Economy and Energy
Year  II - N° 9

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Capital Accumulation in the Brazilian Economy
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Graphic Edition:
Graphic E
Sunday, 13 December 1998.


( Moving the lantern to the bow)

Omar Campos Ferreira
English Version:
Frida Eidelman

Carlos Feu and al. elaborated a study of the Brazilian economy evolution between 1947 and 1992 using phenomenological methodology which is an innovation among us ("Brasil : O Crescimento Possível" , Ed. Bertrand Brasil – 1996). Using data from the National Accounting, they analyzed the effects of the petroleum price shocks in the seventies together with the high international interest rates and the price decrease of our export products. They showed that the GNP increased in the seventies at considerable rates but decelerated at the beginning of the eighties. In the global balance, the GNP would not have been affected but the accumulated capital at the end of the analyzed period was 7% of what would have been expected.

In the present work, using basically the same methodology and with data extended to 1997, we tried to deepen the analysis, searching for the structural causes of failure of the "Brazilian economical miracle".


The basic hypothesis of Carlos Feu Alvim’s work is that the growth limiting factor of the Brazilian economy is capital, since the working force would be underused and the natural resources are still abundant. The occupation of the Brazilian territory is far from accomplished: we have seen in the last decades the opening of areas for colonization such as in the north of Paraná and Goiás state, after the foundation of Brasilia, the Tocantins state, etc. In each opened area, the accumulation cycle is repeated, resulting from the exploration of the "natural capital". Strictly speaking, except for some areas in the south and southeast regions, all national territory is still in the colonization phase, if we compare its economical occupation with that of industrialized countries.

Robert U. Ayres (" Resources, Environment and Economics " - John Wiley/ l978) identifies similarities between the dynamic model of renewable resources and the capital accumulation model. According to Ayres, the natural capital accumulation, such as free animals, trees etc. without exploration is described by the equation proposed by Raymond Pearl ("The Biology of Population Growth " - Alfred Knopf/1925 )

dK / dt = a K ( K* - K ) (1)

where K* is the capital value at equilibrium and a is a kinetic parameter. Equation (1) , also credited to Verhulst, Volterra and Lotka, was already presented in the previous issue of e&e as the logistic law. We also presented two application examples of this law, one of them referring to the projection of the Brazilian population growth and the other to the power evolution of the hydroelectric power plants installed in Brazil: this last case is clearly that of capital accumulation (installed power) , given the equilibrium value ( theoretically the hydraulic potential). Capital accumulation in the Brazilian economy seems to be described by the logistic law, given the low participation of external capital, which would be the exploring element, at least until the seventies. The analysis model proposed in the present work uses equation (1) to describe the net rate of capital accumulation and the finite form

K = K* / [1+A.exp ( -at )] (2)

to describe capital at instant t. In this last equation, A is an integration constant and a is the kinetic parameter. The linear form is also usual

ln [F/(1-F) ] = aK*t + lnA

obtained from (2) by changing the variable F = K / K*


Table A 1 gives the data under analysis. The capital growth rate was calculated as the arithmetic average in the quinquennium and it is supposed to correspond to the median year of the quinquennium; this artifice allows the smoothing of data since the differential equation presupposes the continuity of the variables, but at the cost of loss of sensibility for identifying the function’s singular points.

TABLE A 1 Quinquennial average rates.


































The first analysis aims at verifying if the phenomena follows the logistic law and if so with what approximation. The linear form is used, adjusting the observed data to a straight line by the least square method, determining the value of aK* as the angular coefficient of the adjusted line. It should be observed that the value of K* to be used for the calculation of F is any value , since it is only desired to know the form of the law; nevertheless, it is used a value compatible with the magnitude of K (in this case it was used K* = 2,500). The correlation coefficient obtained in the adjustment was 0.9972, which shows that the data are well adjusted to a straight line (the perfect adjustment would produce CR=1.000)

In the next step the capital variation rate is analyzed and, according to the differential equation, it should describe the parabola dK/dt = a K (K*- K ). Adjusting the calculated rate values to the parabola, where K is the independent variable, a and aK* are obtained separately and the parameters of the logistic curve are completely determined. In graphic No 1 it is observed that the rate records exactly the change in the capital accumulation model which occurred in the seventies. The parabola that would describe the rate variation would show an unexplainable inflection. Considering that the phenomena development has varied, it is not possible to apply a single parabola to the entire analyzed interval and one must analyze separately the intervals before and after the seventies.


Graphic 1

graphic: capital growth rate



The interval 1947 – 1970 is short and the number of points obtained by the quinquennial average is small for the analysis. We prefer to use triennial average rates (table 2), from 1949 to 1967, therefore avoiding as far as possible the uncertainties of the extremities ( model transition). The adjustment to the parabola produced a = 13.5 ´ 10 – 6 and K* = 5,400 ( the unit of K is the centesimal part of 1980’s GNP – 556 billion of 1987 dollars = 5.56 billion dollars) . The adjusted curve is shown in graphic No 2. After calculations, it results that the equilibrium capital is in 1987 dollars, US$ 30.6 ´ 10 –12 ( thirty trillion dollars) which would be attained at the end of the next century. This value seems to be very high but it is of the same magnitude of the present USA capital, estimated here as 20 trillion and still growing.

TABLE 2: Triennial average rates

























Graphic 2

graphic: capital growth rate before 1970


The model post - 70 is less well behaved than the previous one and forecasts are very risky (graphic No 1 – table No 1). For the purposes of this article it seems sufficient to compare the capital effectively accumulated with that which would be accumulated in the pre-70 model ( graphic No 3 – table No 3). It can be observed that conserving the previous model it would have produced at the end of the century the same capital, with a larger potential growth rate than the present one.

 TABLE 3: Capital Effectively Accumulated Compared with that which would be Accumulated in the pre-70 Model

Year 1949 1952 1955 1958 1961 1964 1967 1970 1975 1980 1985 1990 1995 2000
K proj 14,3 17,6 21,5 26,3 32,2 39,4 48,3 62 89 127 180 255 360 503
K real 14,8 17,5 21,3 25,6 30,6 41 49,2 62 103 171 237 311 355 - - -

Graphic 3

graphic: capital accumulation


Graphic no 3 shows the convergence of accumulated capital values with those which would have been obtained with the pre-70 model around 1998. Apparently, the accumulated production between 70 and 98 would have been larger than that which one could expect in the pre-70 model. Nevertheless, the analysis of the accumulated GNP (Carlos Feu, op. cit. chap. 8 ) shows that the advantage existed only until the beginning of the nineties and it became negative from 1992 on, that is, the accumulated production in the period would have been the same in the two models. In the same period , the external debt relative to the GNP increased from 10 to 20% and the internal debt increased from 40 to 80 billion dollars between 82 and 93. Except for the trifles, no economical gain to be recorded.

The lack of social indicators makes this analysis a partial one. Nevertheless, for those who lived during this period it is easy to observe that the education, health and social security services have became considerable worse and that the income distribution increased the privileges of the richer.

Moving the lantern to the bow means to us to learn the lessons from the past in order to avoid the same mistakes in the future. It seems clear that our present misfortune is related with the opening of the economy, even in the imports- substitution model, considered as protectionism, in an unfavorable conjuncture and a climate of national euphoria that overshadowed the best analyses that could be made at that time.

To repeat now the mistake when the financial crisis in the stock markets all over the world indicates a structural problem would be unforgiven. The alienation of the national economic assets in order to maintain an artificial exchange relation through the monetary exchange may become more serious than the indebtedness of the seventies which, at least, did not affect our capacity of choosing.

Brazil, due to the dimensions of its territory, the abundance of its natural resources and the relatively rarefied population, could follow more safely a development path by aiming at the internal consumption. We don’t need to trade furiously with foreign countries, like the Asian countries, and we have not attained saturation in production capacity, like the European countries. Opening the Brazilian economy precipitately , like the government of the military cycle tried to do and how the present elected government is trying to do, continuing the disastrous opening made by the Collor administration, seems to be a historical error. The economical miracle of the seventies was frustrated by the petroleum crisis. It seems that the "competitive insertion in the globalized economy" , intended by the neoliberals will be aborted by the "globalized competition crisis".

The common man, in its simple way to interpret the facts, says that "step by
step, one gets a long way " . But "rustic " sayings are not considered by
the economists in power. Maybe the world market cornucopia is in fact a "sac
of wickedness" manipulated by some modern Machiavelli.

It is a consolation to remember that the country has been under other calamitous governments and survived.



Carlos Feu Alvim

Maybe I’m taking advantage of the privilege of being the final editor, but I would like to make some comments on Omar’s article.

The period up to 1970 represents a phase of initial capital accumulation in which the values described by the logistic function could also be described by an exponential function ( the values of graphic 2 fit well to a straight line which corresponds to an exponential in the integral graphic). It corresponds to a phase in the process in which the internal and external limits of economical growth were noticed. The maximum value of capital stock is, as the author himself underlines, just a reference that will rather be adjusted along the process. I think that Omar’s approach reveals an interesting aspect that I hope is illustrated in the following graphic:

Additional graphic

additional graphic: capital growth rate

In this graphic we represent, besides the average values shown in graphic 1, the annual values of capital variation ( investment – depreciation ). We also show Omar’s adjustment for values prior to 1970 and the values of transfer into the country ( opposite sign of transfer out of the country, from IBGE’s National Accounting). We can effectively verify through the graphics – as it happens in the processes to which the logistic function is better applied – that Brazil until 1970 was isolated from external transfers. The positive transfers of goods and services allowed in the eighties the acceleration of growth which was halted by the transfer out of the country in the eighties.

In the nineties, the development model was reverted , basing itself on open market and globalization paradigms. As a result, the investment pace was drastically reduced (which was recovering in the second half of the last decade). This is happening in spite of the positive transfer of goods and services into the country in the three last years of the series.

These data corroborate, in my opinion, Omar’s conclusions.