Mathematics and economics are complementary disciplines. Most branches of modern economics use mathematics and statistics extensively. Economics is the study of how resources are used as well as an analysis of the decisions made in allocating resources and distributing goods and services. Mathematics is the language of numbers and symbols that can be used to logically solve problems and precisely describe size, quantity and other concepts.
Some complex economic problems could not be described or be acted upon without math to support the logical processes necessary. Math helps quantify or provide measurement and meaning to economic concepts. Math is also used in economic analysis to study existing economic relationships and helps economists study suggested scenarios to see what might happen to the economy if a certain action is applied. Modeling suggests what will happen if certain actions are taken. Simulation of real world situations is possible with economic analysis and modeling and would not be possible without mathematics. Several areas of mathematics can be utilized in economic analysis, including linear algebra, calculus and geometry.
In finance, people deal in random processes where the time series of price are not differentiable, but can be integrated. This requires understanding of the mathematics of measure theory and Lebesgue integrals. To understand how they work, requires clear understanding of Brownian motion and Ito calculus to establish an equivalence between a continuous partial differential equation and an Ito integral.
Constructing the model
Using math theories provides the basis for understanding the problem or question being asked. Once an answer is given to a question asked by the model, it can be used to apply the information learned to a real-world problem.
Mathematics in Practice
There are many ways in which math in economics can be used. Successful economists are those able to master economic concepts and mathematics at the same time. For example, Markus Mobius, a Harvard economics professor, used his skills in mathematics and economics to study social problems, used maths theories to explore the formation of ghettos. Mobius found that economics was inconsistent since it relied on human behavior, but economists can use math theories to ensure that their analysis is as accurate as it can be and that there are no holes in their argument and conclusion.
Since economic concepts can be complex, results using mathematical theories can be misinterpreted based on the representation of data. As an example of the limits of maths in economics, consider the economic problem in attempting to reduce carbon emissions. Politics is involved in action on carbon dioxide reductions. Politics is inextricably linked to economics because economics is tied to behavior and politics influences behavior. Math helps us measure, monitor and predict behaviors, but cannot help to completely overcome political issues. Many industries and powerful companies may be reluctant to make costly changes to comply with tougher carbon emission regulations and there may be little ‘political will’ to force anyone’s hand. Powerful companies can afford lobbyists to persuade politicians to adopt a certain position since many will need campaign contributions to remain in office. The controlling interest of politics in government is known as “political economy” or “the study of allocation by politics.”