# The theory of capital

#### By Bertrand Munier

In Economy and Interest (1947), Maurice Allais places considerable reliance on the theories of capital which emerged from the marginalism of Böhm-Bawerk and Stanley Jevons in the late XIXth century, but also on the contributions made in the 1930s to interest rate theory by Irving Fisher and Friedrich von Hayek’s reflections on Prices and Production (1931), which led their author to his Pure Theory of Capital (1941). It may be noted in passing that some 40 years later these two works were to win their author the 1974 Nobel Prize in Economics.

But Maurice Allais was to go beyond all these contributions, including the last and most complete before his own, by constructing a theory of optimal capital stock and optimal rate of interest – optimal in the meaning of Pareto, or what Allais himself in the 40s and 50s termed maximum social efficiency – which we do not again encounter until thirteen years later in the writings of American economist Phelps to whom it is usually, but mistakenly, attributed, as was pointed out by Thierry de Montbrial (1986). In subsequent contributions, Maurice Allais was to link this optimal capital stock theory with monetary theory, and to make it the basis of a much more general theory of economic fluctuations than that of Hayek (1941), which had hitherto been the most complete. This led him to convictions regarding monetary policy which were close to Fisher’s “100% money” ideas, though they were also based on much more complete modelling. The 2008 crisis will lead to closer and more respectful re-examination of these latest contributions than they had previously received.

Maurice Allais’s approach draws on three concepts specific to the theory of capital:

• The concept of the characteristic period $\Theta(0)$ of the variation in marginal efficiency of the factors of production as a function of their temporal distance from the final output of complex goods or services – a concept that is independent of time and place and is characteristic of Maurice Allais’s quest for universal quantities in economic theory;
• The concept of primary national income, $R_{NW}$, being the sum of the values of  (or of the payments to be made for) the primary factors of production used per unit of time in the economy at a given observation moment;
• The concept of the “characteristic function”, inherited from Stanley Jevons, of which the use made by Maurice Allais will be touched on below.

Let us now consider $\Theta$ the average waiting period between the initial entry of the factors of production into the production process and the ultimate emergence of the desired product, which I shall henceforth call the “average production period”. The primary income – which is proportionate to the effort (the scale of the investment) to be made will be so much the higher as this average period $\Theta$ is longer, all other things being equal. It is therefore clear that this parameter $\Theta$ is characteristic of how “capitalistic” the production concerned is. For example, this parameter will be much higher for automobile production – which calls for a long chain of successive operations – than for the production of ice-cream which anyone possessed of a simple refrigerating machine may make and sell on the sidewalk. In the same way, but on a national scale, we may speak of how “capitalistic” an economy is, if we focus on the average of all the production activities carried on in the economy in question.

In a general way we may use $\phi(\theta)$ to denote the amount of primary income or of net investment needed per unit of time, $\theta$ units of time before time $t$ at which the rewards of the investment are to be reaped. These rewards of the investment take the shape of a flow of final output able to be offered for direct consumption by households. So this function $\phi(\theta)$ characterizes the temporal profile of the investments which must be accumulated, time unit after time unit, until the final output is obtained. This sum of investments is what Maurice Allais calls primary income, as we have seen above.

In Economy and Interest (1947), Maurice Allais then goes on to note that the primary income is equal to the value of the final output yielded at time $t$. In other words, the value of a production obtained at time $t$ is equal, under stationary conditions, to the whole of the function $\phi(\theta)$ from the date of the beginning of the investment to time $t$, the terminal stage of the production if time is considered as a continuous variable.

So this function will be called the characteristic function. But the values taken by this function depend on the level of the rate of interest confronting the investors, as may be grasped intuitively. The rate of interest is therefore a parameter of this function which, with greater rigour, will therefore be denoted by $\phi(\theta,i)$. It can also be shown that in a stationary process the real national income obtained will be maximal for a zero interest rate (Economy and Interest, No. 69). This is a crucial finding, demonstrated for the first time by Maurice Allais in Chapter VII of Economy and Interest, and which will henceforth be termed the “golden rule” of the capital-output ratio of an economy.

In a 1960 article entitled “Influence du coefficient capitalistique sur le revenu réel par tête[Influence of the capital-output ratio on real per capita income], followed up by a paper read to the Congress of the Econometric Society in the US in December 1961, Maurice Allais was to generalise this result to economies under growth, showing that the “pure” rate of interest must always be equal to the real rate of growth of the economy in question.

One of the possible (but not necessary) consequences of this theory of capital is the thesis of the neutrality of the quantity of capital available per capita relative to the marginal productivity of labour – a thesis asserted in the most complete submission relative to this Allaisian theory of capital, entitled The Role of Capital in Economic Development which was published as a long part (pp. 697-1002) of the 1965 treatise coordinated by T. C. Koopmans: The Econometric Approach to Development Planning (North Holland). Under this last aspect Maurice Allais’s pure theory of capital is combined with the General Theory of Surpluses and the vision of the economic dynamic of the same Maurice Allais. More than the price mechanism (whose importance is of the second order in terms of this Allaisian economic dynamic), more even than the quantities of physical means used, it is the pressure of competition, inter-business rivalry, on the one hand and the quality of human training that lie at the origin of economic progress. It may seem astonishing for a theory of capital to lead to such a conclusion, but the one in question certainly deserves greater attention than it has hitherto received. Another fascinating, and perhaps very fruitful, subject for young researchers.

But at this point a final connection must be made between the various facets of Maurice Allais’s economic thought. This time it is the connection between the pure theory of capital and monetary theory. For Maurice Allais established a linear relation between the ratio of national income $R_N$ to maximum attainable income $R_{NM}$, i.e. $R_N/R_{NM}$, and the “pure” rate of interest (the “psychological rate of interest” – a concept belonging to the HRL monetary theory explained elsewhere in this site) such that the monetary policy which determines the rate of interest is at the origin of economic growth and must be optimized for this purpose. In the same way economic fluctuations must be linked with monetary policy and more generally with the organization of the monetary system. For Maurice Allais was to show, in the 1970s, that a system of 100% money is stabilizing, whereas a system of partially backed monetary creation is much more generally destabilizing.