by Mario Fabbri
But even so this analysis is more articulate than those of certain ‘experts’ who, as always, continue to propose the same free-market or centralist remedy, evidently measuring it not against the real situation but on their own inclinations: free-market or centralist.
The typical exponent of one of the two parties only looks and sees the developments that “run parallel” to his own natural proclivities, ignoring or removing all the others.
As a result, he makes proposals that are appropriate in some cases and inadequate in others, and the outcome is only a question of luck as to whether or not his political bent coincides with the type of ongoing crisis, and does not depend on a real understanding of the situation.
1 FABBRI, Fabbrica delle illusioni, pp. 245-247.
2 Some examples of problems for economic mechanisms related to scarcity of the circulating money supply: the crisis which began in England in 1621 and lasted for forty to fifty years until the spread of trade credit (see Fabbrica delle illusioni, pp. 31 ff.), the various attempts to make up for the shortage of gold and silver in the 16th-century American colonies with substitutes, ibid. p. 36, the hyperinflation such as in 1923 in Germany, when the ‘total real value’ of the currency usable for transactions collapsed, ibid.
A quick look at the kind of gross errors produced by the unrealistic use of mathematics by economists.1
On the futile use of mathematics in economic theories
That the impressive mathematical elucubrations of economists have only the remotest of connections with reality is made clear by some monumental oversights, which could not happen or would become immediately apparent if – as physicists or engineers do – they used formulas to measure facts and not just to burnish their image.
Here are two examples of topics comfortably remote from practical matters, which certify that such an abstract use of mathematics, devoid of concrete feedback, makes it impossible either to become a good mathematician or to understand what is really being talked about.
In 1874 Léon Walras, generally considered the founder of mathematical economics, is guilty of a gross mathematical error.
He puts together a huge system of equations that in his opinion describes “in principle” how the market functions, convinced that as he has as many equations as unknowns, it has a solution. He does not realise that it is actually contradictory as follows, the inconsistency of which, with only 3 equations and 3 unknowns, is much easier to see:
x + y + z = 5
x = 1
x = 2
But this crucial oversight, which renders a fundamental part of his celebrated theoretical construction devoid of value, completely escaped the notice of the whole ‘scientific community’: it was discovered by a young Italian scholar2 in 1960, eighty-five years later!
More recently, in the 1960s, the fierce controversy between the two Cambridges on capital theory developed: it was born out of an obscure paradox that had emerged by comparing two hypothetical techniques of agricultural production: one ‘less capitalised’ with many workers who use hoes, and one ‘more capitalised’ with few workers who used ploughs.3 Another theme suitable for elegant but non-realistic reflections.
The apparent absurdity was that under certain conditions a rise in wages would make it more convenient to hire diggers, while we would expect that if wages rise, the number of workers should be reduced.
This unleashed a bitter dispute between members of the opposing schools – free-marketers against left-wing economists – with very subtle mathematical proofs, and demolitions, deductions, counter-deductions…
Too bad that fairly elementary reflection shows that this counterintuitive outcome is only the result of not having considered in its entirety the ‘model’ everyone was heatedly arguing about:
if a huge number of workers were needed to build ploughs – an absurd idea in the real world, but absolutely no problem in the enchanted garden of economists’ models – to stop producing ploughs could make the workers who lose their jobs more numerous than the diggers who are hired. And the spread of hoes in place of ploughs would only be the logical reduction in the total number of workers resulting from a rise in wages.
To those kind readers who feel that theorists like Paul Samuelson or Joan Robinson4 could not possibly have ‘forgotten’ that there are workers even outside of the fields, I would suggest they review their assessments of this specific category of experts.
In fact, this simple possibility escaped them, as it did all the other participants in the debate, fully engaged as they were in outdoing one another in the sophistication of mathematical reasoning while standing shoulder to shoulder in their disinterest for what their formulas might correspond to in reality.
1 For accurate analyses of some gross mathematical errors plaguing today’s economic theories cf. KEEN, Debunking Economics, which is dedicated specifically to the theme.
2 He is Pierangelo Garegnani. Cf. GAREGNANI, Il capitale nelle teorie della distribuzione, pp. 91 ff., summarised in Fabbrica delle illusioni, pp. 187-188.
3 Cf. Fabbrica delle illusioni, pp. 205-210.
4 In truth, Joan Robinson, as she in 1953 encountered the paradox, had the healthy intuition that it was better not to pay attention to it. But ten years later, she could not resist the temptation to pull it out against Samuelson’s ideas on ‘capital’. Cf. B, The Cambridge Controversies in Capital Theory, p. 44.
Story of Ylati land
Once upon a time in the large archipelago in the South Seas, at the other end of the world, lay the ancient kingdom of Ylati, comprising the islands of Frigida, Tepida and Calida.
All three were large and well populated. Frigida was the coldest and furthest south – there all things are upside down – with a conformation that was perfect for growing wheat, the staple diet in Ylati and the benchmark for calculating the value of all things. Its fertile, broad planes were inhabited by robust, hard-working farmers, who made the region the richest and most prosperous in the country.
On Tepida, the middle island, stood Emor, the capital of the Ylati kingdom. There the climate was warmer and wheat production lower. But the inhabitants of Tepida, which included numerous lawyers, notaries, civil servants and courtiers, lived well, thanks also to the taxes sent to Emor by the rest of the kingdom.
On Calida, which was warm and mountainous, the climate was even less suited to farming and the inhabitants were accustomed to living roughly, with what little wheat they were able to coax, with difficulty, from the ground.
One day the old king died and soon after his only son Carlo was crowned.
Carlo was young and full of good intentions, and wanted to increase the prosperity of the kingdom and to win the love of his subjects, but he did not know what he should do. This was partly because the ministers that the old king had left him, who were mainly old and white-haired, thought everything was already functioning perfectly and spent all their time dissuading him, gravely and solemnly, from making any changes.
Among them was, however, a man called Gaetano, an original thinker and highly intelligent, with a deep knowledge not only of the situation of the country but also of the character of its people. He understood the disposition of the young king and found a way of talking to him in private, and after the usual obsequious phrases, which we do not need to repeat here, spoke as follow:
GAETANO Sire, I have always pondered on how to improve the state of the kingdom, and have found some ideas which, I would like to think, could be worthy of attention. Unfortunately ignorance is so widespread in this court that I have never found anyone to share them with, but now generous fate has brought us, in the form of Your Majesty, a person who is able to decide whether they have a little bit of value and even, if he thought it advisable, bring them to pass.
CARLO Noble friend, speak freely, because I am obliged to examine with the greatest attention any suggestion that might bene
fit my people.
GAETANO Your Majesty, I think that to make Ylati as prosperous as possible and to assure you all the riches, splendour and security that to such a noble sovereign are fitting, we must be aware of the differences between the three regions that make up the kingdom, because it is not advisable to treat things that are different in the same way, but we must adapt their treatment to the nature of each one.
So, the island of Frigida, the most fertile and productive, should be the one where wheat production expands so much that it will meet the needs of the kingdom’s whole population. And this will be the source of your wealth.
Tepida, once it is relieved of the worry of having to procure nourishment by work in the fields, will be able to turn itself, particularly here in Emor, to increasing the magnificence of its buildings and the perfection of its arts, becoming a worthy stage for Your Majesty. And this will be the source of your splendour.
Calida, which lives roughly, will be the island that will benefit the most from distribution of the wheat, and as its inhabitants are accustomed to loving their benefactors, they will be very faithful to you. And this will be the source of your security.
CARLO What you say is all very well, but I just do not believe that Frigida will be able to feed the entire kingdom, no matter how fertile and well cultivated it is.
GAETANO It may seem strange, Sire, but it is so. Although it is something new and still unknown here, on the large islands south-east of Ylati, new cultivation techniques and seeds have been found that multiply the harvest three- and four-fold. On Frigida the climate is almost the same as on these islands and some who have already begun to use the new seeds have already obtained the same effects; it is in fact inevitable that their example will spread and soon the whole of Frigida will adopt the new system.
CARLO So then there is nothing for us to do: your proposal will come true by itself!
GAETANO Alas, Sire, human nature will prevent it. We say, and we are cautious, that the new system will triple the harvest. But what would Frigida do with three times as much wheat? Everyone already lives comfortably, and it would be difficult to consume even one and a half times what they consume now. They could, of course, if men were rational, halve the cultivations, and with half the land and half the work they could live comfortably, less stressed and more carefree. But I know those people: they are too hard-working and set in their ways. All would turn out differently: half of them would continue to cultivate the fields and with the new seeds they would easily feed themselves and the other half. The others would go to the towns and invent some imaginary job to keep themselves busy, as solicitors, civil servants or something else, following the example of all those strange professions which the arrival of tithes has fuelled here in Emor. So we would lose many good farmers and the wheat of the rest of the kingdom would not increase by one grain.
CARLO You have looked into these matters thoroughly, I see, not like those old fogies who are always trying to lecture me! But what can we do.
GAETANO Just one thing, Your Majesty. As the new technologies spread on Frigida we will gradually raise taxes, to syphon off the excess that is needed by the rest of the country and to keep the farmers in the fields. Eventually on Frigida people will work as much as they do now but will produce three times as much wheat, and because they will not consume more than one and a half times as much as they do today, all we have to do is fix the tax at five tenths to relieve the island of the excess wheat it could not use. And these tax increases will give two benefits: everyone will be obliged to quickly adopt the new technologies and will continue to cultivate the fields, in line with their vocation of hard-working farmers, rather than becoming solicitors or civil servants, professions much more suited to the population of here and Calida.
CARLO I can see what you are saying, but I do not think that the inhabitants of Frigida, who I know to be very stubborn on these matters, would be pleased to be the only ones paying tax while everyone else eats their wheat for free.
GAETANO Your Majesty, I admit on this I was doubtful too, and afraid the obstacle would be unsurmountable. But then I saw the solution in a flash! We have to tax all the inhabitants of the kingdom in the same way, at the same rate of five tenths!
CARLO My noble friend, I am amazed. The things you were telling were really interesting; I hope I do not discover I was talking to a visionary. A Chief Minister of the State receives one thousand measures of wheat, surely you don’t really believe he would be happy to receive five hundred? And a young civil servant who just manages with four, how would he get by with only two? And when everyone is taxed, as there will be no greater harvests to draw on, except in Frigida, they will all be poorer and everyone will hate me.
GAETANO No, Sire, let me explain myself. Take the Chief Minister. Today the one thousand measures are delivered to him from the royal warehouses. Tomorrow all we will have to do is to add the small formality of handing him, together with his usual load of wheat, a nice payslip with the words “Emoluments of His Excellency, Chief Minister of the Kingdom: two thousand measures. Tax at source: one thousand measures. Net emoluments of His Excellency Chief Minister: one thousand measures”. We will figuratively double the payment and simultaneously tax it figuratively one half, and everything will remain the same, except that the whole world will see that the Chief Minister pays his tax to the last penny. And we will have to do the same with all the courtiers, ministers and civil servants. We will write plenty of payslips containing the three magic words: “Gross, tax, net”. The net is what each one receives and that really does leave the state warehouses, but the other two figures are very important and must always be written exactly and with all numbers well marked, because it must be absolutely plain to everyone in Frigida that all the other taxpayers pay precisely what is due. And also the wheat must not be sent to Calida in a rough and ready fashion as we often do today! No, to give wheat to someone we must first hire him as a civil servant and then, if we wish to give him four measures, we write on his slip that, thanks to his work, he was entitled to eight measures, but because of tax only four remain.
CARLO What you say leaves me thunderstruck; it is totally outlandish, but I can follow it so well that I can imagine one of the less smart beneficiaries who is upset reading his payslip because he thinks that really there were eight measures ready for him, but at the last moment, half were taken away, and he protests he is poor and should not have to pay so much tax. But please continue.
GAETANO Your Majesty, I should rather stop here, because I see that you have understood perfectly, but since you allow me to do so, I would add a couple of things: although it would be nice if the people we hire as civil servants also did something useful, that is not at all necessary. They appear as hired only to enable us to give them the wheat more covertly, and to increase the number of people indebted to Your Majesty. But it is very important that they behave like real civil servants, even if they do not know how to do anything or have nothing to do. They must go to the office every day, at least for some time, because otherwise the hoax would be too evident.
And to avoid making everyone a civil servant, we could also simulate some ventures, especially productive ones, like a large new plantation, even in an unsuitable area, and run by inexpert personnel, which would consume wheat instead of producing it. It would not matter what it is, provided that externally it appears not to donate but to produce, and to each beneficiary is given the appropriate “gross, tax, net” with the numbers clearly written.
And when the whole country is full of people who pay their taxes without complaining, what could the Frigida people object to? The Tax Collector will go to one of them and say, “Here you have two thousand measures of wheat and the tax is one thousand, so only one thousand must remain.” These are the same words that he might have said to the Chief Minister in the capital. But there the one thousand measures appearing as tax did not exist in any place, while here they are real, and must be tak
en away quicktime.
The young king was so taken by Gaetano’s fanciful scheme that he immediately made him Prime Minister, endowing him with all the necessary authority to make real what he had outlined so well in words.
And Gaetano, in addition to being an acute observer of men, was also full of energy and very tenacious and efficiently initiated and organised everything he had devised.
So it happened that the inhabitants of Frigida mastered the new technologies, and boosted the size of the harvest to an extraordinary degree, even more than was originally thought possible. And all the other novelties were also accepted without too much discontent, including the huge increase in nominal taxation, the preparation of the necessary pay slips and the many fake jobs, which in Calida were very popular with those who received them, and were represented with great naturalness and credibility, so that soon the whole country was convinced that there was nothing more honourable than being a tax-paying worker.
Everything was proceeding swimmingly, until one day Gaetano came to the palace to speak to the king.
GAETANO Your Majesty, we must deliberate carefully, because we’re heading toward a serious problem and I fear that if we cannot solve it, all our efforts will have been in vain or perhaps harmful.
CARLO Indeed my dear minister and friend, I do not understand. Everyone is happy, no one suspects anything and our blessed Frigida effortlessly produces much more wheat that we could ever have hoped for.
GAETANO Alas, Your Majesty, that is exactly the problem I was referring to. I calculated that the harvests would increase three-fold, but they have now reached four-fold and continue to grow.