## Mathematics in Economics

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 problems could not be described and complicated problems could not be acted upon without the language of mathematics and its support of logical processes to solve problems. Mathematical modeling is used in economic analysis to study existing economic relationships and it helps economists study what-if scenarios to see what might happen to the economy if a certain action is applied. Economic concepts and relationships can be measured in mathematical indexes, formulas and graphs. Several areas of mathematics can be utilized in economic analysis, including linear algebra, calculus, and geometry. Since economic concepts can be complex, it is important to use care in representing data and relationships in isolation. Results can be misinterpreted based on the representation of data.

### Overview

#### Economics

Economics is “the study of how people choose to use resources which can include land, labor, money, equipment, taxes and investments” (“What is economics?”, n.d.). The broad field of economics has many descriptions each trying to discover a way to make clear what the field covers. De Rooy (1995, xiii) states that economics is about people and “…the things they do.” Decisions have to be made in life and people are constantly making decisions about resources at the individual, company and government levels. Gottheil (2007, p.1) describes economics as “an important branch of the social sciences” that is all about resources. This discussion of resources surrounds the fact that resources are limited and people have needs and wants. Scarcity is a term used to explain these limited resources. Typically, resources have to be distributed to people in the form of goods and services. Gottheil notes that resources are limited but the wants of people are not. The three main problems which Gottheil ascribes to economic study are:

- The problems related to scarce resources and unlimited wants of humans;
- The problem of making choices about allocation of resources to produce goods and services;
- The problem of distributing completed goods and services to people.

#### Mathematics

Large (2006, p.2.) describes the field of mathematics as “the study of the relationship between size, shape and quantity, using numbers and symbols.” These numbers and symbols convey meaning in a clear, concise and consistent way. Mathematics is a way to explain, explore, decipher and analyze complex concepts that otherwise might be resistant to synthesis. Math can also demonstrate whether or not a theory is true. The logical process of problem solving using mathematics can give precise answers to complicated, compound and multi-faceted problems.

#### Mathematics in Economics

Mathematics is helpful in economics because it can help quantify or provide measurement and meaning to economic concepts. Mathematics also plays a large role in the area of economic analysis. Economics uses modeling to describe certain states of being and to analyze economic scenarios. 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. Barnett, Ziegler & Byleen (2008, p. 210) describe mathematical modeling as “the process of using mathematics to solve real-world problems.” The authors further break mathematical modeling into three steps:

- Constructing the model. This step provides the basis for understanding the problem or question being asked. Once an answer is given to question asked by the model, it can be used to apply the information learned to a real-world problem.
- Solving the mathematical model.
- Interpreting the solution to the mathematical model in the context of the real-world problem that needs to be solved.

These steps are repeated over and over again as long as information is needed to solve the real-world problem. Gottheil notes that modeling in economics helps “to understand cause-and-effect relationships in the economy.” Lim (2001, p.2) calls mathematics “a useful tool for the analysis of all economic problems” and says it is “practically indispensable for many.” Lim lists the following mathematical concepts as important to economics:

- Calculus;
- Linear algebra;
- Differential equations.

#### Micro-

There are sub-branches of economics. Two important ones are microeconomics and macroeconomics. Each branch covers different types of decisions. Microeconomics is the study of economic relationships and decisions of the individual. Macroeconomics looks at the economy as a whole. Economists utilize models to analyze both micro and macroeconomics using supply and demand as the foundation (Baumol & Blinder, 2001). “Supply and demand are the most fundamental tools of economic analysis” (McAfee, p. 14). Macroeconomics looks at measures that affect the whole economy including inflation, unemployment, Gross Domestic Product and prices. Aggregate demand and supply are macroeconomic measures that provide “a way of illustrating macroeconomic relationships and the effects of government policy changes” (Riley, 2006). Every part of the economy has an interrelationship with other parts of the economy. As an example, if the population increases, the demand for certain goods will increase. Similarly, as goods become obsolete, demand will decrease. Various economic measures are represented as mathematical variables. Mathematics is a way to track variables under consideration and to model changes in variables.

#### Mathematics in Practice

There are many ways in which math in economics can be used. For example, Cooper (2009) discusses the importance of an increase in housing starts and draws a direct relationship between the decline in homebuilding and the sluggish and declining financial markets. At the current rate of decline, housing starts will fall to zero by November of 2009. In an additional example, Magner (2000, para. 2.) discusses Markus Mobius, a Harvard economics professor, who used his skills in mathematics and economics to study social problems. In his thesis, Mobius “used economic theory to explore the formation of ghettos.” Mobius found that economics was inconsistent since it relied on human behavior, but purported that mathematics can compensate for these changes and variations. Mobius’ strength in math helped him to become an excellent economist. Successful economists are those able to master economic concepts and mathematics at the same time (Magner).

#### Math’s Limits

Scrubbing the Skies (2009) looks at a traditional problem of costs in attempting to reduce carbon emissions from global warming. Interestingly enough, part of the economic problem in this case is the politics involved in getting action on carbon dioxide reductions. Politics is inextricably related 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 forestall change efforts and have the wherewithal to persuade politicians to adopt a position since many will need campaign contributions to remain in office. McAfee (p.7) calls the controlling interest of politics in government “political economy” or “the study of allocation by politics.”

#### Economic Literacy

Many people and groups care about economics including governments and economists. However, economics affects individuals as well. De Rooy introduces a concept called economic literacy where an individual understands the economic environment and how the environment affects the individual. Some people may be frightened away from economic data because of mathematics. Economically literate people can interpret how economic metrics and news affects them and what economic relationships will create a successful environment for them as individuals. As a result, economically literate people will be interested in when conditions signal a recession or when prices rise along with unemployment, for example. Individuals might care about inflation because purchasing power declines with rising inflation. All of these economic concepts are represented in mathematical terms.

#### Economic Concepts

Mathematics can help in visualizing and quantifying economic concepts. Formulas and graphs can be used to describe and display such concepts. Mathematics is also a way to deal with uncertainty in a problem. Many economic terms can be represented mathematically. The terms are used to describe values and behaviors concerning supply and demand, the U.S. economy, producer and consumer theory, imperfections in the market and strategic behavior. The national economy is very complex so it is impossible for one single number or measure to accurately represent it whether as snapshot in time or over a period of time (De Rooy).

#### Mathematics in Price

Mathematics can be use to show relative size or whether something is high or low or large or small. A basic economics concept related to scarcity of resources is price or cost. Price is “the exchange of goods and services for money” (McAfee, 2006, p.7). However, the true cost or opportunity cost is based on what must be given up or what cannot be purchased because funds are allocated elsewhere. McAfee (p.9) calls opportunity cost “the value of the best foregone alternative.” Price-related economic measures include the consumer price index (CPI) and personal consumption expenditures…