THE MYTH OF THE PRODUCTION FUNCTION

THE MYTH OF THE PRODUCTION FUNCTION

(This is an extract from chapter 2 of the unpublished book “Economics for Heretics: Debunking the Myths of Orthodox Economics” by Dante A. Urbina. You can see this and other articles by the same author in his blog "The Heretical Economist": http://thehereticaleconomist.blogspot.com/).

And with what produce?: ecologist criticism of the production function

Let us imagine for a moment that the production function that sustains the orthodox economics is valid. Furthermore, let us imagine that, in fact, we have to carry out an actual production process based on it. Let us think, for example, in the production of a cake. What do we need to do? According to the neoclassical production function –which has the general notation Q = f (K, L)- we would need capital and labor. Get together, then all elements of capital (defined as the set of instruments used to produce): jars, bowls, trays, pallets, oven, pans, knives, etc. Now we gather the elements of the labor factor: basically be our own labor (or the of a chef) incorporated with all the abilities to make cakes. Then, given a technological configuration, ie, an established relationship between the factors of production bringing together the elements of capital (K) and labor (L) which we have listed, we get the product, that is a cake. But we get nothing! It’s not possible... there has to be an explanation...

We try with an intensive increase of productive factors: we get much bigger bowls (K) and we hire several chefs (L)... but still not we get a single cake! “Why?”, we ask ourselves.

The answer is very simple: nothing is produced because there is nothing with what to produce! No matter how many bowls we get or how many cooks we hire if there's no cake dough to cook! In effect, on the basis of the neoclassical production function, we have gathered all the elements of capital and labor but we have not had any account of the raw material. We have listed several things, right. But at no time we have mentioned flour, sugar, eggs, etc. Thus, based on the neoclassical production function, we have tried to be God: we wanted to create something out of nothing! However, it becomes patently absurd in this context: cannot make cake without cake dough. Cannot produce without raw material.

Well, it is precisely on this basis that the great economist Nicholas Georgescu-Roegen, initiator of the ecologist approach, raises his criticism of the production function and orthodox economics. He begins by analyzing the physical basis of the production process (1) and immediately realizes the implications of the First Law of Thermodynamics (according to which “the matter is not created or destroyed, only transformed”): not possible to produce without a material basis. Consequently, the neoclassical production function becomes inconsistent and absurd for not taking into account the nature factor.

And this was to be expected. In the nineteenth century, when was born the neoclassical school, the modernists believed in the “theory of indefinite progress” and they claimed that the resources of nature were endless. Orthodox theorists assumed that belief and built on this basis in economic theory. So, the most essential factor of the economic process was relegated to the sidelines : the ecological factor. However, as rightly said Max Neef: “There is no economy possible regardless the services provided by ecosystems. This is so absolutely clear and so absolutely obvious that is truly a epistemological scandal that in any economics textbook, if you go to index words, may be find the words “ecosystem”, “nature” or “thermodynamics”. They do not exist! Simply they do not exist. Why? Because the economy that is taught is conceived as a closed system in itself that is not related to any other system (...) when obviously it is embedded in a bigger system called biosphere and around which are all services provide the elements of that biosphere. Where would be the economist if it ends the photosynthesis? Economists do would not exist! What would happen with the economy if suddenly all the bees died? There would be no pollination... But no economist presumes that he has to know that. (...) All this happens in a gigantic sea of ignorance on the part of the economy” (2). In other words, there can be no economy without ecology and orthodox economics still does not know it.

“But the problem is easy to solve!”, orthodox economists will say. “We add the variable R (natural resources) in the production function and ready!”. What ignorance! One ignorance comparable only with that ignorance that orthodox economists also show when claim to have understood the process of technological change just because they incorporate a variable “A” to the production function (3).

Let us see. Given a variant “Solow-Stiglitz” (as it is called to the artifice upon which it has been tried solve the problem) of the production function we have that in the form Cobb-Douglas this will be:

Q = K^a.L^b.R^c

such that: a + b + c = 1

As this is a Cobb Douglas production function, this implies complete substitutability of factors, ie, that can be replaced one factor by another (or others) while maintaining the same level of production. But it is precisely where the inconsistency resides. Mathematically, if R (natural resources) tends to zero the reduction may be compensated by increases in K or L maintained the same level of production. The structure multiplicative of the function allows it. However, it is inconsistent in the facts because if R tends to zero necessarily have to do so at some time K and L. First, because they depend on R: the capital goods are products of a previous process which presupposes the nature factor and, in turn, the labor force needed of natural resources to sustain itself  (can anyone imagine what would happen with our productivity if we drank only one glass of water a month?). Second, because the quantity of product that capital and labor can generate depends always and necessarily of the flow of inputs to transform (no matter how quick work the cook or how big is the bowl which has, if he has only one gram of mass he can not do a single cake).

Thus, Georgescu-Roegen criticism to the production function shows clearly that the economy has ecological limits. And that brings us to the central concept of his analysis: “entropy”. Basically the entropy means that the availability of a certain amount of energy, once it has been used, not retains throughout time to the same properties to create useful work. Thus, as soon as the natural resources are transformed, they pass from a state of low entropy to a high entropy and, consequently, it is increasingly difficult transform them into products useful to man. Ergo, the use of our the natural resources have a objective limit: capital and labor can not exploit the nature indefinitely because this is also subject to the Law of diminishing returns.

And that not to mention the problem of the environmental pollution brought about by any production process. In effect, given that, because of the law of entropy-is impossible to achieve 100% efficiency, produce something always and necessarily generate a residue or waste (4) which should be treated. That is, after making a cake you need to clean the kitchen. And the same applies for the whole planet.

Nevertheless, orthodox economics has systematically left aside all this. According to this ecological factor is purely exogenous. But “economics” etymologically means “administration of the house” (5). And our house is ultimately the planet earth. But orthodox economics has shown as evidently a bad manager because, to leave out the ecological factor analysis, necessarily have a large part of guilt in the current global warming problem that we are facing. Conclusion: orthodox economics is a bad economics.

References:

1. Nicholas Georgescu-Roegen, The Entropy Law and the Economic Process, Harvard University Press, Cambridge, 1971.

2. Manfred Max Neef, “Economy and Environment”, conference at the Universidad Austral de Chile, Valdivia, on May 28, 2010.

3. For more details on this misery see the famous Solow growth model in any manual of “advanced” macroeconomics (!).

4. Cf. Nicholas Georgescu-Roegen, The Entropy Law and the Economic Process, Harvard University Press, Cambridge, 1971, p. 231.

5. From the Greek: oikos = house; nomos = order, administration.

You can contact the author of this article in: “Dante Abelardo Urbina Padilla” (Facebook) and dante.urbina1@gmail.com (email)