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Increasing Function
An increasing function is defined as a function with a positive slope. This means that as the input variable increases, the output value of the function also increases. In economic modeling, production functions are typically assumed to be increasing functions.
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Ch.5 The rules of the game: Who gets what and why - The Economy 2.0 Microeconomics @ CORE Econ
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Increasing Function
An economist is modeling a firm's production process. They observe that for each additional unit of labor hired, the increase in total output becomes smaller. For example, the first worker adds 10 units of output, the second adds 8 units, and the third adds only 5 units. Which mathematical property best describes the shape of the function used to model this production process?
Match each economic description with the mathematical property that formally describes the shape of the relevant curve or function.
Analyzing Consumer Preferences
Modeling Production with Diminishing Returns
Contrasting Mathematical Forms in Economic Models
In a standard economic model of a consumer's choice, their preference for a mix of two goods over extreme amounts of just one good is mathematically represented by a concave indifference curve.
An economist is building a model to represent the relationship between hours spent studying and a student's final grade. Arrange the following steps in the logical order they would follow to mathematically formalize the property of diminishing returns to studying.
An economic model describes a consumer's preferences for two goods. The model shows that the consumer prefers a balanced mix of the two goods over having a large amount of one good and none of the other. This property, which reflects a preference for averages over extremes, is formally described by saying the consumer's preferences are ______.
Evaluating a Production Model
In an economic model, a firm's production function, which relates a single input (like labor) to total output, is described as being strictly concave. What is the direct economic implication of this mathematical property?
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Concave Function
The Role of Information in Market Pricing
A small bakery observes that for every additional baker they hire, the total number of loaves of bread they can produce per day increases. Which of the following statements accurately describes the relationship between the number of bakers and the total bread output?
Analyzing Advertising Effectiveness
A marketing firm increases its monthly advertising expenditure for a client from $10,000 to $15,000. During the same period, the client's total sales decreased from 500 units to 450 units. This relationship between advertising expenditure and total sales represents an increasing function.
Economic Examples of Increasing Functions
Match each economic scenario with the type of functional relationship it describes between the two specified variables.
An agricultural firm tests a new fertilizer's effect on crop yield. The table below shows the results, with the amount of fertilizer applied per acre and the corresponding yield in bushels per acre.
Fertilizer (kg/acre) Crop Yield (bushels/acre) 50 120 100 135 150 145 200 150 Based on this data, which of the following statements provides the most accurate analysis of the relationship between fertilizer application and crop yield?
Analysis of Education and Income as a Function
Modeling Economic Relationships
A researcher collects data on the relationship between the average number of hours a student studies per week for a course and their final exam score. The findings are presented in the table below. Analyze the data and determine which statement best describes the relationship shown.
Hours Studied per Week Final Exam Score 2 65 4 75 6 83 8 88 10 91 A marketing firm increases its monthly advertising expenditure for a client from $10,000 to $15,000. During the same period, the client's total sales decreased from 500 units to 450 units. This relationship between advertising expenditure and total sales represents an increasing function.