Economics is Only an Applied Mathematics?

 

INTRODUCTION

Students of economics nowadays mostly encounter the questions of why there are so many graphs and equations in economics that almost every explanations of economic phenomena were being done through mathematics. Some had already declared that the pre-requisite of taking economics are to have good commands and mastery in mathematics, which implied that it is widely accepted throughout the course, mathematical applications would be ubiquitous. The question arises then, is economics have something more to offer? Can it be applied to solve the real world economic problems?

One of the profoundest shortcomings of economics courses these days are that they don’t emphasize on history as a significant tool to properly understand economics in a wider sense. Every theories were actually constructed based on historical events, but unfortunately it seemed as if it were a priori logic that is so well established without referring to any historical occurrences. Thus students were trained to get indulged in doing the mathematical parts in economics without knowing how it came out to be the way it is today.

Therefore, this article seeks to investigate on the historical evolution of the discussions in economic studies, beginning from the era of the moral philosophers, to the era of utilitarians, and finally to the era of pursuing economics as a science. It causes some concerns to what has led to the practice of over-emphasis of mathematics and the deterioration of initial focus on values and morality in economics. In brief, this article suggests that the subject of economic discussion had shifted initially from moral philosophy to utility maximization, and finally to applied mathematics.

 

UTILITY PRINCIPLE

The current learning of Economics, specifically Microeconomics, prevalently applies the framework of ‘Neo-Classical Economics’. Most textbooks base their assumptions using the arguments of Neo-classical Economics which essentially begin with their one most important principle called ‘Utility Principle’. By having this principle as its foundational ground, other theories and discussions subsequently built up upon this fundamental law, such as the mostly known and famous theory in Economics, the ‘Demand-supply curve’ which actually has its fundamental basis from the ‘Indifference curve’. In constructing the indifference curve, economists will deal essentially with the individual utility functions.

It is important to note that the learning of current Macroeconomic theories also applies the similar framework of Neo-Classical economics, which took its foundation from individual theory of Microeconomics (methodological individualism). Therefore, the laws in Microeconomics serve the very underlying principles of Macroeconomic theories as well, thus making both Micro and Macroeconomics dependent on utility theory as their central principle.

‘Utility’ is roughly synonymous with ‘satisfaction,’ ‘well-being,’ ‘welfare,’ ‘happiness,’ ‘pleasure,’ etc. Generally, we can increase our utility by undertaking enjoyable activities or purchasing things we desire. In the words of Bentham: “By utility is meant that property in any object, whereby it tends to produce benefit, advantage, pleasure, good or happiness …”

Whereas in economics (textbooks), utility is defined as the want-satisfying power of a good or service; the satisfaction or pleasure a consumer obtains from the consumption of a good or service. This definition is widely used as to explain consumers’ behaviour in engaging economic activities, particularly demand behaviour, which was regarded as to gain as much pleasure and avoid as much pain as possible.

This idea was later developed to an extent that the economists wanted themselves to be able to measure utilities, that is to quantify the number of utils consumers had gained by doing transactions. In order to mould it into a model, some variables needed to be identified and sorted out. Accordingly, economists had to introduce and formulate (arbitrary) assumptions so that their models can be applied. This practice was, in effect, one of the basic set about for the economists to develop their theory through mathematical proofs.

 

HISTORICAL EVOLUTION OF THE THEORY OF UTILITY

In general, the theory of utility can be traced back to the theory of happiness by Epicurus, then by the Christians, and later by the Muslims. Nonetheless, this article will only deal with the historical evolution of the theory of utility beginning from the eighteenth century.

It is argued that the theory of utility can be situated from the discussion of the distinction between the “value in use” and the “value in exchange” by Adam Smith. The word ‘value’ is observed as having two different meanings, sometimes expresses the ‘utility’ of some particular object (value in use), and sometimes the power of purchasing other goods which the possession of that object conveys (value in exchange). The things which have the greatest ‘value in use’ have frequently little or no ‘value in exchange’; and on the contrary those which have the greatest ‘value in exchange’ have frequently little or no ‘value in use’.

“Nothing is more useful than water: but it will purchase scarce any thing; scarce any thing can be had in exchange for it. A diamond, on the contrary, has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it.” (Adam Smith, 1776).

The distinction of the ‘use value’ and ‘exchange value’ was further discussed and revised by David Ricardo and Karl Marx which subsequently led to the formation of a famously known idea, the labour theory of value. The theory asserts about that from which source does the value came; which Marx and Ricardo tried to prove that it is from the labour, instead of land as opposed to the physiocrats. These types of discussions were categorized under what the economic historians called the Project of Classical Political Economy. The extension of this project then eventually brought the discussion all the way through to the emergence of modern theory of demand in the theory of consumer behaviour, which largely applies psychological-behaviouristic approach.

The original approach in the modern theory of demand is attributable to Gossen (1854), Jevons (1871), and Walras (1874) where utility was regarded as a measurable quality of any commodity and was further assumed to be an additive quality. These early writers merely assumed that utility is cardinally measurable and that the utility obtained from one good is not affected by the rate of consumption of another. Say for example consuming rice of 6 utils was assumed to be exactly a doubled satisfaction than consuming bread of 3 utils. Nevertheless, this assumption was revised to be more realistic as to explain real world consumer behaviour.

Edgeworth (1881), Antonelli (1886), and Irving Fisher (1892), among others, came to realize that utility theory in no way depended upon the additivity assumption. Hence, these writers assumed that utility is a measureable quality that is generally non additive. But the assumption of cardinal measurement still hold until Vilfredo Pareto (1906) came to lay the foundation for measuring utility, by which giving a new interpretation to what have been projected by the previous writers, as to say that utility surface or graphs are actually by ordinal measurement. This means that the number of utils are merely a rank or to put in order to each other, and not an exact measurement of the utilities. This, finally enabled later writers to develop the theory of consumer behaviour using the indifference curve or indifference map, primarily based on these assumptions: rational consumers and full information; between two commodities; non-satiety; ordinal utility; transitivity, and also; the diminishing marginal utility.

 

THE SHIFT FROM MORAL PHILOSOPHY TO THE THEORY OF UTILITY

The current prevalent economic theories taught at most institutions around the world is largely Neo-classical Economic theories, by which the origins of the study of economics can be traced back to the Christian theologian philosopher Thomas Aquinas, or even Plato and Aristotle in the Republic, and Politics and Ethics, respectively; if not Adam Smith as has always been regarded as the father of economics. But as a Muslim economist, we tend to say that Ibn Khaldūn is the real father of economics, mainly because of his significant and ground breaking contribution in his Muqaddimah. In fact, there are numerous other Muslim scholars that have contributed a lot in the study of economics, before and after Ibn Khaldūn era, namely al-Shaybānī, al-Qarashī, Abū Yūsuf, al-Shayzarī, Abū ῾Ubayd, al-Mawardī, Ibn Taymiyyah, Ibn al-Qayyim, al-Maqrīzī and others.

From the all these names of the early writers that is largely included in the study of (what we now call) ‘economics’, we know that their initial concern and focus was more on the study of moral philosophy. As most Muslim scholars, particularly al-Ghazālī, have always been emphasizing, that economics (tadbīr al-manzil) is categorized under the division of practical philosophy (al-ḥikmat al-῾amaliyya), which includes – apart from economics (management of the household) – ethics (management of self) and politics (management of society). All three (ethics-economics-politics) are actually and should be interconnected, grounded in, and directed by the same core of ethico-moral values and principles.

Historically, the study of moral philosophy had shifted to be an independent science of economics in many ways. Take Adam Smith for example. Most of his works were arguably misinterpreted by a number of economists whom in advocate of the capitalistic system, that is largely been criticized for disregarding moral aspects in economic activities, and for inculcating egoistic individualism. Adam Smith whom was known in his time as a professor of ‘moral philosophy’ at Glasgow University, had written a significant work prior to the famous commonly cited book the Wealth of Nations, namely the Theory of Moral Sentiments.

Turkish professor, Doğan Göçmen, illustrated elaboratively on how Smith’s works were misinterpreted, largely by economists that advocated on the practicality of the ‘Trickle-down Theory’. The famous commonly cited passage by Adam Smith from the Wealth of Nations was argued to often be read in a de-contextualised way and without any terminological relations to the Theory of Moral Sentiments, which has primarily and crucially set the background of this passage. In fact, professor Göçmen emphasized and allocated a big portion in his book on the ‘social individuality’ brought by Smith in the Theory of Moral Sentiments, as opposed to the commonly understood as the ‘egoistic individuality’, taken exclusively from the Wealth of Nations.

What has come to our time now is the problem that moral philosophy is not, in fact, a science in the sense that mathematics, chemistry, and physics are. Moral philosophy is the study of right and wrong, good and evil, better and worse. These polarities cannot be translated into quantitative and measurable terms and, for that reason, moral philosophy is sometimes discredited as lacking scientific objectivity. Thus, the effort of many economists to make the study of political economy a natural science draws the subject out of its broader discipline of moral philosophy, which leads in turn to social mischief.

 

OVER-EMPHASIZING MATHEMATICS IN ECONOMICS

Attention should be given to one of the role that tried to make economics as (predictive) science as possible, that is the over-emphasis of using mathematics in economics. The origins of mathematization of economics also been contested among economists. However, and regardless of the precise historical development of such relationship, what seems to be useful to note are Wassily Leontief’s and Gerard Debreu’s main conclusions: “mathematics have allowed economics to progress as a science; and, economics have the same all-social-science epistemological boundaries given the nature of its object of study – society.”

The reason for economists’ struggle to mathematize economics is that the use of mathematical logic has given economics the chance to scientifically progress through a constant dialogue with previous proposed ideas and theories. In Debreu’s words, “the great logical solidity of more recent analysis has contributed to the rapid contemporary construction of economic theory. It has enabled researches to build on the work of their predecessors and to accelerate the cumulative process in which they are participating” (Debreu, 1991).

It is not to be denied that mathematical pursuit in economics should not be disregarded entirely. There are countless actions fruited from the theories propounded by the economists through their mathematical modellings. But somehow here lies the very problems, of which the economy is somehow driven by the statements and convictions of the economists as well. We should recognize and acknowledge the limitations of the economics as being pursued as a ‘science’ and using mathematical proofs, thus arrange it to its appropriate order. Of course, it could usefully serve as an explanatory tool to some extent, but certainly not as the end itself.

The problem lies not on the speed progress and vast development of economics mathematically, but rather on the over-emphasis of mathematical formulations which to the extent that we may overlook and had misdirected the purpose of learning economics at the first place. To add up, even the main considerable purpose of having economics developed mathematically and quantifiably is expectantly to improve its ‘predictive power’, is largely criticized. Let alone the other non-significant purposes. The science of economics should be learned essentially as a science of earning and provisioning for livelihood, rather than only to predict or explain or develop for its own sake!

 

CONCLUSION

Conventional utility theory taught in economics text-books are widely understood as it could result to normalization of a self-interested economic behaviour or aptly greedy behaviour. Nevertheless, as had already contrasted above, the concept of ‘self-interest’ that was meant by Adam Smith is different. Some went to differentiate the terms into ‘selfishness’ and ‘self-interest’, by which Smith always meant to say the latter.

However, it is interesting to note that the concept has some resemblance to the concept  of Farḍ al-Kifāyah that was mentioned by al-Ghazālī in his Iḥyā, which means that by further focusing on ‘improving oneself’, will eventually improve the society as a whole. Nonetheless, the fundamental difference in these two concepts are that the ‘self-interest’ by Smith is still can be based on utility-fulfillment, while al-Ghazālī implied that the behaviour should be rooted by the sense of responsibility and obligation to suffice what is there not sufficient, based on its priorities accordingly.

All in all, the shift of economic discussion from moral philosophy to utility maximization, and finally to applied mathematics has been an intriguing progress to some, whom concerns more on solving real problems. Herewith, we must, first, recognize the limitations and drawbacks of studying economics as an independent science, which consequently bring the need to have interdisciplinary studies of economics with other sciences, especially history and philosophy.

 

REFERENCES.

Debreu, Gerrard (1991). The Mathematization of Economic Theory. The American Economic Review. Vol. 81. No. 1.

Göçmen, D. (2007). The Adam Smith problem: human nature and society in The theory of moral sentiments and The wealth of nations. London; New York, NY: Tauris Academic Studies.

Hudson, M. (2000). The use and abuse of mathematical economics. Journal of Economic Studies, 27(4/5), 292-315.

Kenneth Lux (1990). Adam Smith’s Mistake: How a Moral Philosopher Invented Economics & Ended Morality.

Smith, A. (1776). An inquiry into the nature and causes of the Wealth of Nations. Indianapolis, IN: Liberty Press.

____ . (1759). Theory of Moral Sentiments. Oxford University Press, New York.

Samuelson, P. (1937). A Note on Measurement of Utility. The Review of Economic Studies

Setia, A. (2013). Al-Ghazali on the Proprieties of Earning and Living: Insights and Excerpts from His Kitab Adab Al-Kasb Wal-Ma’ash for Reviving Economies for Communities. Islamic Sciences, Vol. 11 (Summer 2013) No. 1.

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