Luigi Pasinetti - Theoretical Contributions - The Cambridge Equation With The Public Sector

The Cambridge Equation With The Public Sector

Already in the 70's the debate of the original Pasinetti Theorem, and hence the Samuelson-Modigliani's interval, took a turning point, by reaching a second phase in which “many authors proceeded to relax assumptions, trying out new hypotheses and introducing complications of all sorts”. Indeed, already in the 60s some economists, inspired by Kaldor's paper of 1966, began to introduce in the Cambridge model some issues related to financial assets, interest rates and the functioning of financial markets and big corporations. All these contributions, as well as those which were made later in the 1970s and 1980s, were made in order to give the Cambridge model a wider applicability and more explicit realism.

It was in 1972, thanks to a remarkable paper by Steedman, that the public sector was explicitly included in the Cambridge equation. Though 16 years had elapsed since the original paper by Kaldor, no formal attempt had been made in that period to introduce the government sector and its ensuing complications. The case is more striking if one considers that Kaldor was an expert adviser on tax issues, tax theory and public finance. This is due to the aforementioned fact that throughout that period the economists were mainly concerned about the analytical properties of the outcome of the Pasinetti Theorem.

In fact, Steedman's 1972 paper was an original and very constructive way to resolve the theoretical dispute between Pasinetti and Samuelson-Modigliani. Steedman showed that if the public sector was considered, under the assumption of budget equilibrium, the long run solutions were consistent with Pasinetti’s solutions, and never with the "dual" solutions of Samuelson-Modigliani. This means that the introduction of the public sector meant that the profit rate remained independent of the workers propensity to save and of the capital-output ratio (technology).

The "enlarged Cambridge equation", which Steedman arrived at was:

(3.3)

where t_p is the tax rate (average and marginal) on profits. In the case that t_p=0 (there are no taxes on profits), we obtain the original Cambridge equation. As it can be easily seen, neither the workers' propensity to save, nor technology, nor even the tax rate on wages affect to the rate of profit of the economy, and hence they do not affect to the distribution between wages and profits.

Pasinetti entered the debate again in 1989 showing that -whether the government’s budget was in deficit or surplus- the main results of the Cambridge equation hold. If the government budget was not balanced, the Cambridge equation would take the following form:

(3.4)

where s’_c is a “propensity to save of capitalists corrected”, meaning that it takes into account both the direct taxation on profits and the indirect taxation, t_i (on capitalists' consumption) as well as the government propensity to save, s_T, i.e.:

Although the expression of the capitalists’ propensity to save is not as simple as the original, the truly remarkable thing is that no matter what hypothesis are adopted about the government budget, the Cambridge equation continues to hold, by depending on the natural rate of growth divided by the capitalists' propensity to save, independently of workers' propensity to save and the technology.

Equation (4.1) - and (4.2) - can be viewed from another point of view: they can be expressed in terms of profit after taxes:

The long-run rate of profits is given by the natural growth rate divided by the capitalists’ propensity to save, independently of anything else. That is to say, the original Cambridge equation can be said to refer to the rate of profit net of taxes, not to the rate of profit before taxes.

The most important conclusion to be drawn from this analysis is that if we consider two identical economies (with the same natural rate of growth and saving propensities), if the first has a higher tax rate on profits, the second economy will enjoy a higher rate of profits before taxes (and also a higher share of profits in total income). That is to say, the presence of government has a redistributive effect per se in favour of profits and against wages. This important and surprising conclusion should not sound new, for, as stated by Pasinetti: