### The Importance of Mathematics in Economics and Its Applications

The application of mathematics in economics is a translation of economic theory from its verbal form into mathematical language. In economics, mathematics is particularly well suited to the development of theories and models, as it is a powerful shorthand for logic and reasoning. In place of terms, mathematical symbols can be used, and equations can be used in place of sentences. It gives economic models and theories a concrete form, making them more precise and applicable in real-world situations. The following are some examples of mathematical tools that are used in economic analyses:

#### 1. To study Cause and Effect relationship:

Economics is a positive science, which means that it studies cause and effect relationships. The relationship between the variables can thus be demonstrated as a cause and effect relationship. For example, the quantity demanded of a commodity (such as apples) is determined by the price of the commodity. The quantity of apples demanded can then be written as the dependent variable, and the price of apples can be written as the independent variable. When we use mathematics to illustrate such relationships, we can be much more precise. For example, the mathematical relationship between demand for X and its price is written as Dx = f (Px).

#### 2. To analyze more variables:

More variables are analyzed with the help of graphs, which are also used in economics to clarify our discussions. For two variables, the graphs that we typically use are two-dimensional. It is not possible to use graphs when there are three or more variables because the verbal description will become extremely complicated. In such cases, we can turn to mathematics for assistance. In the case of three or more variables, the application of mathematics makes the analysis possible and easier. For example, the application of the matrix method.

#### 3. In order to convert sentences into symbols:

We can substitute mathematical symbols for economic terms and equations for sentences. Findings from mathematical treatment can be interpreted more quickly than findings from graphical and verbal methods, allowing for more rapid arrival at conclusions. A simple formula to express that the quantity demanded of X is dependent on its price is written as Dx = f (Px).

#### 4. To find the slope of a straight line:

It is necessary to use coordinate geometry to demonstrate the relationship that exists between graphs and equations. It is also employed in the determination of the slopes of demand and supply curves.

#### 5. To study marginal concepts:

When it comes to studying marginal concepts, mathematics is equally important in economics as it is in other fields. Calculus, a branch of mathematics, is frequently used in economics because of its versatility. Differential calculus is used to discuss the marginal concepts (marginal utility, marginal product, marginal cost, marginal revenue, marginal profit, and so on) that are commonly used in economics. Differential calculus is a mathematical tool that can be used to solve problems.

#### 6. To determine the values of economic variables:

From marginal values, the concept of integration is applied in order to calculate aggregate values (such as the sum of all revenue, all costs, all profit, and so on). In a similar vein, the concept of integration is used to calculate the surplus of consumers and the surplus of producers. As a result, mathematics is employed to determine the values of various economic variables.

#### 7. To express economic phenomena algebraically:

Algebra is used extensively in economics for the solution of simple, simultaneous, and quadratic equations, as well as for the solution of quadratic equations. It is also used to solve simultaneous equations, as can be seen in multi-market or general equilibrium models, which are examples of matrix algebra in action.

In addition, mathematics can be used to solve linear and nonlinear programming problems, among other things. In a similar vein, game theory, which can be applied in duopoly and oligopoly markets, can be used to solve problems in a mathematical manner.

Despite the fact that we have listed some of the applications of mathematics in economics in the preceding paragraphs, this is not an exhaustive list. Economic theory makes extensive use of a variety of advanced level mathematical techniques such as topology, calculus of variations, and other related subjects, among other things. This article discusses some of the prerequisites for using mathematical and statistical techniques in practice.

**Use and Importance of Mathematics in Economics**

**Quantitative Techniques in Economics**

- Quantitative Techniques (QT) refer to the techniques of using mathematics and statistics jointly.
- QT in economics involves using mathematics and statistics in economic analysis.
- The main purpose of employing QT in economics is to provide diligence in deducing economic theories and measure economic parameters for comparison.

**Mathematical Aspect**

- Mathematical skills help solve different economic problems logically.
- Establish relationships between economic variables through numerical calculation or graphical presentation.
- Key tools: derivatives, integration, transformation, coordinate geometry, linear programming.
- Examples: demand curve, supply curve, profit maximization, cost minimization.

**Statistical Aspect**

- Statistics explain economic events and deal with data and methods crucial for understanding economic problems and formulating policies.
- Analyzes data related to profit and loss, demand and supply, investment, and production.
- Important for evaluating economic indicators and anticipating future economic conditions.

**Importance of Mathematics in Economics**

- Mathematics provides logic and tools to establish relationships between economic variables.
- Simplifies complex theoretical expressions and helps find accurate ratios and coefficients.
- Makes economic theories more concrete, precise, and widely applicable.
- Key areas: logarithms, linear programming, equations, functions, integral calculus, geometry, game theory, coordinate geometry.

### The Use of Statistics in Economics

In economics, the use of statistics is becoming more prevalent. The application of statistics is necessary whenever we intend to conduct empirical studies in economics. We can estimate the required functions by utilizing statistical tools and techniques (such as demand function, supply function, cost function, production function, etc.). The use of statistical tools can also aid in the estimation of economic parameters, which are measures of the effect of one variable on another. The following are some examples of how statistics can be used in economic analysis:

#### 1. To investigate economic variables:

Statistics is required to investigate the many different economic variables. In order to investigate the variability in the values of the variables, measures of dispersion can be used, for example. Inflation rates and GDP deflators (gross domestic product deflators) are calculated with the help of index numbers. Demand, supply, and production functions are all estimated through the use of regression analysis. With the help of time-series analysis, it is possible to predict the trend of certain variables such as income. In order to determine the degree of relationship between two economic variables, the correlation technique is employed.

#### 2. To formulate economic planning:

The government prepares periodic economic planning based on statistics, i.e., data from the past in various sectors of the economy, which are collected from various sources. When the government is aware of the current poverty rate in Nepal, the government sets a target for reducing poverty to a specific level within the next plan period, which is then implemented.

#### 3. The use of diagrams:

The use of diagrams makes the study of economics easier, faster, and more interesting, as well as more efficient. Different types of diagrams, including pie charts and bar charts, are used in the field of economics.

#### 4. For the purpose of determining economic policies:

Statistics assist the government in formulating a variety of economic policies including fiscal policy, export and import policy, interest rate policy, and employment policy, among others. It contributes to the resolution of existing problems in the country.

#### 5. To study Economic Problems:

An economic study of the disparities in income and wealth distributions that exist in a society’s economy. One of the most important goals of a welfare state is to reduce such inequalities between people. However, we will not be able to achieve this goal unless we can determine the extent of the disparity. It is possible to measure and compare the inequalities in income, wealth, and landholding distributions by using the Lorenz curve and the Gini coefficient techniques, respectively. Following the implementation of a policy aimed at reducing such disparities, these techniques are used to determine whether the disparities have been reduced or not.

#### 6. Development of Econometrics:

A new field in economics, known as econometrics, has emerged as a result of the application of advanced level statistics to the study of economics. This field is known as econometrics. In this context, a large number of econometric methods and models have been developed. The Nobel Prize in Economics has been awarded to a number of econometricians in the past.

Statistics has been used to develop many theories in economics in addition to the ones listed above. For example, Engel’s law of expenditure and Kuznets’ derivation of the long-run consumption function (as well as the Phillips curve and the Phillips curve) were both developed using statistical techniques.

The list consists of some of the applications of statistics in the field of economics. This is not, however, a comprehensive list of all possible options. Furthermore, many other advanced level statistics, such as nonlinear regressions, probabilistic and logit models, estimation of simultaneous equation systems, and so on, are also widely used in economics today. In the same way, the simultaneous application of mathematics and statistics in economics has aided in the development of economic models, the verification of their validity, and the revision of those models when necessary.