Since approximately eight years your reviewer studies the subject of economic planning. Especially for a Dutchman it is obvious to start with the books of Jan Tinbergen, the recognized world authority on this field. Yet this has not happened. The reason is that Tinbergen is remembered mainly for his political publications about development aid. Indeed his most recent books Een leefbare aarde (1970) and Naar een rechtvaardiger internationale orde (1976) discuss this theme. These books concern political policies. Moreover, the dry style of this last publication is not really inviting. Incidentally, a good economist is not of its own accord a good politician - and Tinbergen would be the first to admit this.
The books of Tinbergen about economic planning date notably from the late fifties and from the sixties of the last century. These early works have fallen somewhat in oblivion due to the charisma of the "old" Tinbergen and his social and political involvement. But precisely those early works of Tinbergen study economic planning, and explain the use of economic theories. The book Mathematical models of economic growth, which is written by Tinbergen and Hendricus Bos, is an example of this.
A year ago your reviewer finally obtained Mathematical models of economic growth1. And yet the incitement to read the book was still absent. The publication is a typical product of the early sixties, with thick yellow paper and lots of formulas in small type. Besides, Tinbergen has invented a peculiar notation, which is not very common. At the end of the book four pages are needed in order to define all symbols. The reader will understand, that this makes an odd impression, as though the models are eccentric and address experts. But this is definitely not the case!
For Mathematical models of economic growth does address all essential themes of economic planning. And the authors use a careful approach, and guide their reader on his way through the yet complex matter. Each time they start with a simple case, and expand it step by step with new and more advanced aspects. Although scribbling paper must be at hand for some brain-work, generally the arguments of the authors are easy to understand.
The models in the book are intended for the solving of policy problems, but they do not discuss the targets of the policy. Those are selected by the politician, and not by the economist. Among the standard targets are the increase of the consumption, and the preservation of employment2. The economist can help the politician in order to avoid conflicting targets. For the economic causalities are known fairly well. The authors make an abundant use of mathematics, because this allows for a systematic presentation.
The reader will undoubtedly agree, that all policies start with the determination of the national savings. So it is no surprise that the authors first discuss the one-sector models, where the capital is the only scarce production factor. In fact these are all variations of the well-known Harrod-Domar model. In all cases the policy maker tries to find the optimal economic growthpath. In principle it is possible with these formulas to calculate the policy optimum by means of mathematics. Yet the authors do not advocate this, because the reality always turns out to be more complex than the theory3.
A disadvantage of the Harrod-Domar model is the absence of the production factor labour. Since the publications of the economist Solow it is known, that models can be enriched with a so-called production function. The authors give several examples of models with a production function, and they show how she can be combined with the price elasticity of the demand for production factors. Those are absent in the model of Solow, but evidently they are highly relevant for the practice of planning. The aim of the one-sector models is always to make a convenient choice for the national propensity to save.
Once the propensity to save is fixed, the structural development of the economic system can be studied. Preferably the structure must not change too much, because the entrepreneurs benefit from some economic stability4. The analysis of the structure uses multi-sector models. Since those can become quite complex, the authors begin in a modest manner with the theory of two-sector growth models. The models are carefully expanded with new and more complex sectors, until in the end a multi-sector model of the Leontief type has been constructed.
Such models are based on the intertwined matrix, and therefore they require an advanced level of mathematical knowledge. Those who have never seen a Leontief model, will probably drop out, in spite of the efforts of the authors. In the next step the authors introduce also the foreign trade, so that the so-called open economies can be modelled. This is especially an essential element for the developing countries, because those absolutely need imports in order to further economic growth. Since in those situations the state is confronted with product prices on the world market, the prices in the models must be variable.
The final chapter discusses the allocation of the production to various regions. This extension is interesting in particular for large states, such as the former Soviet Union or the United States of America. In that situation the costs of transportation enter the model. Indeed the Leninist planning models always include facilities for regional planning. The central national plan is subdivided into various independent regional plans. This is a phased approach, which is also employed by Tinbergen and Bos. Also in the Netherlands plans have been made for the regional structures, and regional investment funds have been formed. This is merely a mild form of planning, because the policy is limited to the creation of a beneficial economic climate.
For the sake of completeness is must be noted, that in a sense the contents of Mathematical models of economic growth is outdated. For almost all models use aggregated monetary quantities. However, in 1966 the economist Sraffa showed that aggregated monetary quantities vary in an unpredictable way, when the wage level or the rate of interest is changed. Such changes occur for instance due to the technological progress. This is a problem, for the models aim to describe the development of the production, independent of the income distribution. Since the authors are not yet aware of this problem (it is 1962!), they do not elaborate on this criticism on the models.
At the beginning of this review it has already been stated that Mathematical models of economic growth is worth reading for the true lovers. The similarity with the also commended book Volkswirtschaftlicher Reproduktionsprozeß und dynamische Modelle by Eva Müller is striking. That book contains 496 pages, and thus it is clearly more bulky than the 134 pages of Mathematical models of economic growth. Yet both books cover about the same contents, at least approximately. Indeed Müller is more generous with explanations and examples. But yet Mathematical models of economic growth is the winner, with regard to insights and theoretical completeness. The talent of Tinbergen does not belie itself.