Correctly Calculated, Wrongly Thought — GegenStandpunkt
On the Misuse of Mathematics, specifically in Economics
Already at school one learns the difference between subjects in which one can blather in order to gain laurels, and other subjects in which this is not possible. The latter are not only considered to be more difficult to learn, but also to be substantially more solid in their results. Economics is such a subject, and it is said to owe this to the use of mathematics.
A. The False Praise of Mathematics
By using mathematics, a thing called “exact science” is supposed to come about. But what is an exact science? In and for itself, a pure tautology. Just like “white grey” or “old geriatric”. For science consists in deducing precisely the determinations of a thing and to formulate them into judgements that belong to it and not to anything else.
That is why one never learns what a science would be that would not proceed exactly, and what mistakes it therefore would make. Instead, all kinds of advantages of using mathematics are enumerated:
1. Numbers are exact
Just as often, of course, they are inexact. A familiar question: How many decimal places do you want? Exactness is not an immanent property of numbers, but a requirement to be placed on them just as on other determinations of a thing.
Example:
I. Free-falling bodies experience an acceleration of 9.81 m/s².
II. Democracies are states based on the rule of law.
We have, of course, insidiously chosen the second example in such a way that no one will dispute the truth of this judgement. But even if that were the case: then such a sceptic would precisely know what it is that we have said and that he does not consider to be correct.
Any difference in the exactness of both statements is evidently not to be discovered. More than that: any attempt to make statement II more precise and sharper through numbers is silly, completely misses the point. What is it that one wanted to count here? Laws, police officers, court cases, prisoners? There are just as many of these in “unjust regimes”. And to make the comparison complete, imagine what would be an inexact statement in both subject areas:
I. The acceleration is quite high.
II. In Turkey, there are almost conditions of the rule of law again.
In both cases, one does not know what one is up against; it becomes a question of standpoint. In I., the need for numerical values, which is in the nature of the determination given here (high), is not satisfied. There is talk of quantity, but it is not specified. In II. a determination is stated which at the same time is said not to apply. One could just as well say: Turkey no longer is ruled by a proper dictatorship.
2. Numbers are objective
Here we can only repeat our argumentation from above. It is not possible to see why II. should be less objective than I., or how one could make II. more objective. Smart alecks might still object that numbers can at least be ascertained objectively. “Objective” here should therefore mean that there are measuring devices and procedures that establish the quantities in question completely independently of the desires and opinions of the subjects, while a similarly confidence-inspiring “supra-subjective” procedure would not be available for “qualitative” statements. But a moment ago, everyone agreed that democracies are states based on the rule of law, and that without any measuring devices. And, even more importantly: if one wants to measure any quantity, let’s say temperature, one must surely first of all know what it is about in the first place. For it is not possible to obtain objective figures for temperature and to at the same time consider it very subjective what a temperature is, whether such a temperature is present, how it can be ascertained, etc. One requires a whole theory before one can build thermometers. So the nonsense of this conception is that one would like to trust one’s mind less than a technical device that functions as an aid to cognition. But this device itself, just like its purposive use, is an achievement of the mind. As is well known, this is the difference between a measuring device and a divining rod.
3. The language of mathematics is unambiguous
As is well known, that’s why no one understands it. If somewhere in the mathematics book it says:
d/dx tan x = 1/cos²x
then it is the same as the good English sentence
“the first derivative of the tangent function is equal to the reciprocal of the square of the cosine function.”
Because both versions say exactly the same thing, none is more unambiguous than the other. The use of symbols does not create the unambiguousness of concepts and thoughts, but presupposes it; in order to use a notation like d/dx meaningfully, I have to know what the derivative of a function is. And if I have no clue about it or only foggy conceptions, the symbol doesn’t help me. It’s no different in mathematics than in actual life. Think of the traffic signs, for example: If you don’t know what “stop and wait” is, you won’t know what to do with the red light on a traffic light. Think also of the profuse use of symbols in pseudo-sciences: Astrology, alchemy, magic. Here, symbols are vehicles of charlatanry.
It is quite another matter that one can express one’s thoughts imperfectly, for instance ambiguously, through language, but also through symbols. Then it is necessary to ask back, a few additional sentences are due etc. All the examples of how one can be misled by the use of language (“There is a bird in a cage that can talk.”) precisely do not, as they would have it, prove a fundamental defect of language. In order to tell the reader what the misunderstanding is, he must after all also be quickly told the correct understanding; and lo and behold: it can be done! Incidentally, friends of mathematical symbolic language should bear the following in mind. There is hardly a symbol that has as many different meanings as the x of the mathematicians. In each chapter of a book, in each book a different one. Even in the formula above, x is used in two senses: In expressions like tan x, I can insert numbers for x, e.g. tan 0. But I precisely cannot do this with dx, and therefore also not with the total expression.
Sidenote: There are practical reasons why mathematicians use symbols. These are more convenient to use than the corresponding word monsters, and when mathematicians have something to say to each other, they stand in front of a blackboard. The fact that they need such complicated expressions at all is because they have to operate with their objects: Formation of the reciprocal, the square, etc. And such operations can be expressed very well by putting symbols together to form a formula; one can then also calculate with it at the same time. The same applies to the formulas of chemistry.
4. Mathematics is logical
No one who has seriously studied mathematics will claim that there can be no false conclusions. At least in their own efforts, they quickly gain examples of how easy it is to make mistakes here, too. And the history of mathematics is full of them. It is another thing that mathematicians put a lot of emphasis on getting their stuff right; in particular, they don’t let anything pass without proof. But here you go: What should prevent other sciences from insisting on correct conclusions and proofs in their field? And by the way, these things are not even specific to science, but have been the order of the day since mankind left Neanderthal. Even children know when something is “logo”. What is meant by this praise of mathematics is again a rather crooked conception. Namely, that the arguments of the mathematicians could be reviewed, and not in such a way that one comprehends them, i.e. thinks along with them. But in such a way that one could determine the correctness of a proof without getting involved in its content: completely “formally”, and therefore “objectively”. That is not possible in mathematics or anywhere else. Because what is demanded there is a contradiction: one is supposed to think correctly without thinking anything, i.e. without thinking at all.
Formal correctness — a nonsense
The conception that this wrong ideal of formal correctness can at least be practised in mathematics tends to invoke another nonsense. Namely, that mathematics would have no objects and contents. But what is it that mathematicians deal with all the time? The theory of differential equations, for example, deals with differential equations. Duh! And the fact that differential equations are not cabbages and not political systems does not mean that they are nothing; they are just something else. And if someone now wants to know what these differential equations are all about, we can only advise them to study the relevant theory.
Scientific arbitrariness celebrates mathematics as its tool
The reasons that have been given for the use of mathematics are not sound at all. What they have in common is the desire to have a means in mathematics that guarantees proper scientific results, i.e. that automatically and by itself ensures that correct judgements are made and erroneous conclusions are avoided. But if one wants to have correct results, it is not at all clear whether mathematics offers even the slightest assistance in the concrete case. “Correct” means, as we said at the beginning, that the results are in fact determinations of the thing under investigation, that they apply, that they are specific. And why should an arbitrary thing have mathematical determinations of all things? On the contrary: if a scientist decides — for example, for the reasons considered above — to tackle their object of research with mathematical methods, then he is allowing himself a prejudice. For this choice of method is not based on their knowledge of the matter, but, as he himself assures us, is intended to help him gain such knowledge in the first place. So he initiates science by establishing how his results should look — for the very purpose of getting such results in the first place.
In this way, mathematics becomes the opposite of what it is alleged to be. It does not serve as an instrument of greater exactness, but as a medium in which the researcher expresses how he wants to see the objects under consideration. Thus, in the beginning there is arbitrariness: as little as it can be clear that the object of investigation can be grasped mathematically at all, as little is it clear what mathematical qualities can be attributed to it individually. So this is a question of the interest of such a scientist; he decides that and how he wants to see a thing as a quantity, as a function and so on. The objectivity of science is thus doomed before it has even begun. And what then comes after such approaches doesn’t make the overall proceedings any better: there one busies oneself diligently with the material in order to fill one’s very subjective initial ideas with life.
By the way, hardcore advocates of this arbitrariness in science would also prefer to have the matter of exactness understood much more narrowly. According to these sceptics, mathematics should no longer contribute to the correctness of the theory, but merely help to formulate the hypotheses, which one thinks up freely and at will, in a “coherent” and “ironclad” manner. But this conception now actually borders on idiocy: one’s own constructs of thought are not supposed to be correct, but they are supposed to be coherent. Seriously, why don’t such friends of subjective spiritual fruits make it a requirement that the same be put into the world in poem form, in hexameters or otherwise strictly regulated?
In the following, three examples will show what kind of unscientific methods of consideration economists produce when they get down to work in such a very exact manner. In the process, one objection that some readers may still have will be resolved by itself. The objection, namely, that with the decision for mathematics “not much” is yet said. In this regard, only two things should be remembered for the time being. Firstly, according to general opinion, “an awful lot” is supposed to have been decided with mathematics, namely the scientific character of the entire proceedings. And secondly, it is simply not true that mathematics is “nothing”. It deals, for example, with quantities and their laws, and our first example will immediately show how much one has to rape the world and one’s own mind to discover economic quantities that simply do not exist.
B. Three examples
Example 1: The national income or the economy as a number
Everyone knows the national income today; it is in the newspaper at least as often as the president. This is because it is the “most important indicator of economic activity”.
But why should there be a quantity at all that expresses and summarises what happened economically during a year — in other words, that is capable of characterising the economy as a whole. Even if such indicators exist for many technical things — from alternating current to petrol quality — their existence is not a matter of course that would apply everywhere. After all, there are no numbers that could convincingly express how the world political situation or the mental condition of humanity is constituted.
So how does an economist arrive at the desired economic indicator? Unfortunately in such a way that the wish is completely sufficient for him as the father of all further thoughts. So it is not the case that the economy is analysed here and in the process a quantity is discovered, one that matters essentially. Instead, here, inversely and very arbitrarily, a point of view is constructed that promises to deliver the desired quantification.
“We consider the entire national economy — simplified as a model — as a single giant enterprise represented by a box of which we do not (want to) know at first what is going on inside. On the one hand, there is an input and on the other hand, there is an output in a period (for example, in a year) through the production m of the giant enterprise called national economy. With regard to output, we first assume, in the most extreme abstraction, that only one universal good is produced that is equally suitable for all conceivable purposes of use. Let us call this good national income.” (Bartling-Luzius, 22)
Now, it is not to be objected against this definition of the national income by asserting that reality is “simplified” too much and in this sense represented in an “abstract” way. But rather that a completely inverted thought is being called for here. One is supposed to form a conception of the economy — but expressly without wanting to know anything about it. There is no more drastic way to characterise the unscientific nature of this project. But because this works so badly — dreaming up an economy, but one that is still an economy — it is explicitly stated where one has to lie. One should pretend that a universal good is being produced. So one should simply presuppose what would have to be proven, namely that the economy has a uniform and insofar quantifiable output, and this even despite the admitted contradiction with reality.
One can see here how the ideal of mathematical exactness drives economists to come up with highly inexact thoughts. The idea of condensing the economy into a number has led economists to the nonsense of a universal good, and this universal good will now lead them to further funny leaps. For the question of how much universal good, aka national income, is produced is anything but easy to answer, precisely because this beautiful universal good is certainly not produced by Volkswagen or Nestlé.
The usual evasion now is to simply regard every good, be it what it may, as a piece of universal good. The national income “represents the sum of all goods and services” (Henrichsmeyer, 247). Now this happy answer to the question of the existence of the national income — simply to assert that all goods and services together constitute this universal good — again brings with it the very greatest problems:
Problem №1 is, as they say, technical in nature.
“If one wants to arrive at total quantities for an economy, the procedure of measuring with the help of physical units of quantity fails completely. A measurable and additive property common to all goods must then be found.” (Stobbe, 285)
One cannot simply add up apples and pears, haircuts and funerals to get a round sum. Here, unfortunately, mathematical exactness has a very annoying effect. While it does provide the conception of a sum (good!), it unfortunately also provides a few rules for calculating it (bad). (We recall here the well-meaning opinion that with the adoption of mathematical “forms of thought” nothing would yet be “decided”. And yet it is! In order to subsume all the rubbish that occurs in economics under the idea of a mathematical sum, a few adjustments have to be made, precisely because a sum is also something determinate, having its own lawfulness).
Problem №2 is the hot question of what can and may be included in this summation process.
Precisely because the economy is neither a giant enterprise nor a black box at all, it is completely open what should be considered its output. Do apples and pears belong to it? Sure. Haircuts and funerals? Ditto. But what about military manoeuvres and election speeches? Or what about teach-ins or leaflets of our group? Certainly all “produced” things and certainly all “useful”, at least in the eyes of those who produce them. Faced with this double difficulty, scientific economics decides — and this really is a decision, a commitment that cannot be supported by any factual argument — to find the solution once again with the help of the ideal of mathematical exactness. One wants to have numbers, and therefore one simply takes the numbers that exist anyway. Namely the prices of goods and services.
“Instead of such technical attributes [pounds of apples; pieces of funeral], one uses as the property sought, despite all the disadvantages associated with it, the market prices of the commodities.” (Stobbe, 285)
This is not logical, but it is consistent. For the question of the quality to be measured — i.e. being part of the overall economic output — is replaced here by a measurement procedure that is supposed to have the sole advantage of being feasible. Everything that has a price is already thus qualified as a component of the national income. And that also takes care of problem no. 1 en passant. As prices, naturally, all goods can be added up. But because prices are not made to facilitate the formation of the national income for an economist — prices are a practical matter, through which the commodity possessor makes their profit — this neat solution immediately gives rise to a whole new set of problems. For example: there are things that, because they are not intended for sale and profit, have no price, but economists would like to include them because, according to popular opinion, they are at least as valuable as everything that is kept for sale for dollars and pennies. There is the beneficial activity of the state, from motorways and schools to the less tangible goods of security or order. Or there is the hardworking housewife who operates the washing machine, harvests apples in her own garden and spreads lots of motherly love. For example: The fact that prices change — quite simply because money is the object of economic interests and not a measuring device of research — gives the economist cause to ask whether the prices found on the market really reflect the weight with which a product is to be incorporated into the national income. Should one take the current prices, or are those from 1955 more correct? And how does one take into account that since then the milk has become slimmer and the cars have become fatter?
Summary:
The striving for mathematical exactness leads to the greatest confusion, arbitrariness and dispute. And this is precisely because this methodological ideal is the opposite of a proper scientific engagement with the objects. All the worries about measurability, correct prices, statistical procedures, etc. never bring an economist to the simple thought that he may be trying to establish something wrong, a non-existent quantity. Rather, he sees himself confirmed in the fact that it is not easy, but all the more important to strive for accuracy. Therefore, the ideological message, the content of the whole calculation, emerges from such difficulties quite unquestioned, rather strengthened even. Namely, the message that the economy as a whole is to be considered in the same way as any production process that someone undertakes so that a product results afterwards.
This false dogma of the economy as a benefit-generating affair is given credibility by the fact that it is grasped mathematically, i.e. that efforts are made to calculate the quantity of the fictitious benefit as precisely as possible.
And in the face of this highly scientific lie, the simple truth is considered unscientific, namely that the economy is not a communal affair, but is characterised by competition, and that its achievements consist in fat profits and mass misery.
Example 2: The income/expenditure analysis or the economy as point and curve
Using the example of the national income, we have now seen how the macroeconomist brings fictitious quantities into the world. Just as with the national income he imagines that the economy as a whole has a result, so he now imagines under the titles of aggregate income (Y) and aggregate expenditure (A) that the economy as a whole — just as every worker, capitalist, pensioner — has an income, and an expenditure to be made from it. Next, he would like to discover a functional relationship between these two quantities Y and A. The transformation of the economy into a fabulous realm of quantities which, as aggregate economic quantities, cannot play a role at any point in the economic process, he supplements with the programme of filling these very abstractions with life of their own: namely, to make them affect each other or depend on each other as such. For example, he now wants to make aggregate income the reason why aggregate expenditure is so and so high:
“The formulation of such hypotheses in the form of mathematical equations is called behavioural equations. They describe the behavioural dependence of the target quantities on the respective determinants.” (Münnich, 26)
In order to make his scientific goal plausible, which is to present one macroeconomic quantity as determined by the other, he comes up with people’s behaviour. That’s funny: for how should any paltry economic subject behave towards such abstractions as national income and aggregate expenditure? But even worse: “Behavioural dependence of A on determinant Y” is the name of the contradictory programme. Here the economist would logically have to make a choice: Either people’s behaviour is responsible for what is going on in the world, or one quantity is responsible for the other. Either the economic subject with its behaviour is decisive for the national expenditure A. Or the expenditures A are determined by the income Y; then the economic subject with its behaviour towards the target quantities is declared to be meaningless for the connection of A and Y.
Already the term “behaviour” is wrong — it completely ignores the fact that and for what purpose people work for wages, save, make profits, invest money, etc. But this self-created lack of content is obviously what matters to the economist. He uses behaviour as an instance of appeal: he wants to represent expenditure A as a function of income Y. But because he does not have a trace of an argument for this connection either, he opens up a possibility to think of something with this function by referring to people’s behaviour. Somehow, one should imagine, it could be that people make sure that the Y becomes an A — if the Y itself can hardly do anything. And with the same “somehow”, the bridge is also built for everyone to their own everyday actions: if income and expenditure are connected at mother’s home, it will probably be similar in the big world.
“The amount of expenditure … depends on the amount of income … The aggregate expenditure function is therefore A(t) = A(Y(t)).” (Münnich, 101)
We note in passing that the behaviour thing is now over again for the time being. The economic subjects have done their duty. From now on, mathematics has the floor, and the use of its symbolism inspires at least as much confidence as the appeal to the uneducated imagination.
Creation of a function from nothing
Because the world to which the economist has worked his way up consists of quantities, the incarnation of the thought of dependence is a mathematical function. It is one of these that he writes down — right? Not at all. What is indicated here with A = A(Y) is not a determined function. The letters do not stand for something well-defined, as is usually the case in mathematics, for example an arithmetic expression that would actually indicate the connection between the quantities A and Y. The symbols, however solid and awe-inspiring they may look to the layman, stand for the fact that the arithmetic expression that belongs here has yet to be found: No one yet knows what these signs denote — and yet there they are.
“The nature of the relationships, which is not apparent from the general notation of the equation, must be more precisely stated (or specified) in the concrete case.” (Stobbe, 5)
The question of what function the function A(t) = A(Y(t)) is actually supposed to be shows that with the latter he has not determined a law of reality, but constructed lawfulnesses according to the ludicrous principle: First I think up something — “the behaviour of economic subjects is (some) function” — and then I also think up which one it is supposed to be. It’s funny how the economist himself comments on this twisting: he calls the intention to give the quantities a connection “general”, and the demand for “concreteness” then stands for reserving the right to shape it. This works, for example, like this:
“But if we have to make such a stylisation A anyway, then it is expedient to set it up in such a way that it has all desirable mathematical properties that do not bring about a falsification of the economic statement.” (Münnich, 39)
The economist propagates quite bluntly that science does not need to feel constrained when stylising. Admittedly, he doesn’t know what the function looks like, but what he wishes for is a linear function after all. And where there is a will, there is also a way to create one out of nothing:
“By its very nature, one can adjust … every function … by means of a straight line”. (Münnich, 39)
What does he in fact want to adapt to what? Of all things, a function that he does not know, i.e. the unknown curve to his wished for, and therefore called meaningful, linear function:
“we thus arrive at the equation A(t) = a + bY(t)”. (Münnich, 102)
Freshly invented and already in need of interpretation
Given the genesis of this equation, the economist’s wish to explain what it is supposed to say in the first place is very understandable.
“We call the first summand a of the right-hand side of the equation the autonomous expenditure, in order to express thereby that this part of the expenditure is independent of the level of national income”. (Münnich, 102)
These autonomous expenditures small a are indeed funny: Mr. Münnich trusts that no one remembers the core of his intention for construction — namely that he wanted to represent A as being dependent on Y. That is why he introduces an autonomous output component here — and still says himself that “autonomous” means independent in plain English. And this small a is to be explicitly greater than 0. The normal consumer is thus required to perform the small feat of spending small a dollars “autonomously” even at Y = 0, i.e. at zero income. The economist admits this nonsense. However, this time he does not point out that small a makes economic sense, i.e. is plausible in mother’s kitchen world. Instead, he tackles the matter at the exact opposite end. Small a is mathematically necessary:
“The amount of autonomous expenditure is therefore also just a purely fictitious quantity required for reasons of representability of the straight line”. (Münnich, 102)
This is an outright lie: The function A = a + bY for a = 0 would of course be “representable” as a straight line just as well. Unfortunately, it would then be a straight line that passes through the zero point (origin) of the coordinate system. And Münnich does not want such a straight line. (For similar good reasons he puts some restrictions on the size of b).
Why?
As always when there is a lack of motivation in science, the higher motives are almost palpable. Münnich has a second straight line up his sleeve and wants the two together to form a beautiful intersection. This point of intersection is supposed to be exactly the point that the economy ultimately assumes — after all, it would be stupid if one only had equations and straight lines that did not completely establish what exactly comes out of the economy. The equation involved is called A = Y. Münnich calls this an “accounting” equation, which is supposed to mean that this is how, and only how, the economy comes to terms with its many quantities. Münnich is saying that it cannot and must not be the case that something remains of the beautiful Y or that more A comes about than has been. Indeed: we, too, find it difficult to imagine where a leftover Y should be in the world — or, on the other hand, where an overspent A would have torn a hole. But we do not at all share the ideological conception that, with an equation, has taken on scientific forms here. The conception, namely, that the economy would be a well-ordered structure of quantities, an eternal cycle, an equilibrium — or whatever all the images of togetherness or harmony might be called.
The useful application of this so-called equilibrium condition is, of course, to establish an equilibrium point — and that works like this:
“To calculate equilibrium income, substitute equation 1 into equation 2 and obtain Y(t) = a + bY(t), … a determining equation for the quantity of the equilibrium value of national income, which we calculate as Y* = (1/(1-b))*a.” (Münnich, 103)
The economist’s goal of making his idea of an equilibrium national income, i.e. a point where the economy is all right, mathematically conceivable, he has achieved by means of the deception of preparing his behavioural equation with the “parameter values” a ≠ 0 and 0 < b < 1. Without this methodical prescription to his own equation, which by itself does not make these values necessary at all, the intersection point would not have been possible. Quite unabashedly, he calls these presuppositions for the construction of the intersection, which sprang from his evidentiary intention, a “conclusion” (p. 103) from this — as if they would necessarily result, as it were, as a mathematical law from the equation once invented.
And if one looks back at both equations together again, the worst drawback of the whole derivation becomes apparent:
The so-called accounting identity Y = A was supposed to express that A can never ever take on a value other than just Y. The other, the so-called behavioural equation, should therefore always apply because he claims to have obtained it empirically. But if the solution Y* is the only value that simultaneously satisfies both equations, this means that the two equations cannot be reconciled for all other values. The values of Y that the equations, each taken separately, describe, are therefore of an ideal nature. And if the accounting equation A = Y — according to the definition — must always be fulfilled, the other one can never be fulfilled, except for Y*. It is therefore the nonsense of a “lawfulness for spending behaviour” that cannot at all occur in this form in reality. And it must be a lie that economists have found the course of the whole straight line — as they never tire of affirming — by observation in reality. That is why in some economics books this straight line is only drawn dashed, which is supposed to express that it — by the way, the only empirical straight line — is actually not there. Unfortunately, this is very fatal. Fatal for the point of intersection. There is no longer a straight line that could form it, so there is no intersection point, so there is no equilibrium.
Conclusion:
Mathematics is used to bring the economist’s ideological message into the world: the economy is a mechanism. It has an inner coherence that always works out, and people produce precisely that coherence with what they want — their will fits the mechanism like a glove. Their freedom of choice is in accordance with necessity, is the moral of the system of equations. These inverted ideas of the political economist are given credibility by the fact that he grasps them mathematically: A world in which the cooperation of opposing purposes is enforced is supposed to be conceivable as a factual law and mathematically well-ordered through the invention of his mathematical lawfulnesses. Calculability is supposed to lend the world of the economy irrefutable reason and present it therein as just as unchallengeable as nature, whose laws actually have objectivity and mathematical form independent of volition.
Example 3: The microeconomic thought of optimisation or: Every economic subject always calculates its best
In everything that man does and pursues — buying insurance policies, playing the violin or simply hammering a nail into the wall — he can do his thing well or badly. He deserves the predicate “good” if he gets what the respective activity is all about right. He deserves the predicate “bad” if he does not properly meet the requirements of his actions. This may be due to external obstacles, incapacity or bias from other purposes. But no matter. What is good and what is bad is in any case measured by the activity to be carried out; “good” coincides completely with the fact that it is carried out according to its purpose and undisturbed. Therefore, one does not resolve, firstly, to hammer a nail into the wall and, secondly, to do this as well as possible. The one resolution is quite sufficient, everything is contained in it.
Microeconomics now claims that the behaviour of economic subjects can be explained by the fact that they want to do their thing as well as possible: Whatever they do, they optimise, as the scientific expression goes. And from this principle, an understanding of the respective activity as a whole should emerge.
This thought of optimisation is wrong because it makes something the general content of economic activity, which, as we have seen, cannot be a determination of the content of anything in the world at all. What constitutes the individual activities — going to work, buying shares, etc. — is thus simply assumed; their specificity is not deemed worthy of determination or further explanation. Conversely, these economic activities are to be understood as examples, special cases and incarnations of the activity, which in this abstractness is contradictory and empty of content, that consists in doing it well.
In order to transform his false abstraction, i.e. “doing well” as an independent activity, into a scientific object, the microeconomist invokes mathematics, and in particular he thinks of the following section: mathematics has procedures for calculating so-called extrema, i.e. maxima, minima, of functions.
Anyone who has attended a secondary school knows the basic features of this technique under the keyword “curve sketching”, and they have certainly seen it applied. For example, to calculate the highest point or the angle of greatest range in physics for projectile motion. But if mathematics deals with extrema problems and techniques for solving them in such a general way, then this is far from being the false abstraction of optimisation that the economists are aiming for. Just as numbers belong to arithmetic with its rules and techniques, so curves or the functions describing them belong to curve sketching. These are the objects of mathematics, abstract but precisely determined things, and they have nothing in common with the conception of “wanting to do it as well as possible”.
Now, in order to pass off the cause of mathematics as his own, the microeconomist next claims that the economic activities he contemplates consist in finding a maximum for a variable quantity — the so-called objective function. Whether it is working, shopping or investing money — economics proclaims that these are all tasks of determining extrema as a highly scientific aspect of the matter.
How stupid this assertion is, can perhaps best be seen in the example of an economic activity that actually has a quantitative criterion for good or bad performance. When someone speculates on the stock exchange, he wants to make a profit, a surplus in money. And money as a purpose has it that you can never get enough of it. The conception that such a speculator — or a capitalist in general — strives for a maximum profit is, however, fundamentally wrong for this very reason: measurelessness is the principle of profiteering, and not striving for a maximum profit. And as little as he intends to aim for a very specific level of profit, just as little does he have a function or curve that would allow him to establish this “correct” point. After all, it is called “speculation” and not “calculating”, when it is a matter of buying and selling the right securities at the right time. Has the loser perhaps forgotten that he wanted to optimise? Or has he been handed the wrong curve in the lottery of fate?
Better a Mercedes than another BMW
The continuation of theory therefore necessarily consists in the new creation of its objects:
“The aims pursued by the economic subjects under consideration in reality are difficult to grasp and cannot be clearly formulated … One can generally assume a concern for the well-being of the family members and thus that the household will in each case select the assortment of goods that appears most favourable to it and that it can purchase with the available budget … In the older literature, instead of the assumption of the choice of the best possible assortment of goods, the aim of maximising utility — in the sense of a maximum of achieved satisfaction of needs — was formulated. Theorists like Gossen … sought to measure the utility of households in definite units of utility … This is why this approach is referred to as a cardinal quantity of utility. These efforts have not produced the hoped-for success; there has been a general backtracking in budget theory and one confines oneself to making comparisons of utility … One has retreated to an ordinal concept of utility, but still retains the aim of maximising utility, even though this is not measured in absolute quantities … This does not change anything in the result of the analysis compared to traditional approaches”. (Böventer, 11–12)
Of course, the aims of economic subjects are not at all difficult to grasp. People will certainly know what they want, and the economist would only need to ask them, for example. And of course, even without this effort, he already knows what the answers would look like — but this is precisely what bothers him: “in reality” there are manifold purposes and needs, but far and wide there is no “unambiguous” objective function. To “formulate” it correctly is therefore the task of science.
For the “household” — the economists’ stylisation of purchasing and consuming humanity — the quantity to be introduced is called “utility”. Naturally, a consumer distinguishes in the multitude of useful things what serves his specific needs and what does not, or what he then likes better or worse in the individual case. And the limits of his wallet constantly force him to forego one thoroughly desired item when shopping so that he can afford the other. But neither the differences that need makes, nor the renunciation that dear money imposes on one, can be explained by a quantity called “utility”, which is supposed to be more or less present. What should that mean, that a car would bring me more utility than a trip to Tenerife? Either I don’t want to go there at all. Or I would like to have both, but for financial reasons I have to choose between these things, which are not at all comparable. Then I may even have reasons to choose the car (and usually such reasons are again born out of necessity, i.e. that I need the car for my daily obligations, for example). But certainly I do not leave one need unsatisfied because the other gives me “more satisfaction”. After all, hunger is not worse than thirst and vice versa.
The modernisation of utility theory: an optimum of nothing in particular
This idiotic conception of mutually comparable amounts of utility or degrees of satisfaction granted by completely different consumer goods is absolutely necessary, but also completely sufficient for the transformation of shopping into an optimisation problem. Nevertheless, economists have decided to improve on their central mistake. For example, some have taken issue with the fact that because utility does not exist, it cannot be measured convincingly. Although utility shares this fate with all quantities of economics (see national income), this time the economists have fallen for the quirk of wanting to carry out their programme with the explicit renunciation of a measure of utility. The basic idea is this: You can have a group of people line up according to their height. But you can also have these people line up in alphabetical order. In both cases, you can then let the first in line step forward. And this fact, that a linear order can also be produced without a comparison of quantities, but according to a different principle, has inspired economists to carry out their optimisation programme without utility quantities and their comparison: Henceforth, utility maximisation is to be understood as choosing the highest position in a ranking of goods.
We would rather not ask the question of how a consumer is supposed to establish this ranking. Economics considers itself a paragon of scientific honesty when it makes no assumptions about this. But that this hierarchy exists in everyone’s brain box is something it would like to assume in its scientific honesty.
It then considers the question of how to find the way back from the conception of a ranking to the tried and tested curve sketchings of mathematics, which are what one is actually aiming at, to be far more meritorious.
We certainly won’t arouse any astonishment if we summarise here that this path is paved with intellectual cliff-hangers, that it is hardly ever completely understood by students of microeconomics and that even renowned textbook authors fail to present it according to their own quality standards. (e.g. Böventer p. 61: “The concept of continuous preferences is not entirely simple, and we will therefore not develop a general and formally precise definition of this concept …”). And of course it is all mistakes. The most important one should be mentioned here: If, in our example, we have the people line up in alphabetical order, we can then also assign them ranking numbers: Amalie = 1, Anselm = 2, Anton = 3 etc. etc. Eureka, screams the economist, we are back in the quantitative field!
But such ranking numbers are only an alternative way of expressing or registering the ranking under consideration. One uses the fact that the numbers also have an order, one makes a comparison, so to speak. But that doesn’t mean that one can appropriate all the qualities of numbers. Numbers indicate a more or a less — but what should it mean that Anselm is more than Amalie, and Anton even more? And one can calculate with numbers — but what should it mean that Anselm is Amalie twice, etc.?
The economist himself admits this difference with his ostentatious differentiation between “cardinal” and “ordinal” quantities — but only insofar as he is keen to circumvent the vexed problem of measuring utility. And no sooner has he advertised the strategic scientific advantage of mere “ordinal” quantities than he simply forgets the difference, which is still so important, and treats his ranking numbers like normal cardinal quantities. This distinguishing and subsequent forgetting is the secret of the last sentence in the quote: “This does not change anything in the result of the analysis compared to traditional approaches.”
So: First, one is supposed to believe that consumers do not assign a “utility” of varying quantity to the goods, but only indices or ranking numbers according to a ranking order — and then one is suddenly supposed to believe that there is a continuous, differentiable “utility function” equipped with other mathematical conveniences that allows the quantity of utility to be calculated from the quanta of the goods under consideration.
So first the consumer is only supposed to find a shopping bag with 20 cigarettes and two pounds of oatmeal better than a shopping bag with 100 cigarettes and one pound of oatmeal. But then all of a sudden he is supposed to have a function (example Böventer p. 89) u = x₁ x₂, where u = the utility, x₁ = the cigarettes and x₂ = the oatmeal. Of course, we readily believe that wonderful problems of extrema can now be posed and solved. But the fact that this scientific achievement owes itself to a fraud is still abundantly clear even in the result: on the one hand, utility is supposed to be a number where one should not be allowed to think anything; but on the other hand, utility has now suddenly acquired a dimension, namely pieces of cigarettes multiplied by pounds of oatmeal, and has thus become a very substantial, if not necessarily palatable, thing. And what if our consumer has changed his utility function to u = x₁ x₂² for the new year? Then utility is suddenly cigarettes multiplied by oatmeal squared and thus a completely different thing than the year before!
Science has determined: Everything is fine in the world!
In the theoretical efforts of microeconomics, it is impossible to overlook the claim that one must be able to calculate what economic subjects do and pursue. But if, to stay with the household example, the shopper steps out of the supermarket, does microeconomics know what is in his plastic bag? Not at all. For the calculation methods developed with so much effort by theory only work if the utility function postulated at the beginning is known. And not even the biggest braggart among economists will claim that.
So all the formula stuff, which is supposed to be there for calculation, is reduced to a commentary on world events. The comment that the buyer has certainly purchased the most favourable range of commodities within his financial limits.
On the one hand, this comment is the silliest tautology imaginable. Because of course nobody buys Lucky Strike instead of Marlboro if they would rather have Marlboro.
This is just as clever as if a meteorologist did not give a weather forecast, but limited himself to the information that the weather that “prevails” always comes.
On the other hand, this pseudo-certainty provides for an interpretation of buying that has a lot in it. For when shopping, one is confronted with the fact that the objects of need fill the department stores, but that they are by no means destined for oneself. As commodities, useful things have the purpose of earning money for their possessor. Capitalism produces wealth en masse and separates it from the needy individuals. One might call that a contradiction or just shit. But economics transforms this highly uncomfortable and by no means necessary relation (after all, enough is produced) into an eternal problem of humanity, which is supposed to consist in making the best out of limited givens. And from that point of view, a world full of poverty and violence is quite alright.
Of course, this apologetic interpretation cannot be proven. In place of proof, however, there is now the prescription that such a worldview can be carried out according to all the self-imposed rules and chicaneries of science.
Such theorists do not ask themselves what the purchase of commodities is, but how the preconceived good opinion of it, the thought of optimisation, can be expanded ever more precisely. That is why they first come up with a very exact utility. That is why they are so free to next substantiate this utility function much more exactly through abstract orders and hierarchies. And that is why these brothers are so keen on mathematics.
Numbers, functions and equations are not only the insignia and showpieces of erudition, but in fact also the adequate means of expression of the messages that economists are keen on: all factual laws and necessities, all calculation possibilities and equations that work out — in a word, the world of class antagonism and competition is all right.
German source: https://contradictio.de/missbrauch_mathematik_2.html
Literature used
· Henrichsmeyer, Einführung in die Volkswirtschaftslehre, Stuttgart 1978.
· Böventer, Einführung in die Mikroökonomie, 4. Ed., Munich 1985.
· Münnich, Einführung in die empirische Makroökonomik, Berlin 1982.
· Bartling, H.; Luzius, Grundzüge der Volkswirtschaftslehre, 4. Ed., Munich 1983.
· Stobbe, Volkswirtschaftslehre 1, Volkswirtschaftliches Rechnungswesen, 4. Ed., Berlin 1976.
