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Policy Impact Analysis on Individual Welfare
An individual's preferences for daily free time (t, in hours) and consumption (c, in monetary units) are represented by the utility function u(t, c) = (t - 6)²(c - 45). A government is considering two policies to improve citizen well-being:
- Policy A (Income Support): An unconditional cash grant that increases every citizen's consumption (c) by 15 units.
- Policy B (Shorter Work Week): A mandate that increases every citizen's free time (t) by 2 hours.
Suppose an individual is currently at a point where they have 16 hours of free time and 85 units of consumption. Based on the utility function, which policy would this individual prefer? Justify your answer with calculations. Further, analyze and explain whether the same policy preference would hold for an individual who has much more consumption (e.g., c=200) but the same initial amount of free time (t=16).
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CORE Econ
Economics
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Empirical Science
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Economy
Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
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Figure 3.7a - Diagram of Karim's Optimal Choice at a €30 Wage
An individual's preferences for hours of daily free time (t) and units of consumption (c) are described by the utility function u(t,c) = (t-6)²(c-45). The individual is currently at a point where they have 16 hours of free time and 55 units of consumption. Which of the following alternative bundles would this individual prefer to their current situation?
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An individual's preferences for daily hours of free time (t) and units of consumption (c) are represented by the utility function u(t, c) = (t - 6)²(c - 45). What does this specific functional form imply about the individual's underlying preferences?
An individual's preferences for daily free time (t) and consumption (c) are represented by the utility function u(t, c) = (t - a)² * (c - b), where 'a' and 'b' are positive constants representing minimum required levels of free time and consumption, respectively. For any combination where t > a and c > b, what happens to this individual's willingness to give up consumption for an additional hour of free time as their amount of free time increases (while keeping their overall satisfaction level constant)?
An individual's preferences for daily hours of free time (t) and units of consumption (c) are represented by the utility function u(t, c) = (t - 6)²(c - 45). Consider the consumption bundle where t=20 and c=40. Which of the following statements most accurately describes the individual's assessment of this bundle based on the given utility function?
To algebraically verify that the indifference curves for the utility function u(t, c) = (t - 6)²(c - 45) are convex (i.e., they bow inwards toward the origin), a specific sequence of mathematical steps is required. Arrange the following key steps of this procedure into the correct logical order.
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Calculating the Marginal Rate of Substitution
An individual's preferences for daily hours of free time (t) and units of consumption (c) are represented by the utility function u(t, c) = (t - 6)²(c - 45). At the point where the individual has 16 hours of free time and 55 units of consumption, 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)?
Figure E3.1: Mapping Karim's Preferences