At its core, economics is about making sense of the world—how we allocate resources, make decisions, and how those decisions ripple through societies. Yet, to truly understand the complexities of economics, one tool stands out as indispensable: mathematics. It’s not just a support structure; it’s the very backbone that holds much of the discipline together.
Math as a Universal Language
Surprisingly, economics is considered a ‘liberal arts’ subject in many places, but it is actually highly math-intensive. Math is the language economists use to identify patterns, make predictions, and reveal the underlying forces driving economic behavior. Imagine how health data is transformed into insights about disease trends through mathematical models. Similarly, in economics, math allows us to detect patterns in data and forecast outcomes like inflation rates, unemployment, and GDP growth.
Mathematics makes it easier for people from different backgrounds to communicate and understand each other’s work. Whether you are a student in China, a researcher in Poland, or a policymaker in the United States, the language of mathematics transcends cultural and linguistic barriers.
This universality accelerates the spread of ideas and knowledge, allowing the discipline to evolve more rapidly. Moreover, by codifying economic principles into mathematical equations, economists ensure that these principles are accessible to everyone, regardless of their intelligence or background. This democratization of knowledge is essential for the progress of the field, as it allows new generations of economists to build on the work of their predecessors.
The Power of Reduction
A key role of mathematical concept in economics is reduction—the process of simplifying complex phenomena into more manageable components. This might seem counterintuitive, as reducing something inherently involves losing some detail. However, in economics, reduction is vital because it allows us to distill complex systems into understandable models that can be analyzed and tested.
For example, companies can be reduced to financial ratios and performance indicators, as seen in Bloomberg terminals that display companies’ data in numerical form. These figures, while simplified, provide a clear and concise way to compare companies and make informed decisions.
Economists apply this principle on a larger scale, using math to represent entire economies through indices like the stock market. By reducing the complexity of an economy to a single number, such as the GDP or a stock index, economists can track changes over time and make meaningful comparisons across different periods or regions.
Balancing Clarity and Complexity
While reduction involves simplification, it’s not about ignoring the nuances of individual entities—whether they are people, companies, or countries. Instead, it’s about finding a balance between clarity and complexity. Economists often face the challenge of respecting the uniqueness of individuals while also seeking to identify general patterns that apply to larger populations. This is where math becomes essential.
Mathematical models allow economists to strip away the noise and focus on the key variables that drive economic behavior. For instance, the Capital Asset Pricing Model (CAPM) reduces a firm’s value to just two parameters: alpha and beta. While this reduction might seem to overlook many unique aspects of a company, it provides a powerful tool for understanding and predicting stock prices. Without such models, the sheer complexity of the data would overwhelm our ability to see patterns or make predictions.
Objectivity and Stripping Away Emotion
Economics is a discipline that strives to be objective, and mathematics is the tool that allows economists to achieve this. Math helps economists avoid the influence of emotions and biases in their work. By using mathematical models and equations, economists can ensure that their conclusions are driven by logic and evidence, rather than personal feelings.
For example, trade models in economics predict the benefits of trade between two countries based on mathematical principles, regardless of the emotional or political tensions between them. This objectivity is crucial in a field where decisions can have profound impacts on millions of lives. By disciplining themselves with math, economists can make more accurate and reliable predictions.
Objectivity through mathematics extends beyond individual decision-making into the realm of governance. Throughout much of human history, governments have been a source of concern. We need them to maintain social order, but without proper checks and balances, it becomes difficult to hold them accountable. Unchecked bureaucrats can abuse their power, causing widespread suffering.
So, how can we effectively evaluate their policies? Consider monetary policy, for example. Many countries that use fiat currency have failed to manage inflation, leading to hyperinflation. How do we know if bureaucrats are implementing the right monetary policies? We can’t directly converse with them, and they might lie to us. Instead, we focus on what they do, using benchmarks to measure how far their actions deviate from the ideal. This is where math comes in.
The Taylor Rule, developed by Stanford economist John B. Taylor, is one such mathematical tool designed for this purpose. It helps assess how far the Federal Reserve’s actions diverge from what is recommended. While it’s not perfect, it provides a way to objectively evaluate their performance, regardless of the rhetoric they use. Economists have developed many similar rules to give ordinary people a clearer view of how well—or poorly—politicians and bureaucrats are managing the country.
Simulation and a Window into “What If”
Another significant aspect of mathematics in economics is its role in simulations and models. These tools allow economists to explore “what if” scenarios without the need for costly or unethical real-world experiments. For instance, policymakers might want to know the potential effects of a new tax policy. Instead of implementing the policy and risking unforeseen consequences, economists can use mathematical simulations to predict the outcomes.
Simulations are akin to flight simulators used to train pilots—they provide a safe and controlled environment to test different scenarios. In economics, these simulations can reveal potential pitfalls, help refine policies, and ultimately lead to better decision-making. This would be impossible without the mathematical frameworks that underpin these models.
Conclusion: The Compass that Guides
Mathematics is the compass that guides economists through the complexities of human behavior, policy-making, and global markets. It simplifies, clarifies, and objectifies, allowing us to understand the world in ways that would otherwise be impossible. Whether you’re calculating the impact of a new tax policy, predicting the next financial crisis, or simply trying to understand why prices fluctuate, math is the key to unlocking the answers.
Economics without math is like trying to navigate without a map—it’s possible, but you’re much more likely to get lost.
Further Reading
- Recommended Mathematical Training to Prepare for Graduate School in Economics, American Economics Association, https://www.aeaweb.org/resources/students/grad-prep/math-training
- Required Math Skills for Economics, University of Chicago, https://registrar.uchicago.edu/registration/course-catalogs/
- Nobel Prize Answer: Is economics becoming mathematics?
Answer: Is economics becoming mathematics?