Optimal Labor-Leisure Choice Calculation

A consumer's preferences for two goods, t and c, can be represented by a utility function of the form u(t,c) = βt^α + c. Which of the following specific functions represents a consumer who gains satisfaction from both goods, but experiences a diminishing marginal benefit from consuming more of good t?

A consumer's preferences are represented by the utility function u(t,c) = 10t^1.2 + c. This implies that as the consumer consumes more of good 't', each additional unit provides a smaller increase in their overall satisfaction.

A consumer's preferences are described by the utility function u(t,c) = βt^α + c, where β > 0. Match each condition for the parameter α with its corresponding implication for the marginal utility of good t (the change in utility from one additional unit of t).

A consumer's preferences are described by the utility function u(t,c) = βt^α + c, where β > 0. Match each condition for the parameter α with its corresponding implication for the marginal utility of good t (the change in utility from one additional unit of t).

Interpreting Utility Function Parameters

Comparing Consumer Preferences with Quasi-Linear Utility

Consider two individuals, Alex and Ben, whose preferences for two goods, a non-essential good (t) and a composite good representing all other consumption (c), are described by the following utility functions:

• Alex: u(t,c) = 20t^0.4 + c
• Ben: u(t,c) = 20t^0.8 + c

Assuming both individuals currently consume the same positive quantity of good t, which of the following statements accurately compares the satisfaction they would gain from consuming one additional unit of good t?

Evaluating a Consumer Preference Model

Formulating a Utility Function