Introduction to Mathematical Extensions for Economic Analysis

Evaluating the Use of Mathematics in Economics

Analyzing an Economic Model's Representation

An economist makes the following statement: 'The total output a factory can produce depends on two factors. It increases as the number of employees grows, but it decreases if the machinery used is older.' Which of the following equations most accurately and precisely formalizes this economic relationship? (Assume 'O' is total output, 'E' is the number of employees, 'A' is the age of the machinery, and k, m, and n are positive constants that determine the strength of these relationships).

An essential skill in economics is translating verbal descriptions of relationships into formal representations. Match each verbal statement below with the graphical representation that most accurately and precisely depicts the described economic relationship.

Interpreting an Economic Equation

True or False: When constructing an economic model, incorporating additional mathematical variables and equations will consistently improve the model's clarity and its ability to communicate core economic relationships.

An economist seeks to formalize an observation about economic behavior into a clear and precise model. Arrange the following steps into the most logical sequence for this process.

Improving a Vague Economic Model

When an economist moves from a general verbal statement, such as 'people tend to buy more of a product when its price falls,' to a formal equation or graph, the primary advantage gained is the addition of _______, which allows for more exact analysis and testable hypotheses.

Analyzing the Impact of an Economic Event on a Model

Connecting Calculus to Graphical Features

Mathematical Representation in Economic Models

Physical Models in Economics

An economist first writes a detailed paragraph describing how a change in the price of a key raw material affects the quantity of a product a company is willing to sell. Next, she creates a line graph illustrating this relationship visually. Finally, she develops an equation that precisely calculates the quantity supplied for any given price of the raw material. What does this process demonstrate about the nature of economic models?

Match each form of economic model representation to its primary characteristic or function.

Choosing the Right Model for Policy Decisions

Modeling Consumer Behavior

For an economic model to be considered a valid and useful tool for analysis, it must be represented using mathematical equations.

Relationship Between Model Forms

An economist is studying the relationship between the price of gasoline and the quantity people are willing to buy. Arrange the following steps in the logical order an economist would typically follow to develop a formal model of this relationship, progressing from a general observation to a precise representation.

When an economist moves from a detailed verbal description of a market relationship to a visual representation that shows the connection between two variables, they are most commonly creating a ______. This visual tool can then be precisely defined using mathematical equations.

An economist develops a verbal model to describe the market for a luxury good. The model states: 'At lower prices, a small increase in price causes a significant number of consumers to stop buying the good. However, at very high prices, the remaining consumers are less sensitive, and the same price increase causes only a small drop in the number of buyers.' Which of the following graphical representations best illustrates this economic model, assuming Price is on the vertical axis and Quantity is on the horizontal axis?

Communicating Economic Findings

Mathematical Representation in Economic Models