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Analyzing Preferences from a Utility Function
An individual's preferences for daily hours of free time (t) and consumption (c) are represented by the utility function u(t, c) = (t-6)²(c-45). First, derive the formula for this individual's Marginal Rate of Substitution (MRS). Then, analyze this formula to explain how the individual's willingness to trade consumption for free time changes as (a) their amount of free time increases (holding consumption constant) and (b) their level of consumption increases (holding free time constant). Justify your analysis.
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An individual's preferences for daily hours of free time (t) and consumption (c) are represented by the utility function u(t, c) = (t-6)²(c-45). At a point where the individual has 16 hours of free time and a consumption level of 95, what is the value of their marginal rate of substitution (the rate at which they are willing to trade consumption for an additional hour of free time)?
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Analyzing Preferences from a Utility Function
Consider an individual whose preferences for daily hours of free time (t) and consumption (c) are represented by the utility function u(t, c) = (t-6)²(c-45). True or False: According to this model, the more free time this individual has, the less consumption they are willing to sacrifice for an additional hour of free time, assuming their consumption level is held constant.