A Quiet Revolution in Welfare Economics- by Michael Albert and Robin Hahnel



WE BEGIN by reviewing the "old" debate about whether or not central planning can be efficient. In the context of modern mathematical programming techniques and computer capabilities, the "old" debate, brought into focus by Barone's essay "Ministry of Production" published in 1908, has been resolved in the affirmative. 1 We will extend this conclusion to the case where individuals' preferences are endogenous. But the "old" debate assumed that the Central Planning Board would have perfect knowledge of all resource availabilities, all technical capabilities of all production units, and society's social welfare function, and that all the Central Planning Board's instructions would be carried out.

Next we review the "modern" debate about information gathering difficulties and incentive problems in central planning. We analyze a number of iterative techniques designed to help the Central Planning Board gather technical data from the separate units in the economy. We review a number of approaches to formulating society's social welfare function. And we discuss incentives that might be used to induce managers and workers to carry out the plan once it is calculated. We conclude that many information and incentive problems emphasized by critics of central planning are resolvable, and that the most intractable problem-obtaining accurate information from management about productive capabilities-is not unique to centrally planned systems.

Having reviewed the "old" and "modern" debates-both conducted in terms of traditional welfare theory-we reevaluate the different iterative techniques for gathering technical information using our new welfare criteria and discover that all these techniques are cybernetic disasters from a social point of view, regardless of how successful they might be for informing central planners. This leads to our first new criticism of central planning: as necessary as consolidating data from individual production units in the hands of central planners might be for central planning to achieve efficiency, the primary cybernetic task of economic institutions appropriate for achieving self-management is to disseminate information about other production units so the members of each unit can expand their understanding of how their choices impact on others and vice versa. The techniques for processing information in central planning not only fail to do this, but accomplish just the opposite.

Next we discuss the roles inherent in central planning using our new evaluative criteria. We find the interunit roles to be irresolvably authoritarian and discuss the likelihood that their authoritarianism would spread to intraunit roles as well. We point out that apathy is the other side of the authoritarian coin and that the roles defined by central planning relegate individual production units, and most often workers within those units, to just such a condition. In this respect our work provides a theoretical basis for criticisms often voiced by analysts of central planning in practice.

But our most important new criticism of central planning derives from reanalyzing the problems associated with estimating society's social welfare function. We discover that central planning is incapable of providing selfmanaged work activities in accord with their true social opportunity costs. Even giving central planning every benefit of the doubt---eliminating the Central Planning Board from any decision-making role, formulating the social welfare function through strictly democratic procedures, and including different kinds of work activities as well as different final goods in the social objective function to be voted on-we find that central planning is inherently biased against supplying self-managed work roles.

Worse still, treating preferences as endogenous we prove that central planning's inherent bias against supplying self-managed work activities leads to a "snowballing divergence" from optimality in which the economic plan proceeds farther and farther from an optimal use of society's laboring capacities as time goes on. When viewed in terms of human development, this snowballing divergence displays itself as an ever-increasing apathy of the executors of economic activities as they accommodate to the absence of opportunities for self-managed work activities.

We conclude with some observations on how the institutions of central planning might be expected to affect the disposition of classes in public ownership economies. We suggest that the institutions of central planning contribute to the development and strengthening of a coordinator class separate from, and with interests opposed to, ordinary workers in such economies.



9.1 A Centrally Planned Public Enterprise Economy

We begin with a moderately complex model that could be used to calculate a central plan for an economy.


9.1.1 Model 4: The Central Planning Problem

M 4. 1. The time horizon for the plan in Model 4 is t = 1, 2, ... T.

M 4.2. The gross outputs of produced goods i and j in period t are xi (t) and xj(t) respectively, where i, j = 1, 2, ... c.

M 4.3. The number of different processes for making good i are p = 1, 2, ... P(i). The number of different ways to add to capital stocks are r = 1, 2, ...R(s).

M 4.4. There are L different kinds of labor and primary (nonproducible) factors of production, l = 1, 2, ...L, and for each time period there exists a certain amount of each of these factors including man/woman hours for labor categories and physical quantities for land, minerals, etc. The available supplies are taken as "given." Zl(t) stands for the amount of factor I available in period t . Zl (t) stands for the amount of factor l actually used in the production program in period t .

M 4.5. xjp(t) stands for the amount of good j produced in period t via process p. The total amount of good j produced in period t is:

M 4.6. aijp(t) stands for the amount of i needed to make one unit of j via processp in period t .

M 4.7. Ss(t) stands for the stock of capital good s in existence at the outset of period t , where s = 1, 2,...m < c.

M 4.8. dSs(t) stands for the addition to stock of capital good s in period t . And %Ss(t) stands for the fraction of capital good s that physically depreciates in period t , which we assume to be independent of usage.

M 4.9. aljp(t) stands for the amount of primary factor l needed to make one unit of good j via process p in period t .

M 4. 10. Ssjp(t) stands for the amount of stock of capital good s we must have on band to produce one unit of good j via process p in period t .

M 4.11. lisr stands for the total amount of good i that must be set aside (invested) in all prior periods to obtain one unit increase in the stock of capital good s via process r.

M 4.12. iisr(tlt') stands for the fraction of Iisr that must be invested in period t to help produce one more unit of capital good s in later period t ' via process r. Thus, [iisr(t|t')] [Iisr] stands for the amount of i that must be set aside in period t to help get one more unit of stock of s in period t ' via process r, where:

M 4.13. Qi(t) stands for the final consumption of good i in period t .

The Central Planning Board is provided society's "social welfare function" containing society's relative valuation of all final consumption goods and labor activities.2

The simplest case would be a linear social welfare function where vi(t) stood for the relative social value of one unit of consumption good i at period t , and where wl(t) stood for the relative social value of one unit of primary factor I at period t . For all l that correspond to a specific kind of labor activity, the wl(t) would represent the relative disutility of performing an hour's worth of that activity. For all l that stand for nonlabor primary factors there is no reason they would not have wl(t)'s equal to zero, for even with T a finite time period, we do not accumulate stocks of these nonproductive inputs in our model; they simply appear in certain quantities each time period, and would presumably do so in the future.

In the case of a finite time period, however, we would have to set some positive social values on the different stocks of produced goods in the last time period if we are not to totally ignore the well-being of generations to live after time period T .For now, assume the planners know the valuations for capital goods s, ys(T) as well.

An easy way to handle the more general case of a nonlinear social welfare function, where the relative social value of a unit of any final good or labor activity depends on both the absolute and relative amount of the good or activity that was being consumed, would be to simply interpret the vi(t)'s and wl(t)'s as functions of all the Qi(t)'s and Zl(t)'s.

M 4.14. That is

where this formulation allows for the usual substitutes and complements. Finally, we are ready to state the Central Planning Board's programming problem: Maximize social welfare

subject to the following constraints:

1. Producing enough of each good in each year to meet its intermediate, investment, and final consumption uses as expressed by the cXT inequalities

(for i = 1, 2,... c and t = 1, 2,... T):

2. Having at least the minimum amount of all the necessary capital stocks available at each time period for the production of each good as expressed by the mxT inequalities (for s= 1.... m and t = 1,...,T):

3. Having at least the minimum amount of all the necessary primary, nonproducible factors like labor, land, etc., available at each time period for the production of all goods as expressed by the L x T inequalities (for l = 1, 2,... L and t = 1, 2.... T):

For this problem, the givens are the aijp(t)'s, aljp(t)'s, Ssjp(t)'s, iisr(tIt')'s, Iisr's, and %Ss(t)'s, which are production, investment, and depreciation coefficients; and the

's and Ss(0)'s, which are stocks of primary factors and initial capital goods; and the vi(t)'s, wl(t)'s and ys(T)'s, which are the relative values of different goods, work activities, and final stocks. The "decision" variables for the Central Planning Board are the xjp(t)'s and the Qi(t)'s, which imply the ZI(t)'s and Ss(t)'s.



9.2 Round One: Efficiency of Central Planning

9.2.1 Calculating the Plan

Although the only feature essential to our purposes is that the planning model be multiperiod, we have included a limited number of complications that hint at the complexity any realistic situation entails. Model 4 allows:

1. Planning over many time periods

2. A number of different nonproducible, or primary inputs, including different kinds of labor services

3. The necessity of having stocks of different "capital" goods in place as well as intermediate and primary inputs for production to take place

4. A variety of different production techniques for producing a variety of different intermediate and final goods

5. A variety of different processes by which the stocks of "capital" goods can be increased allowing variation in inputs and in the timing of their application

Although we included in Model 4 the possibility that different kinds of labor activities might have different effects on social welfare, and will discuss this case in a later section, the "traditional" debate about the efficiency of central planning considered only final consumption goods to be of welfare significance. It treated different categories of labor only as limiting primary factors. Model 4 can be easily adapted to the "traditional" debate by excluding the second set of terms in the planning board's objective function in the definition of the planner's problem.

The central planner's problem can be formulated as a linear programming problem where the different social evaluations of final goods are presumed constant and production technology is presumed to exhibit constant returns to scale. In the more realistic case of relative valuations of final goods being functions of relative amounts of final goods provided, and nonlinear production technologies, two approaches are available.

We could reformulate the planning problem as a nonlinear programming problem in either the objective function, the constraints, or both. Or more practically, we could incorporate the more realistic elements within the framework of linear programming by using a variety of well-known artifices. To account for economies of scale within a linear framework one can define new activity vectors and new units of output for larger and smaller scale operations. To account for nonlinear social preferences one can define new variables in the objective function for different ranges of output and introduce new constraints limiting the range of possible values these new output variables can take. In this case Model 4 can be interpreted as allowing for these additional elements of realism within a linear framework.

But whether we use artifices to retain linear forms, or explicitly formulate a nonlinear programming problem, solutions maximizing social welfare, and a number of algorithms for finding them, are known to exist, 3 and there is no need to belabor these technical matters here.

The point is that in light of modern mathematical programming theory and computer capacity, the "old" debate about whether a centrally planned economy can be efficient is settled in the affirmative provided one can assume the planning board

1. Has perfect knowledge of initial capital stocks and primary resource and labor availabilities

2. Has complete information about the technical coefficients of all the different production processes

3. Possesses an accurate social welfare function to be used as the objective function in the programming problem

4. Has a sufficiently large computing facility

5. Will have its plan carried out

The "modern" debate about the efficiency of central planning has revolved precisely around whether or not these assumptions can be justified. But before considering various schemes for solving information and incentive problems in centrally planned economies, we first need to address the distribution of final goods among the different consumers and the assignment of particular individuals to specific jobs. For while a Central Planning Board might achieve a socially optimal production plan, this does not guarantee Pareto optimality unless the assignment of work and distribution of final goods is also carried out efficiently.

When the Central Planning Board calculates an optimal plan, it arrives at a complete list of all the inputs each unit is to receive and the outputs each unit should produce. Included among the list of inputs are the number of hours of different categories of labor services that each unit is to use, but this is not the same as a list of who will be assigned to which units. Similarly, when the amount of each product needed in production and for investment is subtracted from the gross output of that good we arrive at the net output of each good available for consumption. But this is not the same as a list of the amounts of each final good to be distributed to each consumer. In other words, even if we assume that an optimal plan has been calculated and carried out, some system of distribution of final goods and job assignments is needed. Obviously inefficiencies could arise in these aspects of a centrally planned economy as well. Next we describe a few ways by which distribution and job assignment could be carried out, along with the necessary conditions for them to achieve Pareto optimality , to illustrate just how markets are, and are not, related to efficiency in central planning.

9.2.2 Distribution of final Goods

1. The Central Planning Board could distribute arbitrary portions of each final good, in each time period, to each member of society.

Of course giving equal portions of each good in each time period to each citizen would be one such distribution. But less egalitarian possibilities abound. To preserve optimality under any chosen scheme, all citizens would have to be free to trade whatever goods they initially received (both within and across time periods), and we would have to assume that the absence of any prohibition on such trading resulted in the successful conclusion of all mutually beneficial transactions. In other words, the government would have to sanction a "white market" in final goods rather than confining such operations to a "black market."

2. Alternatively, the Central Planning Board could create a number of distribution centers to which people were assigned and distribute some particular quantity of each final good to each distribution center in each time period.

Assigning an equal number of people to each center and supplying each center with an equal portion of each good in each time period, again, is one possibility among many. In any case, the members of each distribution center could be left to decide how to distribute whatever goods the center received. But even if we assume that the distribution among members leaves no possible mutually beneficial transactions between members, we would have to assume that centers were permitted to trade their goods (both within and across time periods), and that this trading opportunity resulted in the conclusion of all mutually beneficial transactions between centers in order to guarantee Pareto optimality .

Under both these methods of distribution any degree of egalitarianism is theoretically possible. There are no formal markets in either system. (There is not even any currency.) But as anyone trained in economics will have recognized, the absence of markets is something of a sleight of hand. There are no markets only because all Pareto improvements achievable through exchange are left to individuals to work out for themselves. It is not difficult to visualize how individual barter exchange would quickly lead to more and more extensive "classified" sections in newspapers and eventually monetized markets for final goods. After all, for all the faults we found with money and markets in chapter 7, we never claimed they did not serve a practical cybernetic function in particular situations. In a cybernetic vacuum it is predictable markets would appear. And if the alternative is no information, or information only at great expense of time and effort, it is reasonable to consider the emergence of markets a social improvement. In light of which

3. The Central Planning Board could introduce currency, retail outlets, and savings and loan banks.

Each individual could be given some amount of currency in each time period, and all final goods could be sent to retail outlets. The managers of retail outlets could be directed to adjust prices to ensure that each good disappeared from the shelf on the last day of each month, just prior to next month's deliveries. People would freely loan or borrow from the banks, whose managers would have to finance loans out of savings deposits, adjusting interest rates to eliminate excess deposits or loan applications. Provided the retail (and bank) managers perfected the art of having "empty shelves" just prior to new deliveries, this method would also result in Pareto optimality . And this holds, of course, without regard to how much currency each individual is allotted. 4

Obviously, a number of different criteria could be used in deciding how much currency to give each individual, but the Pareto optimality of central planning would be preserved under any currency distribution provided we assume the production plan is carried out. If one were concerned with economic equality

3a. Each individual could be given the same amount of currency.

On the other hand, if one were concerned that the plan may not be carried out unless individuals are provided strong material incentives to exert effort in their work assignments and develop productive skills, other differential currency disbursements come to mind. For instance:

3b. The Central Planning Board could give out different amounts of currency to employees in different production units according to how closely the unit came to fulfilling its part of the production plan

3c. The Central Planning Board could distribute different amounts of currency to different categories of labor depending on how many years of education were required on average to achieve a certificate of competence in that field

3d. The Central Planning Board could do studies to rate different jobs according to relative difficulty and burdensomeness and design pay scales accordingly

3e. The Central Planning Board could give currency to the personnel departments of production units with which to hire workers. Workers would freely seek employment wherever they chose, and personnel departments would freely hire any they wished from among those who applied. Since this last "criterion" for differential currency disbursement is also one way of assigning people to jobs, we will discuss different systems for allocating labor via "free" labor markets next.


9.2.3 Job Assignment

In examining different possible systems of job assignment we should remember that the Central Planning Board was assumed to have perfect knowledge of the amount of all different "primary" inputs available-including the number of people capable of performing each different kind of labor service. Moreover, as part of calculating an optimal production plan the Central Planning Board calculated the number of people in each labor category to be assigned to work at each production unit. What is less obvious is that in calculating an optimal production plan the Central Planning Board also necessarily calculates the social value (or opportunity cost) of each scarce input used in producing the optimal production plan, including each category of labor. In mathematical programming language, those opportunity costs are called "shadow prices" and are the well-known solutions to the "dual" programming problem. They are easily (and often automatically) generated along with the optimal production plan that is the solution to the "primal" programming problem. This means that the Central Planning Board also knows the opportunity costs of different categories of labor when they are employed to produce an optimal production plan.

1. The simplest method of job assignment would be for the Central Planning Board to send a letter to each individual in each labor category telling him or her where to report to work. The Central Planning Board could make the assignments on any basis they wished-randomly, alphabetically, etc.

2. The Central Planning Board could leave the specific assignments up to associations of individuals in each labor category. The Central Planning Board would send the associations a list of how many of their members should report to each production unit in the economy and let the associations decide who goes where. This might be done within any given association by lottery, seniority, or voting, or with an eye to work and educational incentives. It might be done according to members' work ratings in their previous employment(s) or their academic standing in the educational process that qualifies them as members of the association.

Although the "old" debate did not countenance differential welfare effects of different work assignments, in fact the situation is theoretically symmetrical to that of differential welfare effects of different consumption bundles. In this context, for either of the above systems of job assignments to be Pareto optimal , one must assume that all mutually beneficial trades of work assignments between similarly qualified individuals were both permitted and exhausted before people showed up to work. But under this assumption of ex post "white markets" within labor categories, both assignment system I and 2 would satisfy the criterion of efficiency without resort to formal labor markets.

3. The Central Planning Board could establish a "free" labor market in the sense that individual workers would be "free" to search and apply wherever they chose, and the personnel departments of different units would be "free" to hire whomever they preferred.

It is important to realize, however, that such a "free" labor market could operate in three very different ways.

3a. Under one system the number of workers hired in each category by each production unit, as well as the pay rates for each category of worker, would be determined by the Central Planning Board as part of the overall production plan. The only decisions left up to individual personnel departments would be which individuals to hire into positions -and pay rates already determined by the central plan.

Personnel departments would not be authorized to hire fewer workers of one category and more of another. Nor would they be authorized to pay wages different from those set by the Central Planning Board. In other words, production units would not be permitted to make "input" substitutions or payments differing from nationwide pay scales which the Central Planning Board could set equal to the labor "shadow prices" calculated from the optimal production plan. This would be analogous to the management of a privately owned firm telling its personnel department how many positions of each kind it was to fill, what wages those individuals would be paid, and leaving only the hiring of particular employees to the personnel department.

3b. Alternatively, the Central Planning Board could allocate to each production unit a wage fund and leave to the units all decisions about how many workers to hire in each category and what to pay them.

To determine the size of the wage fund to be given each unit the Central Planning Board would calculate the number of employees in each category who should work in that production unit according to the Central Planning Board's optimal production plan, multiply the number in each category by what the CPB calculated to be the "shadow price" of that particular scarce labor resource, and deliver the sum total as the wage fund of the production unit. Then the personnel department of each production unit could hire whichever individuals in whatever labor categories it wished, paying them whatever it wished, subject only to the constraint of not exceeding its total wage fund. This would be analogous to the management of a private firm giving its personnel department a budget and allowing it to hire and pay from that budget as it deemed fit.

3c. A third system is a combination of the first two. The Central Planning Board would fix the number of employees to be hired in each category in each production unit, as in the first case. But the personnel departments would have discretionary powers over wages they contracted to pay particular employees out of a wage fund that was calculated by the Central Planning Board as in the second case.

This system would be analogous to the management of a private firm determining how many of each kind of worker to be hired, but allowing the personnel department to decide who to hire and how much to pay them within an operating budget.

Although the "free" labor market obviously differs in the three different cases, each has a claim to efficiency under a particular set of assumptions. Under the assumptions of Model 4, planners are assumed to have perfect knowledge about the desirabilities of all goods and work activities, the availabilities of all primary inputs including labor, and the technologies available to all units. Moreover, the quantities of different categories of labor supplied as well as the effort exerted are assumed independent of wage rates. Under these assumptions the Central Planning Board is in a position to calculate optimal allocations of labor as well as "efficiency" wage rates. But once labor supply is assumed exogenous, not only is system 3a perfectly efficient with "efficiency" wages, the Central Planning Board would be free to set wage rates according to any equity criterion without affecting economic efficiency, 5 permitting maximum flexibility regarding the degree of equality (or inequality) in the distribution of labor income.

On the other hand, if the central planners lacked accurate information about the possibilities of substitution between different labor categories in individual units, as well as information about differential preferences for different kinds of work, system 3b would have greater claim to efficiency. But while system 3b is highly flexible in the sense that it allows maximum room for individual negotiation for both prospective employees and employers, it would be inflexible regarding the degree of equality or inequality of labor incomes that could be arranged since the distribution of labor income would be determined by the forces of supply and demand. 6

Finally, if the central planners had accurate information concerning labor availabilities and the production possibility sets of the units, but lacked accurate information on differential work preferences, system 3c would have greater claims to efficiency.

Before proceeding, we consider a final issue regarding labor assignments totally ignored in the "old" debate about central planning and efficiency. Whether the central planners fix hiring quotas and pay rates, allocate wage funds to production units, or fix hiring quotas but leave pay rates to production unit discretion within a budget, if the differential desirabilities of work in different units (units in Siberia versus units in Moscow) are ignored, less attractive units will have difficulty competing with more attractive units for the better workers within categories. The "old" debate did not consider differential preferences regarding work location any more than it did differential preferences for job types. But once we recognize this issue, it is clear all the above "labor market solutions" to the job allocation problem of central planning would be subject to inefficiencies if any such differences were not accounted for. To correct this failing, central planners would have to enable units that proved only able to hire from the bottom of the various labor category barrels to pay higher than average wage rates. In system 3a this would entail authorizing higher pay scales in all categories of employment in relatively less attractive enterprises. In systems 3b and 3c planners would have to allocate larger wage funds to less attractive units.

9.2.4 Summary of the "Old Debate"

We hope our treatment of final good distribution and job assignment served to illustrate the following points:

1. From the perspective of traditional welfare theory and under the terms of the "old debate," not only can efficient plans be calculated via central planning, but the distribution of final goods and job assignments can be carried out in efficient ways that do not necessarily employ currency, formal markets for final goods, or formal labor markets.

2. Although centrally planned systems deemed efficient by traditional welfare theory can, in theory, operate without markets of any kind, the vision is artificial. If one accepts traditional welfare theory's view of the possibility of Pareto improvements through exchange of anything that individuals might value (goods or jobs), any system of central planning that does not employ markets to distribute goods or assign people to jobs would quickly generate them or suffer from distributional inefficiencies.

3. Final goods markets and labor markets can be part of a centrally planned system without affecting the mixture of final goods and job roles. The optimal mixtures can be determined by the central planning procedure with markets used only for distribution and assignment. 7

4. On the other hand, final goods and labor markets can be used in a way that allows them not only to distribute goods and assign jobs that have already been planned, but to influence the quantities of different final goods and jobs the system settles on. We defer explaining exactly how this can be done to our discussion of different ways for determining the relative social values of different final goods and work activities in the social welfare function. But it is important to distinguish here between these two very different uses of final good and labor markets in centrally planned systems.

5. An improved version of the "old" debate, still from the perspective of traditional welfare theory, would be to recognize the symmetry between differential preferences for final goods and differential preferences for different kinds of work by including different job types and locations, along with final goods, in the social welfare function.

6. Still, our major conclusion is that if the central planners are presumed to have all relevant information, an optimal plan can be calculated, and distribution and job assignment could be handled in a number of different ways that would preserve the efficiency of central planning as judged by traditional welfare theory.

But before leaving the "old" form of the traditional debate to focus on the "modern" debate concerning information and incentive problems, we consider the efficiency of central planning under the assumption of endogenous preferences.

9.2.5 The "Old Debate" and Endogenous Preferences

If the Central Planning Board is assumed to know both the developmental as well as fulfillment effects of economic activity-that is, if the Central Planning Board knows the true social welfare function-the demonstration that the central planning can be efficient even under the assumption of endogenous preferences is straightforward. In this case, the different social evaluations of final goods and labor activities in the objective function are interpreted to be not only functions of the relative amounts of different final goods and labor activities consumed in the given time period, but functions of the relative amounts of different final goods and labor activities to be consumed in later time periods as well. In this way the future developmental effects of different production plans would be included in the social welfare function as well. In other words, in our Model 4 we would want 4.14 to become:

If we extend this further knowledge to the Central Planning Board, the plan they calculate would obviously be optimal under endogenous preferences, just as when preferences were assumed exogenous. This completes our review of the "old" debate about the efficiency of centrally planned economies where informational and incentive problems are "assumed away." 8


9.3 Round Two: The "Modern Debate"

The planning bureau cannot be aware of all the information needed for a perfect description of techniques. These are too numerous, complex, and diverse. Only the individual firms or highly specialized industry offices can have precise knowledge of the conditions governing production in their particular field. Some way must, therefore, be found for these firms and offices to participate in the preparation of the plan. 9

What Malinvaud means here by "participate" is to provide information to the Central Planning Board that will allow the Central Planning Board to calculate an optimal production plan. We now investigate procedures for accomplishing this aim. 10