A person's satisfaction from consuming goods (c) and enjoying free time (t) is described by the utility function $u(t,c) = t^2 c^3$. What does this specific functional form imply about their preferences?

Calculating the Marginal Rate of Substitution

Consider an individual whose preferences for daily free time (t, in hours) and consumption (c, in dollars) are represented by the utility function $u(t,c) = t^2 c^3$. If this individual's consumption and free time were both to double, their total satisfaction would also double.

Optimal Choice Analysis

An individual's preferences for daily consumption (c) and free time (t) are represented by the utility function $u(t,c) = t^2 c^3$. Which of the following combinations of free time and consumption would this individual prefer most?

Evaluating Preferences from a Utility Function

An individual's preferences for consumption (c) and free time (t) are represented by the utility function $u(t,c) = t^2 c^3$. Holding the level of consumption (c) constant, how does the additional satisfaction (marginal utility) gained from one more unit of consumption change as the individual's amount of free time (t) increases?

Assessing the Realism of a Utility Model

An individual's preferences for consumption (c) and free time (t) are represented by the utility function $u(t,c) = t^2 c^3$. Match each economic concept with its correct mathematical representation derived from this function.

An individual's preferences for consumption (c) and free time (t) are represented by the utility function $u(t,c) = t^2 c^3$. For this individual, the additional satisfaction gained from one more unit of consumption decreases as their level of consumption increases, holding free time constant.