction serves as a convenient two-stage analysis of a sequence of effects, obviously there are as many “runs” as one wishes to consider. However, in analyzing total effects, three states or runs are usually considered: the “market period” (referring to that period of adjustment in prices which occurs before there is any change in output), and the aforementioned short-run and long-run, during both of which output is changed.

Joint products and unallocable costs. Suppose that an output program yields several joint products, e.g., wool, meat, and leather from sheep; or gasoline and kerosene from crude oil; or heat and light from electrical energy; or passenger-miles and freight-miles from an airline. What is the cost of each of the joint products? Depending upon which one is called the residual, or by-product, a different allocation of costs can be obtained. By calling meat the “basic” product and attaching most of the costs to it, the costs of wool can be made small, and conversely. It is tempting to jump to the conclusion that something must be wrong with the concept of cost or with the economic system if such indefiniteness can result. After all, if costs cannot be uniquely allocated, how can one tell what prices are right? How can one tell on which of the joint products he is making a profit? If costs cannot be assigned, how can one tell which to produce or what prices to charge? In fact, however, the presence of cost that cannot be allocated uniquely among the joint products does not upset anything or prevent unique prices.

If we recall the purpose of the cost concept— that of enabling choices among alternatives according to some criterion of preference—we see that what is required is a way of assessing the consequences of changes in the output. If the airline program is revised to transport more passengers and less freight, or revised so as to transport more passengers with the same amount of freight, what happens to costs? Comparing the costs of alternative programs gives marginal costs, which with the marginal value of the revised output give a basis for a decision. There is no possibility and no necessity for allocating costs into uniquely identifiable parts for each product in order to determine what to produce and what prices to ask. The prices set will be those which allocate the amount produced among the competing claimants and yield a maximum wealth to the producer of the joint products. His power to maximize his wealth will of course depend upon competitors’ access to the market. The function of inducing output does not require an assignment of portions of total cost to each of the joint outputs. What is necessary is a comparison of the total cost of the set of joint products with its value. If the market value of the set does not cover the cost, in an open market, the loss of wealth will induce reduced production (of some or all the joint outputs) and higher prices, until the value of the set of joint products covers the costs. (If joint products can be produced only in fixed combinations, then not even marginal costs of each output can be ascertained; nevertheless, everything said in the preceding two sentences is still valid and applicable.)

Private and social allocations of costs. Throughout the preceding discussion the costs of a choice were assumed to be borne by the chooser; none of the forsaken options are forsaken by anyone else. If Smith builds a swimming pool, the forsaken options—the costs—are all borne by him. The options open to the rest of the community or to any of its members are in no way reduced. So we assumed. If, however, Smith builds a pool and in doing so creates a “nuisance” for his neighbor, Jones, Smith has taken away Jones’s peace and quiet. If Smith’s pool overflows and harmfully floods Cohen’s land, Cohen has had options removed from his range of choice. Being less careful and thereby letting water run over into a neighbor’s land, or having a more riotous time and disturbing the peace, is less costly for Smith if he does not incur the costs of being more careful in watching the water level or in soundproofing his play area.

The situation is similar to that of the factory owner who “dumps” smoke, waste, smells, noises, and night lights on other people’s land. By doing so he keeps his land in better condition and avoids the costs of filtering his smoke, collecting and disposing of his own garbage, etc. He makes others bear some of the costs, instead of bearing them himself. His actions involve a sacrifice of alternative uses of goods, which sacrifice, instead of being borne by the decision maker, is in part borne by or imposed on other people.

”Property rights are not private” is another way to express this situation. The use of “one’s” resources is not subject solely to the owner’s voluntary control, but is in fact and de jure controllable in part by other people. This ability to “use” other people’s resources for one’s benefit, and thereby remove their options, enables one to make other people bear part of the costs of one’s decisions. The costs are divided between the decision maker and outsiders. This division or separation is called a divergence between private and social costs— where social costs are treated as the whole of costs as defined in the earlier portions of this discussion, with private costs being the portion of those costs borne by the decision maker or owner of the resources directly concerned. Social and private costs are not two different costs—they are merely classifications according to the bearer of the cost. If there is no divergence, so that all social costs are private costs, then all the costs of use are borne by the person choosing or authorizing the choice of action. The divergence between private and social costs is also characterized as the presence of “external” costs. [SeeExternalEconomies and diseconomies.]

Parallel reasoning is relevant on the side of benefits. The value of a resource in this use may be incompletely revealed or have incomplete influence on decisions if that value is dispersed so that only a part of it accrues to the decision maker. This is a divergence between private and social value in this use. If the value measure assigned to any particular potential use by the chooser is less than the total value in that use, then there will be a divergence between his private valuation and the social valuation. In this case, values of some uses of resources are not as fully revealed and available as inducements to the competing resource users as are the values of other uses. As a result, the values of some uses will be understated, which encourages more of other kinds of use by leading to an underestimation of their cost. Thus the analysis of external versus private or of social versus private values or costs is an essential part of the analysis of the meaning and role of costs.

But whatever they are called, such effects are commonplace and well-nigh universal. For example, every voluntary act of exchange involves a choice of use of resources that benefits the other party as well as oneself. However, the external effect is “internalized” as an inducement on the acting agents. If you give me “that,” I will do, or give you, “this”; and what you give me reflects the gains you will get from what I do. The external effects of my actions are made internal or effective by your ability to offer me a gain reflecting the value to you. The external costs of my acts are internalized or made effective in controlling my behavior by laws prohibiting my imposing any such costs on you unless I pay you an acceptable amount for the right to do so. Our laws of property and the right to engage in exchange help to make private costs also contain the social costs, and to make private gain reflect social gains. In other words, external effects are usually internalized.

In every society the extent of a divergence between private and social costs (or the presence of external effects) for some resource use depends upon the technological facts and upon the legal structure of property rights. The costs of defining, policing, and enforcing various types of property rights vary. Private property rights, defined as those in which external physical effects are not permissible, may be too expensive to enforce with respect to some effects. But if there is a cheap way to internalize external effects or to make the private costs equal the social costs, then the use of resources will respond more fully to the cost or values of use. If there were some cheap means of excluding other people from enjoyment of some use I may make of my resources, then I could charge them for the availability of that enjoyment and thereby make that value of use effective in my decision as to how to use resources. This is a means of internalizing external effects or of making external effects “inducive” with respect to my choices about resource uses.

Often the costs that must be borne in order to internalize external effects exceed the value of those external effects but may nevertheless be worth incurring if they involve associated revenues and a more profitable, larger enterprise. For example, a golf course provides benefits to neighboring landowners. A golf course builder could buy enough land to build a course and to build homes on the surrounding property, thus internalizing the higher value from proximity to the golf course. Another example is that of the apartment building in which the rental includes the cost of maintenance of common gardens and recreation areas, rather than having each tenant maintain his own area. The purchase of cemetery lots includes a payment for upkeep of the whole cemetery. By such devices, neighborhood effects are made the owners’ effects.

Another important means of internalizing or making external effects “inducing-effects” is the development corporation, which enables a larger venture to be undertaken so that more of the benefited resource owners can be included in the unit of ownership that provides the benefits. If all the land of a suburban shopping center is owned by one enterprise, there can be more complete response to the total value of the shopping center, which includes values external to the component units resulting from their proximity. Similarly, department stores with several departments in one building are a means of “internalizing” values or of making private and social effects converge. Signal decoders and wire transmission systems for television, fences around athletic pavilions to keep out nonpaying spectators, and walls around theaters are examples of devices (not costless) for internalizing and increasing the value of the service to those who provide it, and so are “inducive” to that resource use.

In other cases the value of complete suppression of external effects may be less than the cost. For example, automobile exhaust suppressors and smoke filters are not universally required. As a result, those who create smoke and smog thrust part of the costs of their actions on other people. An especially instructive example is provided by the problem of noisy airplanes. If an airport owner had to compensate the nearby landowners for the noise made by the airplanes using his airport, the landowners would in effect be selling rights to that particular use of their land, and the airport owner could in turn charge the airplane owners. Instead, one of the following solutions is usually adopted: (1) There is no compensation for the noise. (2) The planes are prohibited. (3) The neighboring land is bought up and people are prohibited from living there—even though many would prefer to do so, if they could buy the land at a low enough price to reflect the value of the lost quiet. These extreme policies are sometimes explained by an incorrect presumption that it is impossible or undesirable to buy the rights to “dump” noise on neighboring land; in fact, they are used because neighboring landowners do not have a legally recognized right to the undisturbed use of their land.

As the preceding remarks have indicated, often our legal structure of property rights is such that decisions are made in which only part of the costs are operative in affecting the choice. This may be a result of a deliberate attempt to attenuate the role of costs in decision making or, because of technological features, it may be the result of the difficulty (cost) of defining, policing, and enforcing rights to resources in such a way that private and social costs do not diverge much. Laws may be what they are because those most influential in affecting them may want resources to be used with less regard to the exchange-value measure of costs. It may be thought that the values the people of the society would express in the way they would use resources are inappropriate or improper and therefore should not be so influential in affecting resource allocations. If so, choices about uses of resources should be insulated from those alternative use values (i.e., costs). This can be achieved by suppressing a market place in which market prices would reveal alternative use values, or it can be achieved by not sanctioning private property rights, so that no one can negotiate an exchange that would reveal alternative use values (that is, resources would not be “owned,” in the sense of being salable).

Policing and enforcing of property rights is not performed exclusively by the government. In many cases other forms of control are effective. Etiquette and socially accepted codes act as determiners of rights. These institutions serve, in part, to restrict the extent to which a person can impose the costs of his choices on others. That is, they are often means of inducing behavior of a type that would occur if resources involved were “privately” owned and exchangeable. Custom and etiquette, along with property rules, affect the degree of concentration of costs on decision makers.

External value effects and costs. Still another source of confusion is the confounding of the external price effects of some event with its costs. Cost has been defined as the highest-valued option necessarily sacrificed consequent to action A. Suppose that I open a restaurant near yours, and by virtue of my superior cooking talents attract customers away from you, with a consequent loss of wealth by you of, say, $50,000. So far as youare concerned, my effect on you is as bad as if I had burned your uninsured $50,000 building for the joy and excitement this afforded me. From an analytical point of view, the former loss of $50,000 of value is not a cost, whereas the destruction of the building would have been a cost. Why the difference? Simply that opening a restaurant does not necessarily involve a sacrifice to society at large, while the destruction of the building does. My superior cooking skills do not involve a sacrifice of $50,000 of alternatively valuable output, whereas my enjoying the fire would. My superior cooking may impose a loss of wealth on you because I outcompete you in providing services to third parties. But the $50,000 loss to you is more than matched by the gain in the value of service to the third parties who were formerly your customers but who have shifted to me, and by the increase in my own wealth. No formerly available options are forsaken by society as a whole. Everything that could be done before I opened my restaurant still can be done. That $50,000 is not a sacrificed opportunity—instead, it is a measure of a transfer of wealth from you to two other parties, me and the customers. The distinction between the transfer of rights to uses of resources and the costs of use of goods should be kept clear. For example, when I open a new restaurant service, and the public offers less for your goods and more for mine, they are telling you that the exchange rights formerly attached to your goods—their market value—is being transferred by them to my goods.

The transfer of rights of choice of use and the revision of exchange values consequent to changes in offers by competitors, or consequent to changes in tastes by customers, do not reduce the total set of alternative use options. The transfer changes the person authorized to control the decision as to use. When my superior culinary talents reduce the exchange value of your services (without affecting their physical attributes in any way) and so reduce your wealth, society could in principle take away some of my gains and those of my customers (who gain by accepting my offers rather than yours) and fully reimburse you, while still leaving me and the customers better off than before I entered the market. Such compensation is not possible for true costs.

The person who loses wealth either via transfer of goods or the reduction of their exchange value is suffering a real loss of wealth, but not a cost. That loss is different in principle, in kind, and in fact from a cost. From the private point of view both sources of loss of wealth are “bad” for him. Both are losses of opportunities to him, though only a cost is a loss to the community as a whole. What he loses in the pure price revaluation case, someone else gains.

There are many examples of the use of public policy to reduce such transfers. Taxes have been imposed on innovations or on new products in order to reimburse owners of resources formerly used to produce the displaced products. Sometimes laws are passed prohibiting new, cheaper devices, in order to preserve the marketable wealth of users of older, more costly methods. Sometimes general taxes are imposed to aid those whose wealth is reduced by new methods, e.g., government financing of retraining of displaced workers and low-interest loans to business firms in distressed areas. Taxes on innovations make the innovators count the taxes as part of their costs. The “costs” of innovation are thereby biased upward, with a resultant attenuation of the incentive to introduce new methods or products that would produce a larger total wealth.

Although wealth transfers via market revaluations are not costs, they may influence behavior. For example, if such market revisions of wealth are (somehow) deemed undesirable, steps can be taken to restrain people from taking actions that revise the distribution of wealth, or steps can be taken to redistribute the wealth again so as to restore the status quo ante wealth for each individual. Social policy (laws of property) may be evolved to insulate decisions from these effects or, conversely, to make them more sensitive. But in neither case are these market-price side effects on wealth components of costs.

We conclude by returning to the initial theme. The costs of some event are the highest-valued options necessarily forsaken. We have seen that he who is to forsake those options and he who makes the decision about the chosen option may or may not be the same person. Furthermore, the privately borne costs may be less or greater than the true costs, depending upon laws and upon the structure of property rights.

Armen A. Alchian

BIBLIOGRAPHY

BÖhm-Bawerk, Eugen von (1884–1912) 1959 Capital and Interest. 3 vols. South Holland, III.: Libertarian. → First published in German. See especially Volume 2, pages 248–256, “The Law of Costs,” and Volume 3, pages 97–115, “On the Value of Producers’ Goods and the Relationship Between Value and Costs.”

Clark, John Maurice (1923) 1962 Studies in the Economics of Overhead Costs. Univ. of Chicago Press.

Coase, R. H. 1960 The Problem of Social Cost. Journal of Law and Economics 3:1–44.

Demsetz, Harold 1964 The Exchange and Enforcement of Property Rights. Journal of Law and Economics 7:11–26.

Knight, Frank H. 1924 Some Fallacies in the Interpretation of Social Cost. Quarterly Journal of Economics 38:582–606.

Stigler, George J. (1942) 1960 The Theory of Price. Rev. ed. New York: Macmillan. → First published as The Theory of Competitive Price.

Viner, Jacob 1931a Cost. Volume 4, pages 466–475 in Encyclopaedia of the Social Sciences. New York: Macmillan.

Viner, Jacob (1931b) 1952 Cost Curves and Supply Curves. Pages 198–232 in American Economic Association, Readings in Price Theory. Homewood, III.: Irwin.

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cost

cost / kôst/ • v. (past and past part. cost ) [tr.] 1. (of an object or an action) require the payment of (a specified sum of money) before it can be acquired or done: the magazine costs $2.25. ∎  cause the loss of: driving at more than double the speed limit cost the woman her driving license. ∎  involve (someone) in (an effort or unpleasant action): the accident cost me a visit to the doctor. ∎ inf. be expensive for (someone): if you want to own an island, it'll cost you. 2. (past and past part. cost·ed) estimate the price of. • n. an amount that has to be paid or spent to buy or obtain something. ∎  the effort, loss, or sacrifice necessary to achieve or obtain something: she averted a train accident at the cost of her life. ∎  (costs) legal expenses, esp. those allowed in favor of the winning party or against the losing party in a suit. PHRASES: at all costs (or at any cost) regardless of the price to be paid or the effort needed: he was anxious to avoid war at all costs. at cost without profit to the seller. cost an arm and a legsee arm1 .

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cost

cost sb. XIII. — AN. cost, OF. coust (mod. coût) :- Rom. *costo, f. *costāre stand firm, be fixed, stand at a price, f. CON- (intensive) + stāre STAND.
So cost vb. XIV. — OF. co(u)ster (mod. coûter) :- Rom. *costāre. Hence costly XIV; see -LY 1.

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cost

costaccost, cost, frost, lost, Prost, riposte •teleost • Pentecost • oncost • glasnost •compost • star-crossed • hoar frost •permafrost

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COST

COST (kɒst) Committee for Overseas Science and Technology (of the Royal Society)

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