Capital management under profit-oriented market socialism: an explicit function approach.

I. Introduction

Despite the dramatic collapse of Soviet Communism, predictions of the "death of socialism" may be premature. The system of Soviet Communism comprised at least five important characteristics: (1) socialism (public ownership of the preponderance of the capital stock); (2) central planning (extensive power over and tight control of the economy by a single bureaucratic agency); (3) political oligarchy (consolidation of power within an authoritarian Communist Party apparatus); (4) strict egalitarianism (implying limited wage and salary differentials, and very high job security among the workforce); (5) international activism (pursuit of worldwide socialist revolution by all means including force). The decline and fall of Soviet Communism might well have been the consequence of the latter four characteristics; socialism in and of itself, in the strict sense of public ownership of capital, might not have been a significant contributor to Soviet weakness.

Ever since the negative characteristics of Soviet Communism first began emerging unmistakeably in the 1930s, socialist sympathizers in the West have argued that there are democratic market socialist alternatives to Soviet Communism which would effectively achieve the traditional socialist objective of economic justice without threatening either efficiency or democracy. Oskar Lange's 1936 essay "On the Economic Theory of Socialism" [15] was a major milestone in the development of the economic component of democratic market socialism. What has since become a consensus verdict on Lange's marginal cost pricing proposal in the Western economics profession was first reached by Abram Bergson in his influential 1948 essay on "Socialist Economics" [2]: interesting in theory, but unpromising in practice.(1) Despite this verdict, comparative systems textbooks almost invariably describe and discuss the Langian market socialist proposal.(2)

Moreover, it is clear that Langian market socialism is not the only market socialist possibility, and that there may be other possibilities which are more promising. The two possibilities on which the more recent literature has mainly focused are cooperative market socialism (i.e., labor management), and profit-oriented market socialism. Since the seminal 1958 theoretical contribution by Benjamin Ward [37], a very large literature has developed on the theory of the cooperative firm, and also a reasonably substantial empirical literature, using data from the former Yugoslavia, the plywood industry in the Pacific Northwest, Mondragon in the Basque region of Spain, and so on.(3) However, cooperative market socialism does share with Langian market socialism one important disadvantage: it would represent a relatively drastic departure from the economic status quo under modem industrial capitalism. Given the relatively high level of satisfaction with the economic performance of modern industrial capitalism, among both the economics profession and the general public, a market socialist proposal would necessarily have to be very conservative and incrementalist in order to become a serious political possibility.

Of the three principal market socialist possibilities on which the literature to date has focused (Langian, cooperative, and profit-oriented), the profit-oriented possibility would be the most similar to the existing economic status quo under modern industrial capitalism.(4) Three independently developed profit-oriented market socialist plans have been put forward in the economic systems literature: the "pragmatic" market socialist plan of James Yunker [39; 40; 41; 42; 43; 44; 45; 46], the "municipal ownership" market socialist plan of Leland Stauber [30; 31; 32; 33], and the "bank-centric" market socialist plan of John Roemer [24; 25; 26; 27]. A detailed discussion of the various institutional details of these three proposals would not be feasible here. However, they do share a number of important commonalities, as follows:

Profit-oriented market socialist proposals envision the publicly owned corporations pursuing profits in a competitive business environment, subject to an outside ownership authority representing the interests of the owning public. The public ownership authority would exercise no powers of planning or coordination (it would not be a central planning agency along the lines of the Soviet Gosplan), but it would possess the authority to dismiss managers of corporations which are earning inadequate profits. Competition would be maintained through the decentralization of both business activity and the public ownership authority. Most commodities would be produced by at least several different independently evaluated publicly owned firms. In addition, public ownership authority would be dispersed over a large number of local offices which would operate autonomously and independently of one another. The property return produced by the publicly owned business sector would be collected by the public ownership authority, which would retain a small percentage to meet its administrative expenses and incentive payments to its personnel. The great preponderance of property return would be returned to the general public in some form, either as a direct social dividend payment to each household, or in the form of reduced tax liability. Thus would be achieved a substantial equity gain over contemporary capitalism, under which the distributions of capital wealth and property income are extremely unequal. These plans envision the retention of private ownership in the case of small business and entrepreneurial business. Entrepreneurial business enterprises would be established through private initiative and also by special-purpose public agencies.

At the heart of any proposal for profit-oriented market socialism is a public ownership authority (POA) which would assume the legal rights and financial entitlements which under capitalism are exercised by private capital owners. Yunker's POA is called the Bureau of Public Ownership (BPO), and its authority would be dispersed over several thousand "BPO agents" located in several hundred local BPO offices in various towns and cities. The pragmatic market socialist proposal is distinctive in specifying that each publicly owned corporation would be largely responsible to one single BPO agent, as a means of gaining the perceived advantages of the sole owner situation [40; 44, 129-32]. The agent would retain a very small fraction of the dividends and interest paid over by the corporation to the parent BPO. The BPO agent of a particular corporation would enforce his/her personal interest in high return on the corporation's management through the use of substantial discretionary power in the retention or dismissal of the corporation's chief executive officer.

Unlike Yunker, neither Stauber nor Roemer have suggested proper names for their proposed POA's. Stauber envisions a system of locally owned investment funds (or banks), which would trade among themselves in the various securities issued by the publicly owned corporations. Under this plan, the financial markets would work exactly as they do under capitalism, except for the exclusion of private households from these markets. Financial market trading would not be quite so free under the Roemer proposal, which envisions each publicly owned corporation assigned to one of several hundred public investment banks. Corporations within each bank's group could trade securities with each other and with the group central bank, but could not trade with other banks or corporations outside the group. In contrast to the Stauber plan, under the Roemer plan the profits of each investment bank would be collected by a central national office prior to being redistributed to the public.

The concept of profit-oriented market socialism is motivated by the idea of achieving a substantial equity gain, in terms of a greatly equalized distribution of capital property return, at minimum risk to the efficiency and dynamism of the economy. The concept avoids the perceived problems of other socialist systems: the over-centralization and inflexibility of Soviet-style central planning socialism, the lack of an observable success criterion of Langian market socialism, and the lack of an outside ownership authority of cooperative market socialism. On the other hand, even granting a minimum level of feasibility and viability of such an economic system (e.g., that some level of competition could be achieved despite public ownership of most large corporations), there are several important problems concerning the potential performance of profit-oriented market socialism: agency issues involved in corporate supervision and management, private household saving, the dynamic issues of investment, innovation and entrepreneurship, and so on and so forth. Undoubtedly there are a great many diverse approaches that could be taken to these problems, ranging from informal institutional analysis based on experiences in the communist nations and nationalized industries, through to the higher reaches of axiomatic economic theory.

The purpose of this paper is to try to gain some insights into the potential performance of profit-oriented market socialism by examining one of its core issues using the tools of basic neo-classical economic theory. The core issue is that of the public ownership agency (POA): how big should it be and how much should it take? More specifically, what proportion of the labor force should be assigned to the POA under profit-oriented market socialism, and what proportion of the flow of property return should be retained by the POA under profit-oriented market socialism prior to the distribution of the remainder as a social dividend? The desideratum used here will be maximization of a Benthamite social welfare function. The specification and solution of this problem sheds significant illumination on the potential economic performance of profit-oriented market socialism relative to contemporary capitalism.

The remainder of the paper is organized as follows. The second section develops a general equilibrium model of a hypothetical economy which may serve as a template either for the contemporary capitalist economy or for a profit-oriented market socialist economy. The model addresses the allocation of the overall labor force between "ordinary laborers" and "capital managers," and also the allocation of a so-called "residual" between ordinary laborers and capital managers. The optimal allocation of the labor force and the residual is derived as the solution of a social welfare maximization problem. This optimal allocation serves as a benchmark against which both the capitalist and the profit-oriented market socialist economies may be compared.

In the third section of the paper, such a comparison is undertaken for various numerical specifications of parameter values. The central focus is on a parameter which will be designated herein the "output elasticity of capital management effort" ([Gamma]). Neither the capitalist nor the profit-oriented market socialist economy achieves the maximum level of social welfare achieved when the "assignment coefficient" ([Mu]) and the "distribution coefficient" (v) are set to their optimal levels according to the problem specified in the second section. But it is found that the profit-oriented market socialist welfare shortfall is less than that of capitalism for relatively low values of the output elasticity of capital management effort ([Gamma]), while the opposite holds true for relatively high values of [Gamma].

The fourth and final section concludes the discussion by arguing that much of the disagreement over the potential performance of various plans of market socialism relative to capitalism is attributable to an implicit disagreement over the actual value of the [Gamma] parameter in the real world. The actual value of this parameter is of course an empirical question rather than a theoretical question. The implication is that the actual performance of profit-oriented market socialism is an empirical question rather than a theoretical question. This point possibly would not be so significant, were it not for the fact that numerous pro-socialists and anti-socialists alike apparently believe that their opinions are legitimately grounded in pure theory, and that their opponents are therefore enmeshed in logical errors rather than simply having a different view of empirical reality. No doubt those with especially strong ideological commitments, either to capitalism or socialism, will be inclined to resist the implications of this research. But it is hoped that those without such strongly fixed preconceptions in this matter will benefit from the insights obtained.

II. A General Equilibrium Model

This section sets forth a simple general equilibrium model adapted to the determination of the socially optimal values of two parameters designated the "assignment coefficient" ([Mu]) and the "distribution coefficient" (v). The latter coefficient is closely related to a third coefficient designated the "retention coefficient" ([Alpha]). As explained below, the distribution coefficient v is the proportion of an unobservable "residual" which is distributed to capital managers, while the retention coefficient [Alpha] is the proportion of an observable flow of property return which is retained by capital managers.

We conceive an economy with an unspecified number of identical individuals, each one of whom may perform ordinary labor or capital management. The assignment coefficient [Mu] (where 0 [less than] [Mu] [less than] 1) is the proportion of individuals who work as capital managers; thus 1 - [Mu] is the proportion of individuals who work as ordinary laborers. Aggregate ordinary labor (L) and aggregate capital management effort (E) are derived from the assignment coefficient ([Mu]), and from individual ordinary labor (l) and individual capital management effort (e), through the definitions:

L = (1 - [Mu])/ (1)

E = [Mu]e. (2)

Aggregate output Y is a Cobb-Douglas function of physical capital K, aggregate ordinary labor L, and aggregate capital management effort E:

Q = [K.sup.[Epsilon]][L.sup.[Delta]][E.sup.[Gamma]]. (3)

By "ordinary labor" we refer to that human application commonly recognized simply as "labor" in economic reasoning. This could mean anything from the digging of ditches through the management of large corporations. The meaning of "capital management effort," on the other hand, is any sort of human application not recognized and rewarded by standard labor income (wages, salaries, bonuses, etc.), but rather by various forms of property income. For example, one form of capital management effort consists of corporate supervision such as is provided by members of boards of directors (as opposed to corporate management which is provided by corporation executives). Under capitalism, boards of directors consist of private capital owners, while under profit-oriented market socialism they would consist of representatives of one or more local offices of the public ownership agency. Another example is investment analysis, such as performed by a private investor under capitalism or a POA investment officer under market socialism. Entrepreneurship may also be classed as a form of capital management effort, consisting of investment analysis to determine what sort of new firm to establish, followed by corporate supervision over the firm once it has been established.

The form of the production function allows a convenient technical representation of the difference in opinion between those inclined to the view that under capitalism property income is "unearned" (i.e., those who might look more favorably on profit-oriented market socialist proposals), and those inclined to the view that under capitalism property income is "earned" largely through the capital management efforts of its recipients (i.e., those who would look less favorably on profit-oriented market socialist proposals). In the view of the former, what we observe as property income under capitalism is largely a marginal product return to inanimate physical capital (K in the model); while in the view of the latter, what we observe as property income is largely a marginal product return to capital management effort (E in the model).

Presuming that the theory of marginal product pricing of labor applies to the real world, the coefficient of labor in the production function ([Delta]) can be approximated by the observed share of labor in national income, approximately 0.8 in a modern industrialized economy such as that of the United States. Presuming also linear homogeneity in the production function, the question is then how much of the remaining 0.2 belongs to [Epsilon] (the output elasticity of physical capital K), and how much belongs to [Gamma] (the output elasticity of capital management effort E). Those inclined to the opinion that property income under capitalism is "mostly unearned" would specify in this model that [Epsilon] is "high" (that is, close to 0.2) while [Gamma] is low (close to 0.0); while those inclined to the opposite view would specify the opposite order of magnitude in these parameters.

In the Western world, economists are widely agreed that marginal product pricing of factors of production is both economically efficient and morally legitimate. If skeptical questions are raised, they are usually not about the validity of the marginal product pricing principle itself, but rather about whether the principle applies to the real world. So without asserting anything about whether or not marginal product pricing of factors actually applies either to the existing real-world capitalist system or to a potential real-world profit-oriented market socialist system, let us specify in the ideal model being developed here that both individual ordinary laborers and individual capital managers are paid directly a marginal product wage (equations (4) and (5) below). The aggregate marginal product payments to ordinary labor ([M.sub.l]) and to capital management effort ([M.sub.[Epsilon]]) are then given by the definitional equations (6) and (7) below:

[w.sub.l] = [Delta]Y/[Delta]l (4)

[w.sub.e] = [Delta]Y/[Delta]e (5)

[M.sub.l] = (1 - [Mu])[w.sub.l]l (6)

[M.sub.e] = [Mu] [w.sub.e]e. (7)

The "residual" R is then defined as total output Y less both of these aggregate marginal product payments, while "property income" P is defined as total output Y less the aggregate marginal product payment to ordinary labor alone. The residual R is unobservable, while property return P is observable. Using the Cobb-Douglas production function, the explicit forms of these equations are as follows:

R = Y - [M.sub.l] - [M.sub.e] = (1 - (1 - [Mu]) [Delta] - [Mu][Gamma])Y (8)

P = Y - [M.sub.l] = (1 - (1 - [Mu])[Delta]) Y. (9)

An extreme point of view would be that all observed property return under capitalism is an earned marginal product return to capital management effort: in this case the residual R would be 0, and property return P would consist entirely of the aggregate marginal product return to capital management effort ([Mu][Gamma]Y). At the opposite extreme would be the view that no observed property return under capitalism is an earned marginal product return to capital management (that it is instead entirely the aggregate marginal product return to physical capital: [Epsilon]Y), and that property return P is identical to residual R (i.e., [Gamma] = 0). An intermediate view is then that the residual R is a positive amount, but that the marginal product return to capital management effort ([Mu][Gamma]Y) is also some positive amount. It is this intermediate view which motivates the analysis reported here.

Once we have granted the existence of a positive residual R, our hypothetical economy is presented with a distribution problem. The residual amount is the marginal product payment to aggregate capital ([Epsilon]Y), a nonhuman, inanimate and disinterested entity. Obviously this amount will be divided up among the human ordinary laborers and capital managers. Its division cannot be guided by the marginal product principle, as that principle was already applied prior to the generation of the residual.

We specify the distribution coefficient v(0 [less than] v [less than] 1) as the proportion of R paid to capital managers, and 1 - v as the proportion paid to ordinary laborers. Respectively the aggregate and individual "transfers" to capital managers and ordinary laborers are specified in the following definitional equations:

[T.sub.l] = (1 - v)R (10)

[T.sub.e] = vR (11)

[t.sub.l] = [T.sub.l]/(1 - [Mu]) (12)

[t.sub.e] = [T.sub.e]/[Mu]. (13)

The incomes of individual ordinary laborers and individual capital managers are the sums of the marginal product payments plus the transfers:

[y.sub.l] = [w.sub.l]l + [t.sub.l] (14)

[y.sub.e] = [w.sub.e]e + [t.sub.e]. (15)

The utilities of the two respective categories (equations (18)-(19) below) are then taken to be Cobb-Douglas functions of income (defined in (14)-(15) above) and leisure (defined in (16)-(17) below):

[h.sub.l] = 1 - l (16)

[h.sub.e] = 1 - e (17)

[Mathematical Expression Omitted]

[Mathematical Expression Omitted].

The individual supplies of ordinary labor and capital management effort are obtained from the maximization of utility subject to the budget constraints (14) and (15) and time constraints (16) and (17).

We confront a conceptual problem in determining the individual factor supply functions. In standard general equilibrium analysis, each individual takes the marginal product wage (w) and the transfer (t) to be exogenously determined constants. The resulting labor supply function, using the Cobb-Douglas utility function and representing the human factor as x (which could be l or e as the case might be), is x = [Psi] - ((1 - [Psi])t/w). But in the present context, it would not be appropriate to imagine that the individuals consider the transfers to be exogenously determined subsidies. In the capitalist economy, individual capital owners receive both a marginal product return on capital management effort, and what the present model recognizes as a marginal product return on physical capital. But these capital owners do not directly perceive which is which: rather they tend to interpret all return which they receive as a return to capital management effort. In order to maintain a comparable situation in the profit-oriented market socialist economy, it is convenient to adopt Yunker's stipulation that the social dividend not be paid to individuals on a lump-sum subsidy basis, but rather in proportion to labor income.(5) In this case, the so-called "transfer" to labor under profit-oriented market socialism would definitely be perceived by its ordinary labor recipients not as an exogenous subsidy but rather as a supplement to their marginal product wages.

The above considerations are incorporated into the analysis through the "augmented marginal product wage" concept. If there is no transfer in the economy, the simple wage of an ordinary labor household ([w.sub.l]) is implicitly defined by the income equation:

[y.sub.l] = [w.sub.l]l = [Delta]Y. (14a)

But with the transfer, the "augmented wage" ([w[prime].sub.l]) is implicitly defined by the expanded income equation:

[y.sub.l] = [w[prime].sub.l]l = [[Delta] + ((1 - v)/(1 - [Mu])) (1 - (1 - [Mu]) [Delta] - [Mu][Gamma])]Y. (14b)

An analogous result holds for capital management effort e.

The individual utility functions are taken to be Cobb-Douglas in form, which maintains a symmetry between the production and utility structure of the economy. Maximization of these utility functions subject to the respective "augmented" constraints [y.sub.l] = [w[prime].sub.l] and [y.sub.e] = [w[prime].sub.e]e, where the individuals take the augmented marginal product wages [w[prime].sub.l] and [w[prime].sub.e] to be exogenously determined constants, produces the factor supply equations:

l = [Psi] (20)

e = [Psi]. (21)

The inelasticity of factor supply in these equations is a consequence of two assumptions: (1) the Cobb-Douglas form of the utility function; (2) individual households, whether consisting of ordinary laborers or capital managers, do not perceive any component of their income as an exogenous subsidy. Neither of these assumptions is particularly strong by the usual standards in contemporary economic analysis. The Cobb-Douglas form has of course been widely utilized in production analysis for over 50 years, and it is also frequently to be found in utility analysis. For example, in his major survey of the theory and empirics of labor supply, Mark Killingsworth uses this function as a running example [14, 68-69, 132-35]. And while supply functions of labor are often assumed to be upward-sloping in economic analysis, the fact is that this proposition has not found much support in the econometric literature to date.(6)

Taking the assignment and distribution coefficients ([Mu] and v) as exogenous parameters determined outside the model, equations (1)-(21) constitute a determinate positive model of the economy. In order to determine the socially optimal values of these two coefficients, it is necessary that we specify a normative social welfare function. Among social welfare functions, clearly the additive, or Benthamite, function possesses the longest tradition of usage in economics. Although its origins may be traced well back into the nineteenth century, it remains current in the sense of being formally justifiable [20], and of providing a basis for important contemporary economic policy analysis (e.g., its use, in continuous form, by Mirrlees [17] and many others in the theory of optimal taxation). Since the number of individuals in the economy is not specified, the "sum of utilities" is expressed as the weighted average utility of ordinary laborers and capital managers, with the weights being the respective proportions of the population (1 - [Mu] and [Mu]):

SW = (1 - [Mu])[u.sub.l] + [Mu][u.sub.e]. (22)

To determine the socially optimal values of [Mu] and v, we take the partial derivatives of SW with respect to [Mu] and v, equate to zero, and solve for [Mu] and v. The explicit solution for [Mu] and v is somewhat laborious, so an outline of the derivation is relegated to the Appendix. The optimal assignment coefficient and distribution coefficient ([[Mu].sup.*] and [v.sup.*]) are as follows:

[[Mu].sup.*] = [Gamma]/([Delta] + [Gamma]) (23)

[v.sup.*] = ([Gamma] - [[Gamma].sup.*])/([Delta] + [Gamma] - ([Delta] + [Gamma]).sup.2]). (24)

As indicated, the distribution coefficient (v) is the proportion of the residual (R) transferred to the capital managers. A closely related concept is the "retention coefficient" ([Alpha]), defined as the proportion of property income (P) "retained" by the capital managers. The aggregate transfer to capital managers in the model is [T.sub.e] = v(1 - (1 - [Mu])[Delta] - [Mu][Delta])Y, and their total aggregate income is [Y.sub.e] = [M.sub.e] + [T.sub.e] = [[Mu][Gamma] + v(1 - (1 - [Mu])[Delta] - [Mu][Gamma])]Y. Now consider their total aggregate income as the proportion [Alpha] of property income: [Y.sub.e] = [Alpha]P = [Alpha](Y - [M.sub.l]) = [Alpha](1 - (1 - [Mu])[Delta])Y. Therefore from [Alpha](1 - (1 - [Mu])[Delta]) = [Mu][Gamma] + v(1 - (1 - [Mu])[Delta] - [Mu][Gamma]), we have:

[Alpha] = ([Mu][Gamma] + v(1 - (1 - [Mu])[Delta] - [Mu][Gamma]))/(1 - (1 - [Mu])[Delta]) (25)

v = ([Alpha](1 - (1 - [Mu])[Delta]) - [Mu][Gamma])/(1 - (1 - [Mu])[Delta]- [Mu][Gamma]). (26)

These equations enable us to translate a given v into [Alpha] or vice versa.

Substituting the socially optimal [v.sup.*] into the equation for [Alpha] above, we obtain the socially optimal retention coefficient:

[[Alpha].sup.*] = [Gamma]/([Delta] + [Gamma] + [[Delta].sup.2]). (27)

This represents the socially optimal total aggregate income of capital managers as a proportion of total property income in the economy, within the context of the simple general equilibrium model developed here.

III. Numerical Solutions of the Model

The economic parameters of the section II model - those parameters which are common to capitalism and socialism - comprise K, [Psi], [Epsilon], [Delta] and [Gamma]. In all solutions reported in this section, the K parameter is taken without loss of generality to be unity, in which case the value of the [Epsilon] parameter does not affect any of the solution values. The system parameters of the model are the assignment coefficient ([Mu]) and the distribution coefficient (v).

The socially optimal values of [Mu] and v, in terms of maximization of a Benthamite social welfare function, are given by equations (23)-(24) above. The optimal values are determined by the [Delta] and [Gamma] parameters, respectively the output elasticity of aggregate labor (L) and the output elasticity of capital management effort (E). Once [Mu] and v are determined, the 21 positive endogenous variables of the model are determined from equations (1)-(21), and the normative variable SW is determined from equation (22).

Table I shows the maximum value of SW as a function of a range of [Gamma] values from .001 to .151 by increments of .010, for a [Delta] value of 0.8 and a [Psi] value of 0.5. The value 0.8 is a plausible benchmark for [Delta] on the basis that in a neoclassical economy, the output elasticity of labor equals the share of labor in national output, and in a modern industrialized economy such as that of the United States, the share of labor is approximately 80 percent. The value of [Gamma] is a considerably more nebulous and controversial matter. In this research, a range of [Gamma] values is specified from very small (.001) to fairly large (.151). The value of [Psi] is also a nebulous matter - although hardly as controversial. Presuming positive but diminishing marginal utility of income, this parameter lies between 0 and 1. For purposes of Table I and Figure 1, we will use the "middle of the road" value of 0.5. Sensitivity analysis is presented in Table II below.

Among the more ardent defenders of the contemporary capitalist system, it might be sincerely believed that the real-world capitalist system does closely approximate various plausibly defined social optima. By the same token, among the more ardent proponents of socialism, it might be sincerely believed that some socialist system, such as the profit-oriented market socialist, for example, could at least in principle closely approximate various plausibly defined social optima. But among those maintaining a more neutral attitude, it might be doubted that either real-world system is likely to approach an ideal system. This doubt motivates the following analysis. It is not argued that "free market forces" under contemporary capitalism tend to move real-world assignment and distribution toward the optimal levels indicated by equations (23)-(24). Neither is it argued that "social planning" under a potential profit-oriented market socialist system would be likely to set real-world assignment and distribution at the optimal levels.

Instead it is proposed that under both contemporary capitalism and profit-oriented market socialism, the actual levels of assignment and distribution depart from the optimal levels. Thus the actual levels of social welfare under the two systems will be less than the optimal levels. For capitalism it is specified that the distribution coefficient is unity: that the capital owner/managers, by virtue of their private ownership rights to capital, appropriate the entire residual, considering it to be part of the marginal product return to capital management. The value of the assignment coefficient is a more difficult question: in the following we will explore the consequences of different values of [Mu]. Thus using the superscript "c" to represent "capitalism," we have that [v.sup.c](= [[Alpha].sup.c]) = 1, while [[Mu].sup.c] may equal .001, .010, or .100.

As for profit-oriented market socialism, we will use small values for both coefficients. According to the argument advanced by the proposers of such systems, the key virtue of profit-oriented market socialism is that society has the function of capital management performed efficiently by the personnel of the public ownership authority (POA) at a very small fraction of the cost imposed on society by the class of capital owner/managers under the contemporary capitalist system. This implies that the POA would employ a very small proportion of the labor force under profit-oriented market socialism, and that it would retain a very small proportion of the property return paid to it by the publicly owned corporate business sector to cover its administrative expenses and agent incentive bonuses. This would leave the great majority of this property return available for social dividend distribution to the general population, or for the reduction of household tax liabilities.

In very round numbers, the labor force in the contemporary United States is about 100 million individuals. A POA staff of 100,000 would constitute .001 of 100 million. The retention coefficient under profit-oriented market socialism is taken to be .025 (2.5 percent of property [TABULAR DATA FOR I TABLE OMITTED] return). Thus using an "s" superscript for "socialism," we have [[Mu].sup.s] = .001 and [[Alpha].sup.s] = .025. The corresponding [v.sup.s] under profit-oriented market socialism is then determined by the values [[Alpha].sup.s] and [Gamma] according to the relationship shown at the end of the previous section. These numerical values ([[Mu].sup.s] = .001, [[Alpha].sup.s] = .025, and the corresponding value of [v.sup.s]) would probably satisfy most definitions of "small."

As mentioned above, an empirically difficult question is the appropriate assignment coefficient under capitalism. Clearly it would be inaccurate to count every person under contemporary capitalism who owns some amount of physical or financial capital property as a full-fledged capital manager: many of these people own very small amounts of such property, they work at full-time ordinary labor jobs, and they devote only a small proportion of their working time to activities related to capital management. What is wanted is the number of "full time equivalent" capital managers as a proportion of the total work force; alternatively this may be stated as the proportion of hours devoted to capital management as a proportion of the total number of hours worked, counting both ordinary labor hours and capital management effort hours. In the absence of any apparent empirical proxies for this concept, we will use a range of assignment coefficients under capitalism: [[Mu].sup.c] = 001, [[Mu].sup.c] =. 010, and [[Mu].sup.c] = .100. The lowest of these equals the assignment coefficient under profit-oriented market socialism, while the highest begins to approach the proportion of individuals in the population who might be described as possessing "significant" property incomes, and who might therefore be engaged in "significant" capital management effort.

Table I shows, for 16 values of the output elasticity of capital management effort ([Gamma]) ranging from .001 to .151, and for a "middle of the road" value of [Psi] of .500, the following: (1) the maximum SW presuming that [Mu] and v are set to their optimal values given by equations (23)-(24); (2) the socialist SW presuming that [[Mu].sup.s] = .001 and [[Alpha].sup.s] = .025; (3) the capitalist SW presuming that [v.sup.c] = [[Alpha].sup.c] = 1, and [[Mu].sup.c] = .001, .010, or .100. These figures are graphed in Figure 1. The optimal SW value is traced by a dotted line; the socialist SW value is traced by a dashed line, and the three lines for the capitalist SW are traced by solid lines. Note that the value of SW is a declining function of the value of [Gamma] for all three systems: optimal, socialist and capitalist.

Although both the profit-oriented market socialist and the capitalist economies may be described as sub-optimal according to the Benthamite social welfare criterion, the relative degree of sub-optimality is less for the socialist economy at low values of [Gamma], and less for the capitalist economy at higher values of [Gamma] - except for the case in which [[Mu].sup.c] = .001. In this latter case, the socialist economy is less sub-optimal than the capitalist over the entire range of [Gamma] shown in Table I.

We define the "crossover" elasticity of capital management effort as the [Gamma] value at which the socialist SW "crosses over" (i.e., becomes less than) the capitalist SW. Thus the crossover elasticity is the critical empirical boundary line between a situation in which capitalism is preferable to socialism, and a situation in which socialism is preferable to capitalism. As shown in Figure 1, the crossover elasticity is [Gamma] = .0442 for [[Mu].sup.c] = .100 and [Gamma] = .0653 for [[Mu].sup.c] = .010. Thus in the case where [[Mu].sup.c] =. 100, if [Gamma] [less than] .0442 then profit-oriented market socialism is socially preferable to capitalism, while if [Gamma] [greater than] .0442 then capitalism is socially preferable to profit-oriented market socialism. If it exists, the crossover elasticity for [[Mu].sup.c] = .001 lies beyond .200. But under the assumption of linear homogeneity in the production function, the upper limit on [Gamma], given that [Delta] = .800, is .200.

Table II shows the sensitivity of the crossover elasticity in [Gamma] to variations in the two economic parameters of the model, [Delta] and [Psi], whose values cannot be empirically established with complete certainty. Although we have utilized [Delta] = .800 as a benchmark value in the above, clearly this value is far from certain. Owing to the well-known "unmeasurability of utility," the value of [Psi] is, if anything, even more unsettled. In Table II, the crossover elasticity is shown for five values of [Delta] (.900, .800, .700, .600, and .500) and five values of [Psi] (.100, .250, .500, .750, and .900). Although neither of these parameters have been measured with any degree of certainty by econometricians, the range of hypothetical values specified probably encompasses the informal expectations of likelihood of most economists.

It was determined that if [[Mu].sup.c] = .001, there is no crossover elasticity in the range from [Gamma] = .001 to [Gamma] = 1 - [Delta] for any of the parameter combinations tested. Thus Table II has no section for [[Mu].sup.c] = .001. But for [[Mu].sup.c] = .010 and [[Mu].sup.c] = .100, crossover elasticities exist in the range from [Gamma] = .001 to [Gamma] = 1 - [Delta] for all these parameter combinations. Describing these results qualitatively, it appears that for the most part, the crossover elasticity is a declining function of both the utility elasticity [TABULAR DATA FOR TABLE II OMITTED] of income ([Psi]) and the output elasticity of ordinary labor ([Delta]). Thus the crossover elasticity tends to be high for low [Psi] and [Delta], and low for high [Psi] and [Delta].

IV. Conclusion

This research has attempted to shed some illumination on the potential performance of a profit-oriented market socialist economy through the specification of a simple general equilibrium model of the economy. The model focuses on the "assignment" of the total working force among ordinary labor and capital management, and on the "distribution" of the residual amount left, after the deduction of marginal product payments to ordinary laborers and capital managers, among ordinary laborers and capital managers. The production and utility functions of the model are Cobb-Douglas in form, which enables explicit solution for the optimal values of the assignment and distribution coefficients. Optimality is defined in terms of maximization of a sum-of-utilities (Benthamite) social welfare function.

In the numerical phase of the research, solutions of the model are obtained for various specifications of parameter values. The optimal social welfare value attained with optimal determination of assignment ([Mu]) and distribution (v) constitutes a benchmark against which the capitalist and profit-oriented market socialist economies may be compared. Primary emphasis in the sensitivity analysis is on a model parameter designated the "output elasticity of capital management effort" ([Gamma]). Table I and Figure 1 illustrate the fundamental result that for relatively low values of [Gamma] the welfare shortfall is lower under profit-oriented market socialism than it is under capitalism, while for relatively high values of [Gamma] the welfare shortfall is lower under capitalism than it is under profit-oriented market socialism.

The "crossover elasticity" is defined as that value of [Gamma] which marks the border between the range of [Gamma] in which profit-oriented market socialism does better than capitalism, and the range of [Gamma] in which capitalism does better than profit-oriented market socialism. The sensitivity of the crossover elasticity to variations in three key parameters is investigated in Table II. The parameters include the utility elasticity of income ([Psi]), the output elasticity of ordinary labor ([Delta]), and the assignment parameter under the capitalist system ([[Mu].sup.c]). Within the ranges of parameter values covered in the table, the crossover elasticity ranges from a high of .2734 to a low of .0136.

The reason for the emphasis on [Gamma] is that this parameter provides a convenient technical representation of the difference in opinion between defenders of capitalism who believe that property income is "mainly earned" and proponents of socialism who believe that property income is "mainly unearned." It is not being maintained that these defenders and proponents are consciously aware of this technical representation, nor even that they would be disposed to accept it were it explained to them. Indeed, it is probably safe to assume that most of those with strong opinions on the socialism versus capitalism question would resist any effort to reduce the debate to a "simple economic model," particularly a simple economic model which offers ambiguous indications on the fundamental question of which system best serves the purposes of social welfare. Holders of strong beliefs - whether those beliefs favor socialism or capitalism - might be tempted to dismiss summarily any model which does not provide unambiguous support for their beliefs.

But for those whose opinions are not as firmly fixed, the central result of this research may not seem particularly implausible or untoward. That result is simply that the potential performance of a profit-oriented market socialist economy relative to capitalism is an empirical question which hinges on the empirical value of a parameter which has not yet been estimated with any degree of certitude - nor in fact has it been estimated at all. All empirical work on neoclassical production functions has been based on the form Y = F(K, L), rather than on the form Y = F(K, L, E) which underlies the analysis presented here, simply because no empirical data is available on E.

It is widely believed, by those on both sides of the socialism versus capitalism debate, that "orthodox" neoclassical economic theory tends to support the pro-capitalist side of the debate rather more than it does the pro-socialist side. Specifically, it is often supposed that the marginal product theory of factor pricing, as applied to capital, provides support for the fundamental capitalist institution of private appropriation of property return. Similarly, it is often supposed that for socialism to be supportable from the standpoint of economic theory, drastic departures are required from "orthodox" assumptions: for example, there must be important externalities in production or consumption, or the business sector must be characterized by imperfect competition rather than perfect competition.

The present research may perhaps provide an antidote to this misconception. The model developed in Section II above incorporates the key orthodox assumptions in core neoclassical economic theory: diminishing marginal product of factors of production, diminishing marginal utility of inputs into the household utility functions, marginal product pricing of factors of production under perfect competition, self-interested optimizing behavior by individuals, no external effects of any kind, and so on and so forth. Yet it is shown that none of these conditions are inherently incompatible with superior performance by a socialist economy of the profit-oriented market socialist variety. Should the real-world value of the output elasticity of capital management effort ([Gamma]) be sufficiently low, the profit-oriented market socialist economy would out-perform the capitalist economy. Of course, clearly the output elasticity of capital management effort might be high enough that the profit-oriented market socialist economy would indeed be inferior to the present capitalist economy. But it is important to recognize that this inferiority, should it be the case, does not proceed from any of the orthodox assumptions of neoclassical economic theory, but rather from the empirical value of a model parameter. The potential usefulness of estimates of this parameter is clear.

A final question concerns the generalizability of the implications derived from the model studied in this research. As does any research which aspires to numerical results, the present research incorporates a host of debatable assumptions. Even within the context of orthodox neo-classical theory, there are many alternative mathematical forms that might be used for the fundamental production and utility functions: for example, the CES. More fundamentally, the model is a static model and as such does not explicitly encompass either saving or entrepreneurship. Of course it is well known that property return is frequently justified either as a return to saving (the time preference argument) or as a return to risk-taking, innovation, discovery, and other aspects of entrepreneurship (the Austrian argument) - rather than as a return to capital management per se. Saving is an issue not dealt with at all in this research. It is arguable that the notion of capital management effort utilized herein does indeed encompass entrepreneurship and related activity - but clearly, not everyone would accept this argument.

Yet it is certainly possible that if and when formal analyses are undertaken which examine these alternative facets of the socialism versus capitalism debate, much the same fundamental conclusion will be reached as has been reached herein. That conclusion is that the elements of contemporary economic theory do not suffice, in and of themselves, to arrive at an unambiguous and compelling conclusion regarding the potential performance of profit-oriented market socialist systems which would attempt to mimic capitalism in many important respects. Whatever conclusions these future analyses might reach, they ought probably to be undertaken, if only because of the potential importance of the issue.

Appendix

The problem is to determine the optimal assignment coefficient ([Mu]) and distribution coefficient (v) which maximize social welfare (SW), given the general equilibrium model developed in section II. Substituting l and e from equations (20)-(21) into the production function we have:

Y = [K.sup.[Epsilon]][L.sup.[Delta]][E.sup.[Gamma]] = [K.sup.[Epsilon]] [((1 - [Mu])l).sup.[Delta]] [([Mu]e).sup.[Gamma]] = [Y.sub.0] [(1 - [Mu]).sup.[Delta]] [[Mu].sup.[Gamma]] (A.1)

where [Y.sub.0] = [K.sup.[Epsilon]][[Psi].sup.[Delta] + [Psi]].

The two inputs into the utility function are leisure and income. For both ordinary laborers and capital managers, leisure is 1 - [Psi] from the time constraints (16)-(17) and factor supply equations (20)-(21). Considering both the marginal product wage and transfer components, their respective incomes are:

[Y.sub.l]: [[Delta] + ((1 - v)/(1 - [Mu]))(1 - (1 - [Mu])[Delta] - [Mu][Delta])]Y

= [[Delta](1 - [Mu]) + (1 - v)(1 - (1 - [Mu])([Delta] - [Mu][Gamma])][Y.sub.0] [(1 - [Mu]).sup.[Delta] - 1] [[Mu].sup.[Gamma]], (A.2)

[y.sub.e] = [[Gamma] + (v/[Mu])(1 - (1 - [Mu]) [Delta] - [Mu][Gamma])]Y

= [[Gamma][Mu] + v(1 - (1 - [Mu])[Delta] - [Mu][Gamma])] [Y.sub.0] [(1 - v).sup.[Delta]] [[Mu].sup.[Gamma] - 1]. (A.3)

Substituting income and leisure into the individual utility functions for ordinary laborers and capital managers, and then substituting these utility functions into the Benthamite social welfare function, we obtain SW as a function of [Mu] and v:

[Mathematical Expression Omitted]

where:

[f.sub.1]([Mu]) = [(1 - [Mu]).sup.[Psi][Delta] - [Psi] + 1] (A.5)

[f.sub.2]([Mu]) = [(1 - [Mu]).sup.[Psi][Gamma]] (A.6)

[g.sub.1]([Mu]) = [[Mu].sup.[Psi][Gamma]] (A.7)

[g.sub.2]([Mu]) = [[Mu].sup.[Psi][Gamma] - [Psi] + 1] (A.8)

[h.sub.1]([Mu], v) = [[[Delta](1 - [Mu]) + (1 - v)(1 - (1 - [Mu])[Delta] - [Mu][Gamma])].sup.[Psi]] (A.9)

[h.sub.2]([Mu], v) = [[[Gamma][Mu] + v(1 - (1 - [Mu])[Delta] - [Mu][Gamma])].sup.[Psi]]. (A.10)

Using prime notation for simple derivatives (e.g., [f[prime].sub.1] = [df.sub.1]/d[Mu]) and subscript notation for partial derivatives (e.g., [h.sub.1v] = [Delta][h.sub.1]/[Delta]v), the first-order conditions dSW/d[Mu] = 0 and dSW/dv = 0 may be divided through by the factor [f.sub.1][g.sub.1][h.sub.1][f.sub.2][g.sub.2][h.sub.2] and then manipulated into the following respective forms:

[f.sub.1][g.sub.1][h.sub.1]/[f.sub.2][g.sub.2][h.sub.2] = -[N.sub.1]/[N.sub.2] (A.11)

where:

[N.sub.1] = ([f[prime].sub.2]/[f.sub.2]) + ([g[prime].sub.2]/[g.sub.2]) + ([h.sub.2[Mu]]/[h.sub.2]) (A.12)

[N.sub.2] = ([f[prime].sub.1]/[f.sub.1]) + ([g[prime].sub.1]/[g.sub.1]) + [h.sub.1[Mu]]/[h.sub.1]) (A.13)

and

[f.sub.1][g.sub.1][h.sub.1]/[f.sub.2][g.sub.2][h.sub.2] = -[R.sub.1]/[R.sub.2] (A.14)

where:

[R.sub.1] = [h.sub.2v]/[h.sub.2] (A.15)

[R.sub.2] = [h.sub.1v]/[h.sub.1]. (A.16)

Since the LHS of (A.11) and (A.14) are the same, we have that:

[N.sub.1]/[N.sub.2] = [R.sub.1]/[R.sub.2]. (A.17)

Through substitutions from (A.5) through (A.10) and various of their derivatives into (A.17), we find that:

(1 - [Mu])/[Mu] = ([Delta](1 - [Mu]) + (1 - v)(1 - (1 - [Mu])[Delta] - [Mu][Gamma]))/([Gamma][Mu] + v(1 - (1 - [Mu]) [Delta] - [Mu][Gamma])). (A.18)

Solving (A.18) for v as a function of [Mu]:

v = ([Mu](1 - [Gamma]))/(1 - (1 - [Mu])[Delta] - [Mu] [Gamma]). (A.19)

Therefore, if we can find the optimal [[Mu].sup.*], we can obtain the optimal [v.sup.*] from (A.19).

Through substitutions from (A.5) through (A.10) and various of their derivatives into (A.17), we find that:

([Delta](1 - [Mu]) + (1 - v)(1 - (1 - [Mu]) - [Mu][Gamma]))/([Gamma][Mu] + v(1 - (1 - [Mu]) - [Mu][Gamma]))

=(-[Mu](1 - [Psi](1 - [Delta] - [Gamma])) + (1 - [Psi](1 - [Gamma])))/([Mu](1 - [Psi](1 - [Delta] - [Gamma])) - [Psi][Gamma]). (A.20)

Since the RHS of (A.18) equals the LHS of (A.20), we have that:

(1 - [Mu])/[Mu] = (-[Mu](1 - [Psi](1 - [Delta] - [Gamma])) + (1 - [Psi](1 - [Gamma])))/([Mu](1 - [Psi](1 - [Delta] - [Gamma])) - [Psi][Gamma]). (A.21)

Equation (A.21) determines the optimal [Mu]; substituting this into equation (A.19) determines the optimal v: as shown in equations (23)-(24).

1. Bergson added some nuances to his 1948 essay in an article published in 1967 in the JPE [3]. Note should also be taken of Hayek's rather strident 1940 critique of Lange in Economica [12]. Several other authors have commented on Lange over the years, including Feiwel [9], Domar [7], Milenkovitch [16], and Bennett [1].

2. Several representative textbook treatments of Langian market socialism are as follows: Carson [5, Chapter 19]; Neuberger and Duffy [19, Chapter 8]; Holesovsky [13, Chapter 6]; Elliott [8, Chapter 15]; Gregory and Stuart [11, Chapter 5]; Gardner [10, Chapter 10]; Zimbalist, Sherman and Brown [47, Chapter 13].

3. Benjamin Ward followed up on his 1958 AER article with a book-length treatise published in 1967 [38]. For surveys of the steadily expanding theoretical and empirical literature on cooperative production, see Steinherr [34], Pryor [23], and Bonin, Jones and Putterman [4]. Although the economic literature on cooperative market socialism is predominantly negative, there have been some serious economic advocacies of this system: see Vanek [35, 36], Schweikart [28, 29], Nove [21, 22], and Dreze [6].

4. Prior to the emergence of profit-oriented market socialism in the published literature, there was apparently an oral tradition on the concept. The famous Austrian economist Ludwig yon Mises criticized it under the designation "artificial market" in the revised English edition of Socialism: An Economic and Sociological Analysis [18]. See Yunker [42] for a critique of Mises's critique of the "artificial market."

5. The traditional socialist emphasis on egalitarianism suggests the preferability of equal distribution of social dividend as a lump sum subsidy paid to each household. However, profit-oriented market socialism represents an effort to find a new direction for socialism, and is not unduly influenced by traditional socialist viewpoints. In any event, egalitarianism may be pursued through progressive taxation and the welfare system, and does not have to be pursued through the distribution of social dividend. Yunker [43, 45] presents a comprehensive case against equal distribution of social dividend income and for unequal distribution in proportion to household labor income.

6. Tables 3.2, 3.3 and 4.3 in Killingsworth's survey [14] contain some 73 labor supply elasticity estimates for men: the mean estimate is -0.134 with a standard error of 0.185. By standard statistical methodology, the null hypothesis that the supply elasticity of labor for men is zero cannot be rejected.

References

1. Bennett, John, "Planning under Market Socialism When Iteration Is Incomplete." Journal of Comparative Economics, September 1985, 252-66.

2. Bergson, Abram. "Socialist Economics," in A Survey of Contemporary Economics, edited by Howard Ellis. Philadelphia: Blakiston, 1948, pp. 412-48.

3. -----, "Market Socialism Revisited." Journal of Political Economy, October 1967, 655-73.

4. Bonin, John P., Derek C. Jones, and Louis Putterman, "Theoretical and Empirical Studies of Producer Cooperatives: Will the Twain Ever Meet?" Journal of Economic Literature, September 1993, 1290-320.

5. Carson, Richard L. Comparative Economic Systems. New York: Macmillan, 1973.

6. Dreze, Jacques H. "Self-Management and Economic Theory: Efficiency, Funding, and Employment," in Market Socialism: The Current Debate, edited by John Roemer and Pranab Bardhan. New York: Oxford University Press, 1993, pp. 253-65.

7. Domar, Evsey, "On the Optimal Compensation of a Socialist Manager." Quarterly Journal of Economics, February 1974, 1-18.

8. Elliott, John E. Comparative Economic Systems, second edition. Belmont, Calif.: Wadsworth, 1985.

9. Feiwel, George R. "On the Economic Theory of Socialism: Some Reflections on Lange's Contribution." Kyklos, 1972, 601-18.

10. Gardner, H. Stephen. Comparative Economic Systems. Chicago: Dryden Press, 1988.

11. Gregory, Paul R., and Robert C. Stuart. Comparative Economic Systems, second edition. Boston: Houghton Mifflin, 1985.

12. Hayek, Friedrich. "Socialist Calculation: The 'Competitive Solution,'" Economica, May 1940, 125-49.

13. Holesovsky, Vaclav. Economic Systems: Analysis and Comparison. New York: McGraw-Hill, 1977.

14. Killingsworth, Mark R. Labor Supply. Cambridge: Cambridge University Press, 1983.

15. Lange, Oskar. "On the Economic Theory of Socialism." Review of Economic Studies, October 1936, 53-71, and February 1937, 123-42. Issued in book form with contributions by Benjamin Lippincott, ed., and Fred M. Taylor: University of Minnesota Press, 1938. Reprinted by McGraw-Hill, 1964.

16. Milenkovitch, Deborah D. "Is Market Socialism Efficient?" in Comparative Economic Systems: An Assessment of Knowledge, Theory and Method, edited by Andrew Zimbalist. Boston: Kluwer-Nijhoff, 1984, pp. 65-108.

17. Mirrlees, James A., "An Exploration in the Theory of Optimum Income Taxation." Review of Economic Studies, April 1971, 175-208.

18. Mises, Ludwig von. Socialism: An Economic and Sociological Analysis, revised English edition. New Haven: Yale University Press, 1951.

19. Neuberger, Egon and William J. Duffy. Comparative Systems: A Decision-Making Approach. Boston: Allyn and Bacon, 1976.

20. Ng, Yew-Kwang, "Bentham or Nash? On the Acceptable Form of Social Welfare Functions." Economic Record, 1981, 238-50.

21. Nove, Alec. The Economics of Feasible Socialism. London: George Allen and Unwin, 1983.

22. -----, The Economics of Feasible Socialism Revisited. New York: Harper Collins Academic, 1991.

23. Pryor, Frederick L., "The Economics of Production Cooperatives." Annals of Public and Cooperative Economy, June 1983, 133-73.

24. Roemer, John E., "Market Socialism - A Blueprint: How Such an Economy Might Work." Dissent, Fall 1991, 562-75.

25. -----, A Future for Socialism. Cambridge, Mass.: Harvard University Press, 1994.

26. ----- and Pranab Bardhan, "Market Socialism: A Case for Rejuvenation." Journal of Economic Perspectives, Summer 1992, 101-16.

27. Roemer, John E. and Joaquim Silvestre. "Investment Planning in Market Socialism," in Market Socialism: The Current Debate, edited by John Roemer and Pranab Bardhan. New York: Oxford University Press, 1993, pp. 108-19.

28. Schweikart, David. Capitalism or Worker Control? An Ethical and Economic Appraisal. New York: Praeger Publishers, 1980.

29. -----, Against Capitalism: Reviews of Capitalism or Worker Control. Cambridge: Cambridge University Press, 1993.

30. Stauber, Leland G., "The Implications of Market Socialism in the United States." Polity, Fall 1975, 38-62.

31. -----, "A Proposal for a Democratic Market Economy." Journal of Comparative Economics, September 1977, 235-58.

32. -----, A New Program for Democratic Socialism. Carbondale, Ill.: Four Willows Press, 1987.

33. -----, "A Concrete Proposal for a Market Socialism for Large Enterprises: Reactions from West and East and Further Discussion." Coexistence, September 1993, 213-35.

34. Steinherr, Alfred. "The Labor-Managed Firm: A Survey of the Economics Literature." Annals of Public and Cooperative Economy, April-June 1978, 129-48.

35. Vanek, Jaroslav. The General Theory of Labor-Managed Market Economies. Ithaca, N.Y.: Cornell Univ. Press, 1970.

36. -----, The Participatory Economy. Ithaca, N.Y.: Cornell Univ. Press, 1971.

37. Ward, Benjamin. "The Firm in Illyria: Market Syndicalism." American Economic Review, June 1958, 566-89.

38. -----. The Socialist Economy: A Study of Organizational Alternatives. New York: Random House, 1967.

39. Yunker, James A. "A Survey of Market Socialist Forms." Annals of Public and Cooperative Economy, April-June 1975, 131-62.

40. -----. "The Microeconomic Efficiency Argument for Socialism Revisited." Journal of Economic Issues, March 1979, 73-112.

41. -----. "A New Perspective on Market Socialism." Comparative Economic Studies, Summer 1988.

42. -----. "Ludwig von Mises on the 'Artificial Market.'" Comparative Economic Studies, Spring 1990, 108-40.

43. -----. "The Equity-Efficiency Tradeoff under Capitalism and Market Socialism." Eastern Economic Journal, January 1991, 31-44.

44. -----. Socialism Revised and Modernized: The Case for Pragmatic Market Socialism. New York: Praeger Publishers, 1992.

45. -----. Capitalism versus Pragmatic Market Socialism: A General Equilibrium Evaluation. Norwell, Mass.: Kluwer Academic Publishers, 1993.

46. -----. "Agency Issues and Managerial Incentives: Contemporary Capitalism versus Market Socialism," in Research in Political Economy, edited by Paul Zarembka. Greenwich, Conn.: JAI Press, 1994, pp. 1-61.

47. Zimbalist, Andrew, Howard J. Sherman, and Stuart Brown. Comparing Economic Systems: A Political-Economic Approach, second edition. Orlando, Florida: Academic Press, 1989.