Interpreting the Sign of the Derivative of the Optimal Free Time Function
The sign of the derivative of the optimal free time function () with respect to the wage () reveals how an individual's choice of free time responds to a marginal change in their wage. A positive sign for the derivative indicates that a wage increase leads to more free time, while a negative sign signifies that a wage increase leads to less free time.
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Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Ch.3 Doing the best you can: Scarcity, wellbeing, and working hours - The Economy 2.0 Microeconomics @ CORE Econ
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Interpreting the Sign of the Derivative of the Optimal Free Time Function
An individual's optimal amount of daily free time, t*, is determined by their hourly wage rate (w) and their non-labor income (I). The relationship is given by the function: t*(w, I) = 12 + (0.5 * I) / w. Which of the following expressions correctly represents the rate at which the optimal amount of free time changes as the wage rate changes?
Calculating the Marginal Effect of Wage on Free Time
Labor Supply Response to Policy Change
An individual's optimal choice for daily free time (t*) is described by the function t*(w, I) = 18 - (2w / I), where 'w' is the hourly wage rate and 'I' is daily unearned income. Assume both w and I are positive values. A student claims that for any positive wage and unearned income, a small increase in the wage rate will always lead to a decrease in the optimal amount of free time. Is this claim true or false?
An individual's optimal daily free time (t*) is a function of their hourly wage (w) and daily unearned income (I). Match each optimal free time function with the correct mathematical expression that represents how t* changes as the wage rate (w) changes, holding unearned income constant.
An individual's optimal daily free time, t*, is determined by their hourly wage, w, and daily unearned income, I, according to the function: t*(w, I) = 20 - 0.5*w + I/w. The mathematical expression that represents the rate of change of optimal free time with respect to the wage rate is ____.
A microeconomist wants to determine how an individual's optimal choice of daily free time, represented by the function t*(w, I), responds to a small change in their hourly wage rate (w), assuming their unearned income (I) remains unchanged. Arrange the following steps into the correct logical sequence for conducting this analysis.
Explaining the Analytical Approach to Labor-Leisure Choices
An economist observes that for a particular group of individuals, the rate at which their optimal daily free time (
t*) changes in response to a change in their hourly wage (w) is consistently represented by the expression-100/w². Given thatt*is a function of both wage (w) and unearned income (I), which of the following functions fort*is consistent with this observation?Comparing Economic Models of Labor-Leisure Choice
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Negative Derivative of the Optimal Free Time Function Leads to Reduced Free Time
A new company creates a mobile app that allows people to pay someone to wait in line for them at a popular new restaurant. Despite the fact that both the person paying and the person being paid willingly agree to the exchange, the service is widely criticized as being unfair. Which of the following best explains the basis for this societal objection?
An economist observes that after a country-wide increase in the minimum wage, many low-wage workers who were previously working two jobs have started working only one, thereby increasing their leisure time. Let t* represent the optimal amount of free time and w represent the wage rate. Based on this observation, what can be inferred about the derivative of the optimal free time function with respect to the wage for this group of workers?
Labor Supply Decision Analysis
True or False: For an individual choosing between work and leisure, a positive value for the derivative of their optimal free time function with respect to their wage (dt*/dw > 0) indicates that the opportunity cost of an hour of free time is the dominant factor in their decision-making when wages rise.
Analyzing a Freelancer's Work-Leisure Choice
An individual's optimal amount of free time, denoted as t*, changes in response to a change in their wage, w. Match each mathematical expression for the rate of this change (the derivative) with the corresponding behavioral outcome.
Analyzing Worker Responses to Wage Increases
An empirical study finds that for a specific group of workers, a 10% increase in the hourly wage consistently leads to them choosing to work fewer hours and take more vacation time. This observed behavior indicates that for this group, the derivative of the optimal free time function with respect to the wage, , has a ________ sign.
An employee receives a significant pay raise. In response, they decide to reduce their weekly work schedule to pursue a personal project. Arrange the following steps in the correct logical order to determine the sign of the derivative of this employee's optimal free time function with respect to their wage.
A government is considering a significant income tax cut, which would increase the net hourly wage for all workers. Advisor A predicts this will lead to people working more hours, thereby boosting economic output. Advisor B predicts that people will choose to work fewer hours, spending more time on leisure activities. Which of the following statements provides the strongest economic justification for Advisor B's prediction?
True or False: For an individual choosing between work and leisure, a positive value for the derivative of their optimal free time function with respect to their wage (dt*/dw > 0) indicates that the opportunity cost of an hour of free time is the dominant factor in their decision-making when wages rise.