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Marina's Work-Leisure Choice with Variable Productivity
This example introduces Marina, a writer who, like Karim, faces a trade-off between consumption and free time. A key difference from the fixed-wage model is that Marina's earnings are not constant per hour. Her income is tied to her productivity, which is highest at the beginning of her workday and diminishes the more hours she writes.
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CORE Econ
Economics
Social Science
Empirical Science
Science
Economy
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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Marina's Work-Leisure Choice with Variable Productivity
MRT as the Derivative of the Feasible Frontier Function g(t)
Analysis of a Production Possibility
A farmer's feasible frontier shows the trade-off between tons of grain produced and hours of leisure per day. If this frontier is a downward-sloping curve that is bowed inward toward the origin (concave), what does this shape imply about the farmer's production process?
An individual's feasible frontier, showing the trade-off between daily consumption and hours of free time, is represented by a downward-sloping curve that is bowed inward toward the origin. This shape implies that the opportunity cost of an additional hour of free time, measured in terms of consumption given up, is constant.
Reasoning Behind a Concave Feasible Frontier
A student has 24 hours in a day to allocate between studying for an exam and free time. For every hour of free time they take, they lose an hour of study time. However, due to fatigue, each additional hour of studying results in a smaller increase in their final exam score than the previous hour. If the final exam score is on the vertical axis and hours of free time are on the horizontal axis, what is the shape of the student's feasible frontier?
Match each economic scenario describing a trade-off with the shape of the feasible frontier that represents it. Assume the first item mentioned in the scenario (e.g., 'leisure time') is on the horizontal axis and the second item (e.g., 'income') is on the vertical axis.
If an individual's feasible frontier for a trade-off (e.g., between goods produced or between leisure and consumption) is represented by a curve that is bowed inward toward the origin, it indicates that the opportunity cost of the item on the horizontal axis is ________ as more of that item is chosen.
Comparing Production Scenarios
A student is modeling the trade-off between their final grade in Economics and their final grade in Chemistry, given a fixed number of total study hours. The feasible frontier for this trade-off represents all possible combinations of grades they can achieve. Which of the following underlying assumptions about their studying process would produce a feasible frontier that is a curve bowed inward toward the origin (concave)?
Evaluating Production Models
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Declining Productivity and Variable Hourly Income
Marina's Income as a Production Function
A freelance writer's productivity, measured in pages written per hour, is highest during their first hour of work and declines with each additional hour they work on a given day. Their income is directly proportional to the number of pages they write. Which statement best analyzes the opportunity cost of their free time?
Programmer's Productivity and Opportunity Cost
Diminishing Productivity and the Feasible Frontier
Comparing Work-Leisure Trade-offs
A freelance graphic designer's productivity, measured by projects completed per hour, is highest during the first hour of their workday and decreases with each subsequent hour. Given that their income is directly tied to the number of projects completed, the opportunity cost of taking an hour of free time is lower at the beginning of the workday compared to the end of the workday.
A consultant's productivity, and therefore their effective hourly earnings, is highest at the beginning of their workday and decreases with each additional hour worked. Match each point in their workday with the corresponding opportunity cost of taking one more hour of free time.
For a worker whose productivity, and thus their effective hourly income, diminishes with each additional hour they work, the opportunity cost of taking one more hour of free time ________ as the total number of hours worked per day increases.
A baker's productivity decreases throughout their workday. They produce 10 loaves in their first hour, 8 in their second, 6 in their third, and 4 in their fourth. They are paid a fixed price per loaf. Arrange the following decisions to work an additional hour in order from the one that adds the most income to the one that adds the least income.
Evaluating a Freelancer's Decision
A freelance editor's productivity declines the more hours they work in a day. In their first hour, they can edit 10 pages; in the second, 8 pages; in the third, 6 pages; and in the fourth, 4 pages. They earn $5 for each page edited. What is the opportunity cost for the editor if they decide to take the third hour of their workday as free time?