Often, people hear about how economics is quite maths-heavy. For some people, this is a driving reason for studying economics, with the course being a synthesis of mathematics and social science. On the other hand, this can put certain people off the course. So, what mathematics can you expect to use in your economics studies and how does this relate to the real world? To answer this question, we need to take a dive through the world of pure mathematics and how it can be applied to different situations involving economics.
I put forward to the reader a question: wouldn’t it be useful if we could model something as complex as our economy? The short answer: yes. The long answer: is this even possible? This is where game theory comes into play. Over time, mathematicians have realised that if we treat the economy like a ‘random’ game of chance, we could apply theories of game theory to agent-based models. Ideas in game theory often crop up in economics, the most famous example being Nash Equilibria. Furthermore, we could model risk and stability through metrics like leverage (the ratio of risky assets to equity) and amplify shock through some sort of probability function with given parameters. Treating markets as games means that, from a mathematical standpoint, it can be easy to understand the different outcomes and what they mean for the economy.
Modelling problems like the above often crop up in economics, which introduces our next main use of mathematics in economics: calculus. Calculus often proves itself as an economist’s mathematical weapon of choice. Ideas of rates of change (with reference to derivatives and partial derivatives) are seen in optimisation problems, where calculus is used to determine the best possible outcome as a policy, for example. In the real world, the bulk of economic research consists of economic analysis of different situations like the above. Ideas which seem entirely unapplicable to fields outside of STEM can often be applied in a peculiar way. The most notable example of this is the Black-Scholes Equation, first seen in physics but which made its way to economics to be dubbed the 'Trillion Dollar Equation'. Littered in this equation you can find references to partial derivatives, with its derivation relying almost entirely on calculus.
Ultimately, the most capable economists view mathematics as a tool, not a foe; this can be seen from their willingness to apply mathematical concepts which sometimes can be seen as useless from a pragmatic viewpoint. To summarise, most mathematical applications in economics can be simplified down to a few branches: game theory, calculus, linear algebra, and Bayesian probability. Most importantly, these concepts are not used in isolation. Rather, they are utilised all at once to help economists better understand the complex nature of humans and their interactions within a market or economy.
Writer: Wajidullah Nabi
Editor: Ritisha Baidyaray
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