THE LOW RATE of saving in less developed countries is one of the important obstacles to their rapid growth. While various measures to raise the rate of saving have been taken in some of these countries, the extremely low levels of income prevailing in them put fairly narrow limits on what can be achieved in this direction. Against this background, there has been a tendency to use monetary expansion as a source of finance for investment.

## Permissible Monetary Expansion

One of the forms in which savings become available is through a limited expansion of the stock of money, which helps to finance investment in the economy and thus to produce an expansion of output. Money holdings generally tend to rise as real income increases.^{1} If, however, monetary expansion outstrips the growth in the amount of money that the community is willing to hold because of increases in real income, people may be persuaded to hold this amount of money only by a rise in prices, which has the effect of raising national income in money terms more than real national income. Alternatively, excessive monetary expansion may produce an expansion of imports and a contraction of exports, so that external reserves tend to contract. An expansion in the stock of money which is greater than that which people are willing to hold, given the rise in real income which has taken place over the period, is therefore likely to produce either excessive price increases in the economy or pressures on external reserves, or both. To that extent such an expansion in the stock of money cannot be considered as savings in the sense adopted here. The amount of monetary expansion which can take place without creating such pressures cannot therefore exceed certain limits, which depend on the growth in real income over any given period and on the proportion of their real income which people are willing to hold in the form of money.

Assuming that the proportion of income held in the form of money remains constant, it can be shown that the permissible increase in the stock of money in any year *t*, is given by the following expression:

or

where *M*_{t–1}= stock of money in year *t* — 1; Δ*M _{t}* =

*M*—

_{t}*M*

_{t–1};

*Y*

_{t–1}= real income in year

*t*— 1;

In many less developed countries since World War II, the proportion of income which people have been willing to hold in the form of money has tended to increase. If the assumption that *k* is constant is dropped, the extent of permissible monetary expansion clearly depends also on the rate at which this proportion is tending to increase. When this rate is taken into consideration, the expression for the increase in the stock of money in any year changes into

or

where *a* is the annual rate of change in *k* expressed as a fraction of *k*, i.e.,

## Monetary Expansion and Investment

The permissible amount of monetary expansion calculated in this way for a particular year can be related to the amount of investment in the economy during that year. The amount of investment necessary to make income grow at the specified rate depends on the amount of increase in income and on the capital-output ratio prevailing in the economy. Assuming that investment in one year brings about an increase in income in the next, it can be shown that the amount of investment is given by the expression:

where *I _{t}* = investment in year

*t*;

*c*= the incremental capital-output ratio; and

If the whole of the increase in the stock of money could be used to finance the sort of investment that is necessary to increase income at the given rate, the proportion of investment that could be financed in a noninflationary manner by the increase in the stock of money is given, when the *k* ratio is constant, by

and, when the *k* ratio is changing, by

If the rate at which income is growing is constant over the relevant period, i.e., if *b*_{t+1} = *b _{t}*, then these two equations resolve into the simpler ones given below:

and

The significance of these expressions in quantitative terms may be illustrated by making certain reasonable assumptions about the values of the various ratios. Assume first a rate of increase of real national income of 5 per cent per annum and a capital-output ratio of 3. In equation (6), it is assumed that *k* is constant. In equation (7), where *k* is assumed to increase, *a* (the rate of change of *k*) may be given the value of 0.05; i.e., it may be assumed that the *k* ratio is increasing at the rate of 5 per cent per annum. On this basis, the result obtained for equation (6) is 0.317 *k*_{t–1} and for equation (7) is 0.651 *k*_{t–1}. The latter is more than twice the former indicating how important a role a positive rate of change in the *k* ratio plays in these calculations. If alternative values of 0.2 and 0.3 are assumed for *k*_{t–1} then, for equation (6), it is found that the permissible expansion of the stock of money constitutes 6.3 and 9.5 per cent, respectively, of investment in the year. For the same values of *k*_{t–1}, for equation (7), the permissible expansion of the stock of money would constitute 13.0 and 19.5 per cent, respectively, of such investment.

## Inventories and External Reserves

The capital-output ratio used in these calculations is normally based on the fixed investment necessary to produce an increase in output. The results of the calculations made above may, therefore, be interpreted as showing the proportion of fixed investment that can be financed from the savings implicit in monetary expansion. Under this interpretation, the entire volume of savings in the more usual sense of the term would finance the rest of such fixed investment. If this approach is adopted, however, the savings implicit in monetary expansion cannot really be treated as being available in full for financing fixed investment. Such monetary expansion must first help to finance whatever expansion is necessary in the country’s holdings of inventories and in its holdings of external reserves.

As the economy expands, inventory expansion is likely to proceed at a more or less equal pace. The same applies to reserve expansion, though the extent of desirable reserve expansion will depend also on the initial level of reserves, the extent to which trade expansion accompanies or helps to foster the growth in national income, and variations in the tendency toward fluctuations in the country’s balance of payments. If the initial level of reserves is too high, some drawing down of reserves may be justified. If it is too low, there may be a case for first building them up to adequate levels. If the present level of reserves is more or less adequate, a less developed country may consider it advisable to ensure growth in reserves at a rate commensurate with growth in the country’s national income.

It should be clear that the use of the savings implicit in permissible monetary expansion for the purpose of financing necessary inventory expansion and reserve growth does not imply any dissipation of such savings. Such use of these savings can in fact be regarded as investment necessary for the growth of the economy. It is because this investment was not taken into account above in calculating the investment necessary to produce then required growth of the economy that provision for separate financing of such investment must be made.

It is possible to treat investment in inventories and in reserves as a part of the total investment in the economy necessary to produce the desired growth in income. The effect would be to raise the value of the incremental capital-output ratio, *c* (used for the purposes of the calculations earlier in the paper). However, the needs of such investment are often neglected in calculating the capital-output ratio for the economy and must then be taken care of separately. In practice, it is convenient to consider the investment needs underlying the capital-output ratio in terms of fixed investment only, and there is no objection to doing so provided the needs of the other two types of investment are taken into account separately. The reason is that the mechanics of monetary expansion are such as to make it useful to treat the needs of inventory expansion and reserve growth separately from those of fixed investment, and to consider these needs as first charges on the form of savings represented by the permissible expansion in the stock of money. The expansion of a country’s foreign reserves automatically accounts for an equivalent expansion of its stock of money. Again, the financing of inventory expansion is the traditional function of monetary expansion. If left to themselves, inventory expansion and reserve growth are likely to absorb automatically whatever portion they need of the savings which permissible monetary expansion represents. Any excess of such savings over these needs may then be usefully related to the volume of fixed investment in the economy.

Assuming that both inventories and foreign reserves grow at the same rate as the national income, so that their ratios to national income remain unchanged as income grows, the volume of financing required for these two purposes is given by:

where *F*_{t–1} foreign reserves in the year *t*—1;

*F*=

_{t}*F*—

_{t}*F*

_{t–1};

*V*

_{t–1}= inventories in the year

*t*— 1; and Δ

*V*

_{t}=

*V*—

_{t}*V*

_{t–1}.

## Financing of Fixed Investment

Only to the extent that permissible monetary expansion in any country is greater than the requirements of inventory accumulation and the expansion of foreign reserves can this form of savings be used to finance fixed investment. The excess of the expansion in the stock of money over the requirements of these two purposes is given by the two expressions below, depending on whether *k* is constant or is tending to change over time.

The result will be positive only if the first term within the large brackets is greater than the second. The possibility of the result being negative, or at best very small if positive, is clearly much greater if *k* tends to be constant as in equation (9). The result is more likely to be positive and relatively large where the tendency of the proportion of income held in the form of money to increase is at all strong, i.e., where the value of *a* is positive and large relative to *b _{t}*. In either case, the result would, of course, depend on the value of

*k*

_{t–1}and, given

*g*(which might not vary much between countries), on the value of

*e*.

If permissible monetary expansion is not adequate to cover the needs of inventory expansion and reserve growth, the excess of the latter over the former would have to be added to the volume of fixed investment for the financing of which savings in the more usual sense of the term must be found. Alternatively, we could say that the available volume of savings in the usual sense of the term would have to be reduced by this excess to find out how much fixed investment in the economy it is possible to finance.

The expressions for the proportion of fixed investment that can be financed by the excess of permissible monetary expansion over the needs of inventory expansion and reserve growth, provided there is such an excess, are given by:

If the rate of growth of income is constant, so that *b*_{t+1} = *b _{t}*, these equations will resolve into the simpler ones given below:

## Conclusion

Equation 14 shows that, on the given assumptions, the proportion of fixed investment that can be financed from monetary expansion, after allowing for the financing of the expansion of inventories and foreign reserves, depends on the values of a few simple elements, namely,

*k*_{t–1}, the initial proportion of income held in the form of money (0.2 or 0.3)

*a*, the annual rate of change in *k* (0.05)

*b _{t}*, the annual rate of growth of income (0.05)

*e*, the ratio of foreign reserves to income (0.01)

*g*, the ratio of inventories to income (0.01)

*c*, the incremental capital-output ratio (3.00).

If, for illustrative purposes, these elements are given the values shown in the parentheses against them, the proportion of fixed investment that could be financed by monetary expansion would be 6 per cent or 13 per cent, depending on whether the value of *k*_{t–1} was taken at 0.2 or at 0.3. The proportion of fixed investment that can be financed by monetary expansion in any particular country can easily be calculated by inserting the appropriate values of these elements into the equation.

## Expansion monétaire et développement économique

### Résumé

Une certaine expansion de la masse monétaire constitue une des formes de l’épargne. Cette expansion contribue au financement des investissements, et donc à l’accroissement de la production. Une expansion excessive de la masse monétaire risque cependant de provoquer soit des hausses de prix, soit des pressions s’exerçant sur les réserves en devises, l’un de ces effets n’excluant d’ailleurs pas nécessairement l’autre. Les limites de l’expansion monétaire admissible dépendent de la progression du revenu réel et de la proportion de son revenu réel que le public est disposé à détenir sous forme de monnaie. Elles dépendent également du taux auquel cette proportion a tendance à s’accroître.

Etant donné que l’expansion monétaire doit d’abord financer l’accroissement nécessaire des stocks et l’augmentation souhaitée des réserves en devises, on ne saurait considérer qu’elle puisse être consacrée en totalité au financement de l’investissement dans l’équipement. L’accroissement des stocks se fait généralement au même rythme que celui du revenu. Dans l’ensemble, on peut admettre que la progression des réserves en devises a lieu elle aussi au même rythme que celle du revenu.

En admettant que le revenu augmente à un taux constant, l’auteur montre que, dans ces conditions, la proportion de l’investissement dans l’équipement que l’on peut financer à partir de l’excédent de l’expansion monétaire admissible par rapport aux besoins de l’expansion des stocks et de l’accroissement des réserves, si tant est qu’un tel excédent existe, peut se représenter comme suit:

où *k _{t}–1* représente la proportion initiale de revenu détenue sous forme de monnaie,

*a*est le taux annuel de changement de cette proportion,

*b*est le taux annuel d’accroissement du revenu,

_{t}*e*est le rapport entre les réserves en devises et le revenu,

*g*est le rapport entre les stocks et le revenu, et

*c*est le rapport marginal capital/production.

## La expansión monetaria y el desarrollo económico

### Resumen

Una de las formas de mantener ahorros consiste en una expansión limitada del medio circulante. Esta expansión ayuda a financiar las inversiones y, por ende, a aumentar la producción. Ahora bien, una expansión excesiva del medio circulante traería probablemente consigo un alza de los precios, o presiones sobre las reservas externas, o ambas cosas a la vez. Los límites de una expansión monetaria permisible dependen del crecimiento del ingreso real y de la proporción de sus propios ingresos reales que el público esté dispuesto a mantener en forma de dinero, así como también del ritmo en que dicha proporción tienda a aumentar.

Puesto que la expansión monetaria debe en primer lugar financiar el incremento necesario de los inventarios y la deseada expansión de las reservas externas, no se le puede considerar como enteramente disponible para el financiamiento de inversiones fijas. Es probable que el incremento de los inventarios guarde proporción con el crecimiento del ingreso. En general, cabe suponer que la expansión de las reservas externas también marche al unísono con el crecimiento del ingreso.

Partiendo de la hipótesis de que el ingreso crece a una tasa constante, la proporción de las inversiones fijas que puede financiarse con el excedente de una expansión monetaria permisible, una vez cubiertas las necesidades de incrementar los inventarios y las reservas, caso de que exista dicho excedente, se demuestra de acuerdo con estas suposiciones como equivalente a la ecuación

representando *k*_{t–1} la proporción inicial del ingreso que se mantiene en forma de dinero, *a* el porcentaje anual de variación de dicha proporción, *b _{t}* la tasa anual de crecimiento del ingreso,

*e*la razón entre las reservas externas y el ingreso,

*g*la razón entre las existencias y el ingreso y

*c*la razón incremental capital-producción.

Mr. Ezekiel, Assistant Chief of the Special Studies Division in the Research and Statistics Department, is a graduate of the University of Bombay. He taught economics at St. Xavier’s College, Bombay, and at the University of Bombay, and was Financial Editor of *The Economic Times*. He has contributed a number of articles to economic journals and is the author of *The Pattern of Investment and Economic Development*, to be published shortly by the University of Bombay.

Jacques J. Polak, “The Capacity of the Banking System to Finance Development,” in *Memoria, V Reunión de Técnicos de los Bancos Centrales del Continente Americano*, Vol. 2 (Bogotá, 1957), pp. 171–81.

The savings implicit in increased holdings of money are additional to those usually listed in programs of economic development and can, therefore, be considered separately here. They are not, however, additional to savings in the national income accounting sense, where savings are defined as income minus consumption.