# How Mathematical Models are Used in Social Science

Instructor: Usha Bhakuni

Usha has taught high school level Math and has master's degree in Finance

In this lesson, you will learn about mathematical models and how they are used in social sciences. It explores their use in economics, sociology, political science, and history.

## Mathematical Models

A mathematical model is a mathematical representation of a real-world situation. Generally, mathematical models include a set of input parameters and a process to generate output. It simplifies real-world problems to these basic blocks. Models are used for describing an event, making predictions, analysis of data, understanding complex relationships, etc.

### Mathematical Models in Social Sciences

Social sciences is the study of human society and social interactions. It is a vast field of study and includes a multitude of study areas. In this lesson, we will explore the use of mathematical models in each of these areas. However, as social sciences deal with human behavior, it is not always possible to quantify and mathematically represent the parameters involved in these studies.

### Economics

Economics includes the study of macroeconomics, which focuses on aggregate economy conditions, and microeconomics, which focuses on the behavior of individuals.

Mathematical models are used extensively in economics for representing relationships between various quantities, such as price, production levels, demand, employment, and investment.

The demand-supply model represents how the economy behaves with the change in demand and supply of goods. It states that with the increase in demand of a good, its price increases; with increase in production, the price decreases. The model can also reveal ways in which the economy is interconnected, i.e., how the change in price in one market affects other markets. It also helps to analyze the equilibrium state of the economy, which is the state at which demand equals supply.

Mathematical models are also widely used in economic forecasting. These models are used for predicting economic cycles or trends in economic parameters such as GDP, inflation rate, unemployment rate, and interest rates, based on historical data. There are mathematical models that can help predict consumption behavior.

### Sociology

Sociology is the study of social systems and behavior of humans in a society.

Sociological studies involve extensive use of statistical analysis. Regression models are typically used to study the relationships between various social parameters to conclude how or why a social phenomenon occurs.

Mathematical models in sociology include game theory models used to study social phenomena. Examples include coordination games, which are used to study the behavior of two individuals, forming the basis for social conventions. It is also used to study racial segregation in the population with the help of Schelling model, which examines the individual choices and behaviors that lead to collective segregation. It states that people segregate themselves based on their preferences and incentives and the equilibrium is achieved when there is complete segregation. The Schelling model is a good example of the potential of models to oversimplify real-world situations, as it does not take into account discriminatory housing practices or other active forces leading to housing segregation.

Network analysis in mathematics is also used to analyze social networks, how humans are connected to each other and how they behave in various social conditions. For example, models of social influence examine the reactions of humans in social situations.

### Political Science

Political science deals with the system of government, political behavior, and activity.

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