Shape of an Indifference Curve

Positive Parameters in Cobb-Douglas Function and Positive Marginal Utility

An individual's satisfaction is derived from consuming two desirable goods, Good X and Good Y. This means that, all else being equal, their satisfaction should increase if they acquire more of Good X, and it should also increase if they acquire more of Good Y. Given that the quantities of X and Y are always positive, which of the following mathematical functions, U(X, Y), correctly represents this relationship for all possible positive quantities of X and Y?

Mathematical Verification of a Preference Principle

An individual's preferences for two items, apples (A) and bananas (B), are described by the utility function U(A, B) = 15A - 2B. According to this function, this individual always gains more satisfaction from consuming an additional apple, and also always gains more satisfaction from consuming an additional banana.

Evaluating a Utility Function Model

An individual's preferences are represented by a utility function, U(X, Y), where X and Y are quantities of two different goods. Match each utility function below with the correct description of its marginal utilities, assuming the quantities of X and Y are always positive.

Analyzing Preferences for Goods and Bads

Evaluating Player Satisfaction Models in Game Design

Interpreting the Mathematics of Preferences

For a utility function representing an individual's preferences for two desirable goods, the 'more is better' principle is mathematically expressed by the condition that the ______ for each good must be positive.

An individual's satisfaction from consuming two goods, X and Y, is represented by the utility function U(X, Y) = 20X - X² + 10Y. Assuming the quantities of both goods must be positive, for which range of values for good X does this function satisfy the 'more is better' principle with respect to both goods?