A note on labor theory of value based on Luigi Pasinetti 

The basic problem of labor theory of value is that it is too narrow. Labor does not include resources. In practice, the labor theory of value adds an extra concept, rent, to complete the value chain. But there is no intrinsic relation between the labor part of value and rent.

Luigi Pasinetti is generally regarded as the heir of the labor theory of value. We will discuss his work, Pasinetti, L. [1977], Lectures on the theory of production, MacMillan,  on labor theory of value. In his work, rent takes the following form,

R = f(N) – N*f’(N)

R: rent

f(N): output as a function of the amount of labor

N: number of labor

Here f’’(N) is assumed to be negative.

We will analyse the property of R = f(N) – N*f’(N). First assume f(N) is linear.  R = 0.  We can add a tiny term that makes f(N) satisfies condition f’’(N) <0, such as f(N) = N + a*ln(N), where a is small. In this case, R will be very small. This shows the model doesn’t reflect reality well. In his theory, the rent is entirely determined by the function of output based on labor, that is, R = f(N) – N*f’(N). The amount of resource has nothing to do with value. This is the fundamental problem for the labor theory of value.

In an Arrow Debreu world, people can survive easily on Mars. Similarly, in a Luigi Pasinetti world, people can survive easily on Mars. That is their common problem.

The following are some additional comments on labor theory of value, based on Luigi Pasinetti presented on Wikipedia.

K = W

K: Capital

W: Total wages

In this model, capital is working capital, the total wages of the workers. This might not reflect the most important part of the capital, the fixed investment or fixed cost in production.

I/K = g_n,

I: Total investment

g_n: natural rate of growth

In our theory, there is no natural rate of growth. The rate of growth is determined by our ability to utilize resources. The growth rate can be high, can be low, can be positive, can be negative. There is nothing natural about the growth rate.

In the labor theory of value, equilibrium is determined by the subsistence wage rate. This is different from the marginal utility theory, where equilibrium represents the optimal state, or Pareto optimal state.

The key factor in determining high return is the ability to maintain monopoly or oligarchy. Otherwise, competition will drive return, or wage, to low levels. Many factors, such as propensity to save by labor or capitalists, in the standard models are not very important.

Moreover, the production function has been a powerful instrument of miseducation. The student of economic theory is taught to write O  f(L,C), where L is a quantity of labour, C a quantity of capital and O a rate of output of commodities. He is instructed to assume all workers alike, and to measure L in man-hours of labour; he is told something about the index-number problem involved in choosing a unit of output; and then he is hurried on to the next question, in the hope that he will forget to ask in what units C is measured. Before ever he does ask, he has become a professor, and so sloppy habits of thought are handed on from one generation to the next.³¹

— J. Robinson

·       From Harcourt, G. and Laing N. (eds.) [1971], Capital and Growth, Penguin Modern Economics Readings.    P 47

The third point is of a methodological nature, and is probably the most important of all. Following the Classical economists, Pasinetti thinks that it is possible to frame the study of natural economic systems, i.e., economic systems free of institutions. In these natural systems it is possible to deduce a series of characteristics, principles and general laws, which are independent of the institutions that have to be introduced in later stages of investigation. These institutions are the ones that shape the features of real economic systems: for instance, a capitalist system or a socialist system. As he says, “is a distinctive feature of the present theoretical scheme to begin by carrying out the whole analysis at a level of investigation which the Classical economists called ‘natural’, that is to say, at a level of investigation which is so fundamental as to be independent of the institutional set-up of society”

Pasinetti, L. [1981], Structural Change and Economic Growth: a Theoretical essay on the dynamics of the wealth of nations, Cambridge University Press  p.xii.

The second finding is that because of changing consumer preferences over time, it is inevitable that (short term) sectorial imbalances will arise due to the changing structure of the demands for goods. Therefore, this will be a permanent source of disequilibrium in the system.

Comment: Disequilibrium is a concept attached to equilibrium in economic theory. It is different from the concept of non-equilibrium in physics.