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An economist models a person's satisfaction with consumption (c) and free time (t) using the utility function U(c, t) = 10c * (40t - t²), where 't' is hours of free time per week. This model suggests that beyond a certain point, having too much unstructured free time can lead to boredom and decreased satisfaction. At what point does an additional hour of free time start to decrease this person's total utility, assuming consumption is held constant?
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An individual's satisfaction from consumption (c) and free time (t, measured in hours) is represented by the utility function U(c, t) = c * t². If this individual currently has 10 units of consumption and 5 hours of free time, what is the approximate change in their utility from one additional hour of free time?
An individual's satisfaction is described by the utility function U(c, t) = 5c + √t, where 'c' represents units of consumption and 't' represents hours of free time. According to this function, the additional satisfaction gained from one extra hour of free time is the same whether the individual currently has 4 hours or 9 hours of free time.
Interpreting Marginal Utility of Free Time
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Match each utility function, which depends on consumption (c) and free time (t), with its corresponding mathematical expression for the marginal utility of free time.
Analyzing Preferences for Free Time
An individual's preferences for consumption (c) and free time (t) are represented by the utility function U(c, t) = √c * √t. If the individual currently has 100 units of consumption and 25 hours of free time, the marginal utility of an additional hour of free time is ____.
An individual's satisfaction is represented by the utility function U(c, t) = 10c + t³, where 'c' is consumption and 't' is hours of free time. The individual currently has 4 hours of free time. Arrange the following steps in the correct logical order to find and interpret the marginal utility of an additional hour of free time.
An economist models a person's satisfaction with consumption (c) and free time (t) using the utility function U(c, t) = 10c * (40t - t²), where 't' is hours of free time per week. This model suggests that beyond a certain point, having too much unstructured free time can lead to boredom and decreased satisfaction. At what point does an additional hour of free time start to decrease this person's total utility, assuming consumption is held constant?
An individual's preferences are such that each additional hour of free time adds to their overall satisfaction, but each successive hour provides less additional satisfaction than the previous one. For example, the fifth hour of free time is less valuable to them than the fourth. Which of the following utility functions, where 'c' is consumption and 't' is hours of free time, best represents this individual's preferences?