Deriving and Interpreting the Marginal Rate of Substitution
A consumer's preferences for two goods, a composite good (x) and leisure time (t), are described by the utility function U(x, t) = x + 4ln(t), where 'ln' is the natural logarithm. First, derive the expression for the consumer's marginal rate of substitution (MRS), which represents the rate at which they are willing to trade units of the composite good for an additional hour of leisure. Second, calculate and interpret the value of the MRS when the consumer currently has 8 hours of leisure time.
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Deriving and Interpreting the Marginal Rate of Substitution
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A consumer's preferences are represented by a utility function, U(x, y), where the utility is separable in one of the goods. Match each utility function with its corresponding Marginal Rate of Substitution (MRS), which represents the rate at which the consumer is willing to trade good y for an additional unit of good x.
A person's satisfaction is described by the utility function U(c, h) = c + 8āh, where 'c' represents units of a consumption good and 'h' represents hours of leisure. If this person currently has 4 hours of leisure, they would be willing to give up ______ units of the consumption good to gain one additional hour of leisure.
A consumer's preferences for two goods, a composite consumption good (c) and hours of leisure (t), are represented by a utility function that is separable in leisure time: U(c, t) = c + v(t). Arrange the steps below in the correct logical sequence to determine the consumer's marginal rate of substitution, which is the amount of the consumption good they are willing to give up for one more hour of leisure.
A consumer's preferences for a consumption good (c) and hours of free time (t) are represented by a utility function of the form U(c, t) = c + v(t). The consumer's marginal rate of substitution (MRS), which measures their willingness to give up units of consumption for an additional hour of free time, is given by the expression MRS = 15/t. Which of the following functions for v(t) is consistent with this MRS?
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