In my interactions with aspiring students of Economics I have often been left bemused with this one question, “Do we need Math to study economics?”
In the dilemma of choosing between discouraging them or lying, I have often taken the third path of responding by saying, “Math is not hard, it makes Economics even more interesting!”
Demystifying Math or the need to know it and know it well for Economics is not an easy job, especially when students, more often than not, opt for Humanities or Social Sciences to escape the dreaded Math. So is Math a prerequisite for an undergraduate (UG) programme in Economics and how much?
This one has been a long-standing debate, with its proponents arguing that the nature of economic reasoning is best exposed mathematically. In the words of the French economist, Gerard Debreu, “A formal model of an economy acquires a mathematical life of its own, it becomes an inexorable process in which rigour, generality and simplicity are relentlessly pursued”.
On the contrary, notable economists like Paul Krugman have said, “As I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth”.
While it is certainly not an exaggeration that Math has found its way into Economic theories as old as Adam Smith’s Wealth of Nations, there is a queer feeling of insecurity, diffidence and even scepticism among economists and aspiring economists on the overwhelming invasion of Math into the discipline since the late 19th century.
The early dalliance with Math was justified as an effective tool to present economic ideas but economists like Walras, Fisher and Cournot took this affair to unprecedented levels and very soon, much of the credibility of economic theories rested on the mathematical models and derivations used.
Elaborate discursive presentations were now offered in the form of crisp mathematical equations with the potential for analysing multiple complex scenarios, the interaction of various forces and so on, through slight tweaking of these equations. Interestingly all three of these economists and many other established ones were trained in Mathematics, Engineering or Pure Sciences.
Inherently, Economics has appealed and enticed students from other disciplines like Math and Physics for its problem-solving and real-world application giving it an edge in the job market.
Richard Freeman, in his article titled ‘Its Better Being an Economist (But Don’t Tell Anyone)’ argues with evidence from the American job market on how in the PhD world, an economist faces a way better chance to be employed in comparison to a mathematician or physical scientist and how quantitative economists are paid 60% more than mathematicians, when few mathematical economists could make it in mathematics!
The truth, unnerving as it may be for some, is that mathematics has naturally established a secure place in economics where rationality is assumed to be the premise for human behaviour and all economic variables are measurable.
Economic Optimisation, that accounts for a major part of undergraduate training, including problems on cost minimisation, profit maximisation so on, need basic calculus knowledge as a prerequisite.
Originally developed by John von Neumann, the game theory, an applied mathematical theory, was significantly used in economics by John Nash and others, winning the Nobel Prize for their contribution to understanding strategic oligopoly market behaviour.
Linear algebra is also extensively employed in economic analyses wherein economic aggregates are assumed to have linear relationships. The celebrated input-output analysis that fetched Wassily Liontief the Nobel has its basis entirely in linear algebra. It follows that knowledge of vectors and matrices are fundamental to economics students.
Further, statistics and probability, that aid in analysing and forecasting empirical data, are indispensable tools for economists or econometricians and undergraduate economics students need sound training in both the theory and statistical software packages used for data analysis. It is hardly surprising then that mathematical economics and econometrics have emerged as standalone courses globally.
Having said that, one must not forget that economics has its foundation in human behaviour and interactions that are far more indefinite, unpredictable and subtle than what mere numbers can capture. Bombarding economic theories with mathematics by virtue of being a mathematician indeed risks missing out on essential economic truths or solving problems in reality.
Further, economic responses, individually and collectively, rarely happen in isolation or vacuum since humans are as much political, social and emotional beings, simultaneously.
Therefore, employing Math in Economics to attain scientific respectability alone could be damaging to the discipline.
In conclusion, we may follow the rules set by the famous economist Alfred Marshal:
(1) Use mathematics as a shorthand language, rather than as an engine of inquiry
(2) Keep to them until you are done
(3) Translate into English
(4) Then illustrate by examples what are important in real life
(5) Burn the mathematics
(6) If you succeed in (4), burn (3)
(Dr Pushkarni Panchamukhi is Assistant Dean, School of Economics at RV University in Bengaluru. Views expressed are the author's own)