The Influence Math Has on Economics

For as long as economics has endured as a subject of study, mathematics has played a huge part in both the examination and the interpretation of economic concepts. It has endowed us to spot relationships between variables and correlations between quantities. Mathematics acquires the accuracy, rigor, and the scope to deal clearly with complex systems, which makes it highly valuable as a method for interpreting and evaluating economic methods. What is an economic model? An economic model is a simplified version of reality that allows us to examine, interpret, and make predictions about economic behavior.

The purpose of a model is to take a complex, real-world situation and reduce it down to the fundamentals. If done correctly, it can give the economist a better understanding of the situation. Mathematics can help us to simplify and better analyse data. In this essay I will be taking you through how much mathematics influences economics and what economists think of it.

Mathematics is a language. Once an economic problem is translated in mathematical terms then the logic of mathematics itself allows you to come to a conclusion. This is because it’s a very good deductive tool. Therefore it allows an economist to make more precise and accurate assumptions. It also fits the basic definition of a universal Linguists who don't consider math a language cite its use as a written rather than spoken form of communication. Math is a universal language. The symbols and organization to form equations are the same in every country of the world. E Roy Weintraub explains that “there is no denying that mathematics is the language of contemporary microeconomic theory as well as that of empirical and experimental (micro)economics. This is because the language of mathematics offers levels of abstraction, precision, and rigor that do not exist in the language of anecdotes, metaphors, rhetoric, and stories” therefore implying that mathematics offers the precision that certain economic models lack.

The basic economic assumption is that the producer wants to maximise their profit and that the consumer wants to maximise their utility. This is where a topic in mathematics comes in- differential calculus. This is when the highest point or the lowest point of a function is to be obtained. Without a high level maths prowess this wouldn't be possible, and that’s why students who do a mathematics degree later go on to do economics. Proving that the mathematics skills are key to economics and are highly transferable. However the most important thing to be noted would be that economists use mathematics to save money, even in counter-intuitive ways, therefore further endorsing their reliance on it.

By using a simple profit maximization graph, economists can recommend that a company only sells 90% of the available seats instead of 100% to make the most money. Economists also use mathematics to establish long term success, even when some factors are unpredictable. For example, an economist working for an airline uses statistical forecasting to determine the price of fuel two months from now. The company uses this data to lock in fuel prices, or to hedge fuel. Bijan Vasigh, author of the book- Introduction to Air Transport Economics; explains that Southwest gained a financial advantage over other carriers due to its fuel hedging strategy.

Mathematical application allows us to create simulations that would forecast business outcomes, and if used correctly would benefit the wider economy. The maths in decision making is when economists determine the probable outcome or the risk of an event. “For example, hospitals want to know what the risks are of dying from an operation and if the benefits are worth it. The National Institutes of Health explains the relationship between litigation pressure and rates of C-sections and VBACs. Because of the increased risk of litigation, some states ban vaginal birth after C-section, or VBACs. This policy was likely made after an economist assessed what the statistical risk was to the mother and weighed it against the cost of a malpractice lawsuit based on this number. Thus, the decision is an economic one. Economists working for pharmaceutical companies make similar math computations to assess if the risk of taking a drug outweighs its potential benefits.”(National Institutes of Health: Relationship Between Malpractice Litigation Pressure and Rates of Cesarean Section and Vaginal Birth After Cesarean Section)

Even though the maths involved is quite simple, it can be very effective and this is why many economic students take at least a year of calculus, statistics and forecasting courses called econometrics. Even though maths is already proven to be a big element in economics it still has a lot of potential. “Economists currently do not calculate the effects of rainforest depletion or water pollution into things like profit maximization or business costs, for example- Quentin Grafton and Wiktor Adamowicz, authors of;The Economics of the Environment and Natural Resources; explain that economic standards such as GDP are inadequate when measuring the health of the economy. A new field is emerging called natural resource accounting, which attempts to attribute a dollar value to these costs.”

Some economists believe that mathematics is unreasonable and ineffective in the natural sciences, including economics. K. Vela Velupillai wrote that it’s “Unreasonable, because the mathematical assumptions are economically unwarranted; ineffective because the mathematical formalisations imply non-constructive and uncomputable structures.” This basically means suggests that the aid of mathematics in economics is unjustified and aimless. Another economist, Herbert G Grubel and Lawrence A Boland, saw that “In a survey, 250 economists express the view that there is too much mathematics in professional journals.” This further bolsters the argument that many economists are disliking the ideology that economics is slowly becoming a lot like mathematics. Alfred Marshall, for example had a strong skepticism regarding the use of mathematics in economics. He wrote “I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules.

Use mathematics as a shorthand language, rather than an engine of inquiry. Keep to them till you have done. Translate into English. Then illustrate by examples that are important in real life.”(1906 Alfred Marshall). It further implies that even if mathematics is useful and imperative, it can still have it’s limitations and downsides. Economics is considered to be a social science and this concludes that it should be more based on the psychological and biological side of the subject. The subject needs to be studied at a more experimental level if it is to tackle the more complex and challenging concepts within the subject. If economists perform mathematical calculations with imperfect information then in turn their models are rendered futile in times of a natural disaster. A fundamental assumption in economics is that people act rationally, but humans often make irrational decisions based on fear or love. These two factors and many others cannot be regarded for in an economic model. Therefore it makes an unpredictability in the model and the model is no longer precise or accurate anymore.

Conclusion

In conclusion, I think that the way economics is being influenced by mathematics in the modern era is vaguely the direction we should be taking. Although the psychological route is also very interesting and elucidating, the future of economics is taking more of a business route. Mathematics is being used as a tool and a language, therefore making it a valuable and advantageous servant to economics. However, as the famous economist, John Maynard Keynes mentioned “mathematics is a good servant but a bad master”. This underlines the fact that too much of something is bad and economists often stray away from logical thinking when using too much of it.