All economic theories have some implicit or explicit definition of productive activities in the economy.2 In other words, they don't hold all sectors in society as productive of its wealth. For example, it is common to view `public administration' as a consumer of social wealth, regardless of its necessity for political stability etc. A consistent definition of productive sectors is crucial to understand the real surplus capacity of society.
This issue has been addressed in heterodox economic literature (for example Shaikh and Tonak, 1994). The analysis among Marxian economists is constrained to capitalist society were an activity is considered `productive' if it produces material effects or products within capitalist relations of production. This definition, however, requires several qualifications to handle the realities of modern societies, especially involving other relations of production.
From the standpoint of materialist social theory, I will propose a definition that is simpler and hopefully more coherent.
Let us first define a sector as an activity involving labor and material resources, integrated with other such activities. Productive sectors must be considered `necessary' or `basic' in some specific economic sense because the concept implies that a fraction of its surplus supports the unproductive ones.
If the criterion is to produce commodities within capitalist firms, complications arise when one e.g. considers the armaments industry producing weapons for the state. Were it under state ownership, it would be labeled unproductive. But if it suddenly was privatized, it would become productive. Yet in the latter case the state would still have to finance its arms by taxes, so the net effect of the change on the other sectors would be none.
This example also shows that the material relations of social production become obscured by the money flows. To handle the inter-relations between different economic patterns, in different times, our analysis must start with more fundamental variables of production and consumption.
Here one can detect another complication with the criterion above. Consider an economy were all sectors except two are producing commodities within capitalist relations of production. The two remaining are public `health care' and `education' who are unproductive in capitalist society. But they arguably produce a significant part of the workers' consumption. A sector supported by the surplus labor of workers in the other sectors, yet provides their necessary means of consumption? Such a notion really puts doubt in this criterion.
The division of the total social product might however serve as a basis for a more coherent definition.
We first define an economy consisting of n sectors. The level of aggregation is not necessary to specify here. Data published by national accounting agencies usually contain about fifty to one hundred sectors, but we might as well define our economy in greater detail.
The production relations between the n sectors form a (n ×n) production matrix A, describing the technical conditions of production.3 A matrix element aij is defined as the output of sector i necessary to produce a unit of output from sector j.
The production matrix will obviously change its structure and values over time as economic patterns alter, innovations are applied, new sectors are formed and old ones disappear. It should be emphasized that it strictly deals with inputs of production. An electrician might need a bank account, but there is no technological reason why she couldn't perform her service without consulting a bank.
All sectors in the economy require some set of workers. Let c be the (n ×1) worker's consumption vector that describes the bundle of goods and services they consume for some time period.4 An element ci denotes their consumption of sector i:s output.
Note that workers' households for example can't consume insurances or military defense even though they pay for them, only material effects and products such as car reparations, education and oranges. Thus there will be several sectors with zero input in c.
With a production matrix A and workers' consumption vector c for some time period, we can handle several types of economies with different mixes of relations of production. This makes it possible to propose a more general definition of productive sectors that covers societies where capitalism not necessarily dominates.
To restate what has been said above: it is not sensible to view sectors that produce the workers' consumption bundle as unproductive. Further more it is clear that while workers don't consume jumbo jets, they do consume air travel that requires them. In turn, the production of jumbo jets requires various components that you wouldn't find in any household's shopping list.
There exists a bundle of goods and services necessary to sustain the worker's consumption bundle, which we can write as a (n ×1) vector c* . It is defined by the following relation: c* = Ac* + c Þ c* = (I-A)-1c . (Here I is the n ×n identity matrix.) An element c*i denotes the quantity of sector i:s output required to sustain the worker's consumption bundle. This also provides a rational basis for a definition of productive sectors:
Definition: Sector i is productive if c*i ¹ 0 , i.e. any sector that directly or indirectly sustains the workers' consumption bundle is productive.
If our economy is specified at industry level we can tell what industries are productive. If it is in greater detail we will gain information on what functions of it are productive. Our definition has some theoretical implications that are addressed below:
(a) If social production and consumption can be described by A and c, the definition is general and can be applied to a large variety of economies, including state capitalist enterprises, public sector, workers' co-operatives, peasants producing for markets and the Soviet-type economies.
Changes in A and c also make it logically possible for some sectors to shift from unproductive to productive, or vice versa, over time.
(b) The total labor-time performed by the workers in the productive sectors can now be divided into `necessary labor' required to produce their part of the consumption bundle and `surplus labor' that forms the material basis for the surplus product. Productive labor not only supports the entire working population and its dependents, but also the ruling classes of the political-economic system.
To the extent that capitalist production dominates, the ratio of surplus to necessary labor can be held equivalent to the `rate of surplus value' as Marx does in the first volume of Capital.
(c) In modern capitalist economies the more obvious unproductive sectors are public administration and the police-military apparatus, but also capitalist activities such as armaments, private guards, wholesale trade, advertisement, financial and juridical services, luxuries etc.
It is clear that such sectors or subsystem of sectors must be financed by a fraction of the surplus of productive ones, since they don't serve as input in the production of those goods and services. The surplus of the productive sectors is thus the upper limit to the size of unproductive activities. Improvement in labor productivity in such activities won't either increase the rate of surplus value.5
An appropriate definition of productive activities is crucial to understand the surplus capacity of society and to analyze where and in what is this capacity is being utilized. The definition proposed in this paper is simpler, more general and has a stronger connection to materialist social theory than what has been previously suggested by Marxian economists.
It can be used in empirical estimates of the surplus. However, the accuracy of such studies will depend on the level of aggregation of national accounting data. But if a country has a large armaments industry or public sector, one could expect the estimates to diverge significantly from the traditional definition.
1The arguments posed here I owe to Paul
Cockshott's posts on OPE-L in 2003.
2By economy we mean here activities dealing with labor-time and resources in direct relation to each other, excluding the `domestic economy' of households.
3It can be empirically approximated for some reasonable time period using input-output tables of the economy.
4Excluding the fraction of ruling groups who actually work, such as `top management' in modern capitalist firms. Depending on their privileges, their consumption will diverge significantly from the workers in the sector.
5The economic impact of unproductive activities may
however vary. See for example `military-keynesiansism'.