Deriving Angela's Optimal Choice in a Specific Example by Equating MRS and MRT

An individual's preferences for consumption (c) and hours of free time (t) are represented by the utility function u = 4√t + c. Given a choice between two options, which one would this individual prefer?

Option A: 16 hours of free time and a consumption level of 10. Option B: 9 hours of free time and a consumption level of 15.

Interpreting a Utility Function

An individual's preferences for consumption (c) and hours of free time (t) are represented by the utility function u = 4√t + c. What is the marginal rate of substitution (the rate at which this individual is willing to give up units of consumption for an additional hour of free time) when they have 9 hours of free time?

Consider an individual whose preferences for consumption (c) and hours of free time (t) are described by the utility function u = 4√t + c. This individual's willingness to give up consumption for an extra hour of free time is the same regardless of how much consumption they currently have, assuming their amount of free time is held constant.

Evaluating a Policy Change

An individual's preferences for consumption (c) and hours of free time (t) are represented by the utility function u = 4√t + c. Consider two situations:

Situation A: The individual has 9 hours of free time and a consumption level of 20. Situation B: The individual has 9 hours of free time and a consumption level of 30.

How does the individual's willingness to trade consumption for an additional hour of free time (the marginal rate of substitution) compare between these two situations?

Analyzing Preferences from a Utility Function

An individual's preferences for consumption (c) and hours of free time (t) are represented by the utility function u = 4√t + c. This individual is indifferent between two bundles of goods: Bundle X, which consists of 16 hours of free time and a consumption level of 12, and Bundle Y, which consists of 25 hours of free time and an unknown consumption level. What must the consumption level be in Bundle Y for the individual to be indifferent between Bundle X and Bundle Y?

Evaluating a Job Offer

An individual's preferences for consumption (c) and hours of free time (t) are represented by the utility function u = 4√t + c. Which of the following statements accurately describes how this individual values an additional hour of free time?