An individual's preferences for daily free time (t, in hours) and daily consumption (c, in dollars) are represented by the utility function u(t, c) = (t-6)(c-45)^2. Based on this function, which of the following statements most accurately describes this individual's preferences?

Decision Making with a Utility Function

An individual with the utility function u(t, c) = (t-6)(c-45)², where 't' is hours of free time and 'c' is dollars of consumption, would be indifferent between a bundle of (t=7, c=50) and a bundle of (t=7, c=40).

Calculating the Marginal Rate of Substitution

An individual's preferences are represented by the utility function u(t, c) = (t-6)(c-45)², where 't' is hours of free time and 'c' is dollars of consumption. Holding free time constant at 10 hours, which of the following consumption levels would this individual prefer the most?

Evaluating a Utility Model

An individual's preferences for daily free time (t, in hours) and daily consumption (c, in dollars) are represented by the utility function u(t, c) = (t-6)(c-45)². Which of the following combinations of free time and consumption would this individual find least desirable?

An individual's preferences for daily free time (t, in hours) and daily consumption (c, in dollars) are represented by the utility function u(t, c) = (t-6)(c-45)². Assuming the individual has more than 6 hours of free time, the specific level of daily consumption in dollars that would provide the least satisfaction is ____.

An individual's preferences for daily free time (t, in hours) and daily consumption (c, in dollars) are represented by the utility function u(t, c) = (t-6)(c-45)². Assuming this individual always has more than 6 hours of free time (t > 6), which statement best describes how their level of satisfaction changes as only their consumption (c) increases from a value below 45 to a value above 45?

An individual's preferences for daily free time (t, in hours) and daily consumption (c, in dollars) are represented by the utility function u(t, c) = (t-6)(c-45)². Calculate the marginal rate of substitution (MRS), which measures the rate at which the individual is willing to trade consumption for an additional hour of free time, at the point where they have 16 hours of free time and $55 of consumption.