How is it that one party rather than another receives the profits from production? In terms of property, how is it that one party rather than another owns the product? The traditional answer is that the "owner of the firm" owns the product and gets the profits from the production process. But we have seen that the role of being the firm is not a property right. Firmhood is a contractual role; it is determined by the structure of contracts–by who hires what or whom.

The contractual nature of firmhood leaves the open question; how is it that one party rather than another owns the product? This raises the whole question of property appropriation–a question that has been systematically neglected in political economic theory. Economics focuses on the transfer of property rights in the marketplace. But to be transferred, a property right must first be created or initiated, and it will be eventually terminated. Property appropriation is concerned with the creation and termination of property rights.

How is it that one legal party rather than another owns the product of a given production process? Consider a non-institutional technical description of a specific production process. A specific set of people perform certain labor services which use a given plant and machinery and various other materials to produce certain outputs. But that process is not just a technical activity; it is embedded in a matrix of legal institutions of property and contract. This surrounding set of legal structures will determine which legal party owns the product. But how? What is the legal mechanism or right that determines who owns the product?

The standard answer is that the right to the product is included in or attached to the ownership of some asset such as the ownership of the firm or the ownership of the means of production. As the owner of an animal owns its issue, so the owner of that asset owns the product. The rights to use an assets, the use-rights, are distinguished from the right-to-the-product or right-to-the-fruits.

The assumed legal institutional setting is a private property market economy. In such an economy, this so-called "right-to-the-fruits" does not exist as a legal right separate from the use-rights. The ownership of the product is determined by the use-rights together with a certain legal fact-pattern. The "right-to-the-fruits" is only a shorthand way to refer to the appropriate fact-pattern.

The point can be easily seen by considering the abstract economic description of a production process. Let direct materials, labor services, and the services of capital be the inputs needed to produce the outputs of a production process specified by a given production function. There are numerous ways this technical production process could be legally organized in a free market economy. The owner of any one of the inputs could purchase the complementary inputs, e.g., the owner of the direct materials could hire the capital and the workers. Or another party entirely could hire the capital and the workers, and could purchase the direct materials. In any case the party who hired the inputs, the hiring party, would bear the costs of the input services and materials used-up in the production process. Assuming those were all the required inputs, that hiring party would have the defensible legal claim on the produced outputs.

In no case was the hiring party required to purchase any "right-to-the-fruits" over and above the use-rights of the hired inputs and the purchase of the direct materials. Economic theory contemplates no markets for "rights-to-the-fruits," only markets for the inputs. The inputs are symmetrical between themselves in the capitalist marketplace, and that symmetry precludes a right-to-the-product being preassigned to one particular input. To acquire the ownership of the produced outputs, the requisite fact-pattern is the ownership of all the input services and input materials used-up in production. Bearing all those costs is both necessary and sufficient to have the defensible claim on the product.

When the owner of one of the inputs (e.g., capital) acquired the other inputs and laid claim to the product, it is sometimes said the the ownership of the non-marketed input included the "right-to-the-fruits." But this claim is easily refuted by considering a rearrangement of the use-rights. Let the owner of input B hire the capital instead of vice-versa. Then the new hiring party (the owner of B) could lay claim to the product without having purchased any so-called "right-to-the-fruits." It was sufficient to purchase the use-rights, i.e., to hire (or already own) all the factors used in production. The ownership of the new non-marketed input (input B) does not suddenly incorporate the elusive "right-to-the-fruits." In each of the cases, a party claimed the outputs because the party had borne the costs of the inputs consumed in production. The usual "right-to-the-fruits" is just a misleading way to refer to that fact-pattern.

Consider the example mentioned above of the jus fruendi whereby the owner of an animal had the right to its issue. A cow is rented from a farmer for a month to produce milk and, during that time, the cow gives birth to a calf. The farmer, not the renter, would have the right to the calf. The person renting the cow didn't pay for the relevant inputs. There were two concurrent production processes, the short-term process of producing milk and the long-term process of breeding the cattle. The farmer was engaged in the long-term process, the farmer had paid those costs, and the farmer would have the defensible claim on the issue, the calf. The farmer's "right to the issue" is a shorthand description of that set of facts. The farmer's claim to the issue was ultimately based on having borne the relevant costs of producing that yield.

The uncritical acceptance of the right-to-the-fruits concept leads to a neglect of the whole topic of property appropriation in economic theory. If the right to the product was part and parcel of the ownership of certain assets, then the product was not "appropriated"; it was pre-owned by the asset owner. Indeed, conventional economics does not even recognize that appropriation takes place in production. The non-recognition of appropriation in production is one of the remarkable "achievements" of the field called the "economics of property rights" [viz. Furubotn and Pejovich 1974; Demsetz 1988].

Philosophers follow Locke and discuss appropriation as the birth of private property rights in some primordial state where goods were held in common or were unowned. Economists follow suit and discuss the formation of private property rights out of common ownership. For instance, Harold Demsetz [1967] considers how private property in land with fur-bearing animals was established as a result of the growth of the fur trade. John Umbeck [1981] considers how rights to gold deposits were created during the 1848 California gold rush on land recently ceded from Mexico. Yoram Barzel [1989] considers how the common property rights to minerals under the North Sea were privatized. Indeed, Barzel considers examples of non-owners obtaining benefits from unmonitored private property (e.g., an employee making a personal use of a company coping machine) as cases of the private appropriation of common property. But in Barzel's book [e.g., his Chapter 5, "The formation of rights"] as elsewhere in the economics of property rights literature, there is no recognition of the appropriation of the outputs and the symmetrical termination of rights to the used-up in inputs in the normal production process. The question of property appropriation in production has simply not been addressed in economic theory.

Our analysis has shown that the naive right-to-the-product concept is misleading. The product is not pre-owned by certain asset owners. The product is defensibly claimed by the legal party who fits a certain contractual fact-pattern, the party called the "hiring party." Thus new property claims are being made after all; the products of production are appropriated by the hiring party. To accurately describe the legal structure of production in a private property market economy, the concept of appropriation must be rehabilitated. Property appropriation occurs not just in some primordial original position or initial distribution, but in the normal day-to-day process of production.

Prior to the neoclassical marginalist revolution, the structure of property rights was considered part of political economy [e.g., J.S. Mill's Principles of Political Economy, especially Book II, Chapters I and II, 'Of Property' and 'The Same Subject Continued']. In the recent revival of interest among economists in property rights, e.g., in the work of Coase, Alchian, Demsetz, Furubotn, Pejovich, Williamson and many others, there has been no rigorously specified theory of property appropriation in production. The literature is informal and largely metaphorical; it often uses the methodology of "as if." It is "as if" the firm was a "coalition" of factor suppliers each contracting for a share of the product with the entrepreneur as the residual claimant [e.g., Alchian 1984]. It is "as if" the firm was just a nexus of contracts–"nothing more than a set of contracts" [Ross and Westerfield 1988, 14]. It is "as if" piece-workers were selling their product [e.g., Cheung 1983]. It is "as if" employees with "profit-sharing" joined the entrepreneur in getting a share of the residual profits. These are all metaphors.

The core metaphor is the distributive shares metaphor which pictures the factor owners as getting shares in the product. Income is pictured as being distributed within a firm "as if" each factor supplier had a contractual claim on a fixed or variable share of the product. In the usual treatment of marginal productivity theory, each factor is pictured "as if" it "produced" and then "received" a share of the product. It is "as if" all this were the case, but what is actually the case in terms of property rights?

As a description of property rights, the distributive shares picture is quite misleading and false. The simple fact is that one legal party owns all the product. For example, General Motors doesn't just own "Capital's share" of the GM cars produced; it owns all of them. Economists are, of course, aware of this "legalistic" fact, but apparently feel "called upon" to metaphorically reinterpret the product as being "shared" or "distributed" in order to account for the income received by the input suppliers. How else can one account for the other factor incomes if one factor is pictured as owning all the product?

A social scientist should resist the temptation to improve upon the "superficial" legal facts with the "deep" economic metaphor of distributive shares; the legal facts suffice to explain the factor incomes. Property can take either a positive or negative form as assets or liabilities, i.e., as property rights or obligations. By "product," economists mean only the positive product, the output assets produced in production. But there is also a negative product. To produce the output assets, it is necessary to incur the liabilities for using up the inputs. And one can "own" or hold liabilities just as one can own assets.

The simple fact which accounts for the other factor incomes without the benefit of the distributive shares metaphor is the fact that the one party who owns all the positive product also owns all the negative product, i.e., also holds all the liabilities for the used-up inputs. General Motors not only owns all the GM cars produced but also holds all the liabilities for the factors such as steel, rubber, glass, and labor used up in production. The money paid out to satisfy these liabilities represents the costs of production. The suppliers of the steel, labor, and other factors, instead of being joint claimants on the product, are only creditors of that one party who owns all the positive and negative product. One party owns all the outputs but that party does not receive its value in net terms since that party must also satisfy the liabilities for the inputs.

In order to accurately describe the structure of property rights in production without the distributive shares metaphor, it is necessary to expand the usual concept of "product" to include the negative product (input liabilities) in addition to the usual positive product (output assets). This bundle of property rights and obligations will be called the whole product, i.e.,

WHOLE PRODUCT = OUTPUT ASSETS + INPUT LIABILITIES.

In order to describe this more-complex notion of the product, we must use lists or "vectors" of commodities. Vectors give a list of different types of commodities as in a shopping list. A shopping list might have 3 pounds of hamburger and 2 gallons of milk. Since these are different types of commodities, it does not make sense to add them together (3 lbs. + 2 gallons = 5 whatevers??); that would be "adding apples and oranges." But one can add together two separate lists by adding likes to likes. For example, if a neighbor also had a shopping list with 2 pounds of hamburger and 1 gallon of milk, then the lists could be combined or added to yield 5 pounds of hamburger and 3 gallons of milk.

Consider a simplified example of a production process where Q = F(K,L) units of output are produced during a time period using the capital services K and the labor services L. We will use vectors or lists, where the different types of commodities are always listed in the same order as follows (with commas in between):

(outputs, capital services, labor services).

In the simple example, the positive product is the vector of output assets (Q, 0, 0), the negative product is the vector of input liabilities (0, –K, –L), and the whole product is the sum (Q, –K, –L):

(Q, 0, 0) POSITIVE PRODUCT

+( 0,–K,–L) +NEGATIVE PRODUCT

= (Q,–K,–L) = WHOLE PRODUCT

In property theory, as opposed to price theory or value theory, the notion of the whole product replaces the notion of the residual or profit. There is no single residual quantity of property. One cannot subtract the liabilities for the used-up inputs of steel, glass, and rubber from the output of cars to obtain a property residual. The vector notion of the whole product is needed to deal with the property rights and obligations whose net value is the residual profit. Technically feasible whole product vectors are the production vectors used in the modern production set representation of technical opportunities. In the economics literature, a whole product vector is also called a "production possibility vector" [Arrow and Debreu 1954, 267], an "activity vector" [Arrow and Hahn 1971, 59], a "production" [Debreu 1959, 38], or an "input-output vector" [Quirk and Saposnik 1968, 27]. The economics literature, however, does not give a property theoretic interpretation of these vectors as assets and liabilities; the outputs are simply listed as positive and the inputs as negative.

The property theoretic importance of whole product vectors lies in the fact that it is precisely these whole products which are appropriated in production.

There are two ways that a party can acquire the legal title to an asset:

The first or initial acquisition of the legal right to an asset is called the appropriation of the asset. Legal rights to assets are transferred from a prior owner by contract (or gift), but what is the legal mechanism of appropriating an asset?

There are similarly two ways that a party can dis-acquire or give up the legal title to an asset:

In this second case, the owner would give up and surrender the legal right and claim to the asset but not by transferring it to another party (e.g., when the asset is consumed or used up in production). That is the original sense of the word "expropriation." According to Black's Law Dictionary;

Thus appropriation initiates a property right to an asset and "expropriation" (in its original sense) terminates it; in between, the property right is transferred. However, since the word "expropriation" is commonly understood today in the other derived sense meaning the compulsory transfer of assets to the government, we may use an alternative expression. Instead of saying the "expropriation of assets," we may say the "appropriation of liabilities." Thus instead of the appropriation and expropriation of assets, there is the appropriation of assets and liabilities. If we do use the word "expropriation," it will be in its original sense as the opposite of appropriation–as the termination of title.

The termination of the legal title to an asset is called the appropriation of the liability for the used-up asset. Legal rights to assets are given up through transfers to other parties by contract or gift, but what is the legal mechanism to terminate legal title to an asset, i.e., to appropriate the liability for a used-up asset?

In production, the outputs are produced and the inputs are used up. Prior to the productive activity, the output-assets were not yet created and the legal right to the inputs had not been terminated. In production, a question arises. Who is to appropriate the liabilities for the used-up inputs and who is to appropriate the outputs? The output-assets and the input-liabilities are precisely the whole product. Hence the basic question about the structure of property rights and obligations in production is:

"Who is to appropriate the whole product?"

This fundamental question has both a normative and a descriptive interpretation. Who ought to appropriate the whole product and who in fact appropriates the whole product? We consider here only the descriptive question of specifying the legal mechanism of appropriation of assets and liabilities in a private property market economy.

Elsewhere the author [1982, 1985b, 1986] has mathematically formulated double entry bookkeeping so it could be extended from numbers representing monetary amounts to lists or vectors of numbers representing amounts of different types of goods and services with no commensurate monetary values. This allowed ordinary money-based accounting to be extended to property accounting which deals directly with vectors of property rights. Property accounting inside the firm traces the stocks and flows of property rights including the appropriation of assets and liabilities that is involved in production. By evaluating all the property rights at the values assigned by monetary accounting, property accounting can be collapsed into ordinary monetary accounting so that one can see where the appropriation of assets and liabilities goes on behind the scenes in ordinary accounting. Conventional economics has not probed into the stocks and flows of property rights underneath ordinary accounting, and that has allowed it to ignore the role of appropriation in production in favor of various pictures such as the distributive shares metaphor.

It is interesting that the question of appropriation does not seem to be sharply posed in the economic, legal, or philosophical literature. When the question of appropriation is discussed, then it concerns not day-to-day production and consumption but some original or primal distribution of property as in John Locke. Yet new property is created and old property is consumed in everyday production and consumption activities, not just in some mythical "original position." Moreover, when appropriation is discussed, it is limited to assets and neglects the symmetrical treatment of liabilities.

An appropriation, since it only involves one legal party such as a corporation, is not as public as a legal transfer between parties. Indeed, it is only the contested appropriations which involve two or more parties that come to the attention of the legal authorities. Examples include the negative (ownership) externalities which have received so much attention in the "Law and Economics" literature (a literature which does not even pose the question of appropriation in normal production). For example, a property damage suit arises out of a situation where one party, the plaintiff, has de facto appropriated certain liabilities which the plaintiff believes should be appropriated by another party. If the court agrees, then the resulting damage payments are an example of a legally enforced appropriation of liabilities by the defendant.

But such examples are rare whereas the matter of appropriating liabilities arises whenever property is consumed, used-up, or otherwise destroyed in all production or consumption activities. The matter of appropriating assets arises whenever new property is created such as in any production activities. If contract is the normal legal mechanism for transferring property, what is the normal legal mechanism for the appropriation of the assets and liabilities created in production and consumption?

When no law is broken so that the legal authorities do not intervene to hold a trial, then there is a laissez faire or invisible hand mechanism that automatically takes over. That is, when the Law does not intervene to reassign the liability for a used-up asset, then that liability is automatically left in the hands of the last legal owner of the asset. If that party does not voluntarily appropriate the liability then the party can seek redress by trying to get the legal system to intervene and reassign the liability.

If appropriable new assets are produced as a result when certain commodities or assets are used up, then the legal party that voluntarily appropriated the liabilities for the used-up assets would naturally lay claim on the produced assets. In the absence of any reassignment of the liabilities, the legal authorities would consider that claim as being defensible. Hence we have the normal legal mechanism governing how assets and liabilities are in fact appropriated in normal day-to-day activities of production and consumption.

This invisible hand mechanism could be personified using an "Invisible Judge." The Invisible Judge rules in the lowest court in the land (the market) and always issues the same ruling: "Let it be"–namely, let the costs lie where they have fallen. When a party goes to court to seek redress, then the party is appealing the verdict of the Invisible Judge. When a party bears the costs of production and then assumes the ownership of the positive product, the Invisible Judge has, in effect, awarded that prima facie right. Anyone seeking to contest it would have to go to a higher court to overturn the verdict of the Invisible Judge.

It is this laissez faire mechanism which determines who in fact appropriates the whole product in normal production activities. One party purchases all the requisite inputs to production, including labor, and then that party bears those costs as the inputs are consumed in production. Hence that party has the legally defensible claim on the produced outputs. In this simple manner, one party legally appropriates the whole product of production (input-liabilities and output-assets).

Given a production activity, the legal party who legally appropriates the whole product of the production activity will be called "the firm." The descriptive question of who is to be the firm is answered by the laissez faire mechanism. The whole product appropriator is the party who hired (or already owned) the inputs and assumed those costs as the inputs were used up in production and thus could lay claim to the produced outputs. Hence the determination of who is the firm, i.e., who appropriates the whole product, is based on the direction (not the terms) of the hiring contracts. If Capital hires Labor, then Capital is the firm. If Labor hires the capital, then Labor is the firm. If some third party (such as an entrepreneur or even the State) hires both the capital and workers, then that third party is the firm. Hence the determination of who is to be the firm is decided in factor markets by who hires what or whom.

There is, of course, the legal form of the stock corporation which is owned by its shareholders. But prior to the hiring contracts, a corporation is only a capital owner. It is the direction of that hiring contract which determines whether the capital-owning corporation hires in Labor and is thus the firm, or whether the corporation is only a capital supplier whose business is hiring out its capital to another party who uses it in production and who is thus the firm (whole product appropriator). There is no necessity for another party to "buy the firm"; hiring the capital will suffice. The ownership of the means of production thus embodies no legal obligation for Capital (the owners of the capital) to be "the firm," i.e., to appropriate the whole product produced using that capital. The ownership of capital is, of course, quite relevant to the question of marketplace power, the question of which party has the power to make the hiring contracts in its direction.

It is part and parcel of the neglect of appropriation in economics that all income is pictured as being the result of the sale of some factor. In property terms, that is only a transfer or exchange (factor in return for its price) so again appropriation is squeezed out of the picture.

Being the hiring party, and thus the whole product appropriator, is a contractual role. It is not the ownership of some specific asset, factor or the performance of any specific service. The whole product is thus not a return to some asset, factor, or service. It is a return to the contractual role of being the hiring party (the last legal owner of the used-up inputs). Moreover, it is a return in terms of property, not simply a value return. In the textbook model of perfectly competitive equilibrium (under constant returns to scale), there are no pure or economic profits so the net value of the whole product is zero. It is because the whole product is not a return to a factor that its value can be competed down to zero in the textbook model of competitive equilibrium. This does not mean that the hiring party gets "nothing." The hiring party gets no net value in that instance, but still gets the whole product in terms of property. It gets (the role of being) the firm. Moreover, the property mechanism of laissez faire appropriation operates regardless of whether the price mechanism is in equilibrium or disequilibrium and regardless of whether the markets are competitive or noncompetitive.

The whole product and its value, the pure or economic profit, is not a return to some factor. It is of no avail to postulate hidden or implicit factors in the economists' description of the production process. At best, some hidden factor might be priced so that the profits would be exactly zero when the factor is taken into account. Hidden factors are just "fudge factors" for economic theorists; they don't change the structure of property rights involved in production. The whole product, even if of zero value, is still appropriated; it still accrues to the contractual role of being the hiring party.

The "explanation" that profit is a return to risk-bearing is quite tautologous when "risk-bearing" means bearing the costs of production (appropriating the negative product). By the market mechanism of appropriation, the party that appropriates the negative product also appropriates the positive product and thus nets the profits. Moreover, "risk-bearing" is, in theory, an insurable function (e.g., crop insurance for production uncertainty and hedging on futures markets for price uncertainty). When risk-bearing is thus priced out as an insurance cost, the pure profit that remains is not a return to risk-bearing; it is still a return to the contractual role of being the hiring party.

Profit theory has always been a perennial sore-spot in economic theory because it does not fit the mold of income as a return to a factor. Pure profits are what is left after all the factors have been priced out. It is the role of property appropriation in production that explains why one party rather than another receives the whole product, and thus receives its value, the pure profits.

The conventional wisdom does not even formulate the (descriptive or normative) question of the appropriation of the (whole) product in everyday production activities. This blind-spot is best illustrated by the voluminous literature on the "economics of property rights" which does not even raise the question. It treats appropriation in the context of the private apportionment of previous common property rights, not in normal production.

One reason for this conceptual gap in the conventional wisdom is the "ownership of the firm" myth. This myth is typically sustained by the failure to conceptually differentiate the firm, i.e., the party undertaking a given production or business activity (specified in a non-question-begging way), from the corporation currently undertaking the activity. The "appropriation blind-spot" is supported by identifying the firm with the corporation. For instance, it is said: "There is no need for a corporation to 'appropriate' its products; the corporation already owns the results of its production activity." Such an argument is a truism based on the question-begging use of phrases such as "its products" or "its production activity." The original question of appropriation must be constantly reformulated to avoid question-begging "answers." How did the products become "its" products or how did the production activity become "its" production activity.

Consider an example. Barbara Smith uses certain raw materials to produce widgets using a widgetmaker machine with a given serial number in a specified building. So far nothing is determined about the institutional setting, e.g., about who owns the produced widgets. Then we add the institutional information that Company A employs Barbara Smith, supplies the raw materials, owns the machines, and owns the building. Then Company A would certainly own the products but for what reasons? Ownership of the machine and building, the "means of production"? No, the machine and building could have been leased by Company A from some other party, and Company A would still own the produced widgets. Company A's claim on the product is based on its bearing the flow of expenses for the inputs used up in producing the widgets–the worker's labor, the raw materials, the machine-time, and the floor space in the building. In our terminology, by voluntarily accepting or appropriating the negative product, Company A established the legally defensible claim on the positive product. Thus Company A appropriated the whole product in accordance with the laissez-faire mechanism of appropriation.

It was the pattern of input contracts which determined who bore the input costs and which thus determined what was the "product of Company A"–not the "ownership of the means of production" or the ownership of Company A. If the building and machinery had been leased from Company A to Company B, and if Company B paid for the worker's time and the raw materials, then Company B would own the produced widgets even though the ownership of the means of production and of Company A was unchanged.

Since conventional economics does not pose the question of appropriation in production, it has not conceptualized the simplest and most fundamental of the laissez-faire or invisible hand mechanisms, the market mechanism of appropriation. Given a normative principle, an invisible hand mechanism might under certain conditions satisfy that normative principle. For instance, the fundamental theorem of price theory asserts that in the absence of externalities, a competitive equilibrium in the price mechanism is allocatively efficient. The corresponding fundamental theorem of property theory (Chapter 14) shows that in the absence of certain property externalities, the laissez-faire mechanism of appropriation satisfies the basic norm of property appropriation (developed in the next chapter).