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?