An individual's level of satisfaction from consuming two goods, Good X and Good Y, is described by a function of the form $U(X, Y) = X^\alpha Y^\beta$, where X and Y represent the quantities of the goods consumed. Below are four potential models for this individual's preferences. Which model represents a situation where the individual's total satisfaction decreases as they consume more of Good Y, assuming their consumption of Good X remains constant and positive?

Analysis of a Preference Model

Evaluating a Preference Model

Consider a person's satisfaction from consuming two goods, which is represented by the function $U(x, y) = x^{0.5}y^{-0.2}$, where x and y are the quantities of the two goods. According to this function, this person's satisfaction will increase if they consume more of good y, while the consumption of good x remains constant and positive.

Parameter Conditions for Increasing Utility

Deriving and Interpreting Marginal Utility

A consumer's satisfaction from two goods, X and Y, is represented by a utility function of the form $U(X, Y) = X^\alpha Y^\beta$. Match each specific utility function below to the correct description of its marginal utilities. Assume the quantities of goods X and Y are always positive.

Evaluating and Correcting a Preference Model

Designing a Consumer Preference Model

A person's satisfaction is modeled by the function $u(c, t) = c^{0.7} t^{0.3}$, where 'c' is consumption and 't' is free time. The marginal utility of consumption, which measures the change in satisfaction from an additional unit of consumption, is given by the formula $0.7c^{-0.3}t^{0.3}$. Given that 'c' and 't' are always greater than zero, the value for the marginal utility of consumption will always be ________.