Point C as the Hypothetical Choice in Figure E3.4
In the analysis of Figure E3.4, Point C represents a hypothetical optimal choice. This point illustrates the bundle of goods and leisure an individual would select if their wage rate remained at the original level (), but their income was increased just enough to achieve the same level of utility as the final point (D) reached after the actual wage rise.
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Ch.3 Doing the best you can: Scarcity, wellbeing, and working hours - The Economy 2.0 Microeconomics @ CORE Econ
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Point C as the Hypothetical Choice in Figure E3.4
Simplification of the Utility Equivalence Equation in Figure E3.4
An individual's daily well-being is modeled by the expression
w × t², wherewis their hourly wage andtis the hours of free time they choose. Initially, their wage is $20 per hour. After a promotion, their wage increases to $25 per hour, and they are observed to choose 16 hours of free time per day. An economist wants to determine the level of well-being at the new wage and then find the hypothetical choice of free time (t_H) that would provide this same level of well-being if the individual were still facing the original $20 wage. Which equation correctly represents the relationship needed to findt_H?Formulating a Utility Equivalence Equation
Calculating Hypothetical Free Time for Utility Equivalence
An individual's satisfaction from their daily choices is modeled by the expression
w × t², wherewis their hourly wage andtis the hours of free time they enjoy. This individual's wage increases from $50/hour to $72/hour. At the new, higher wage, they are observed to choose 10 hours of free time. To find the hypothetical amount of free time (t_H) that would provide this same level of satisfaction if they were still earning their original wage, the following equation must be solved:50 × t_H² = ____ × 10².An analyst is studying a person whose daily satisfaction is represented by the formula
w × t², wherewis the hourly wage andtis hours of free time. The person's wage increases from $49/hour to $64/hour, and at the new wage, they choose 7 hours of free time. The analyst states that to find the hypothetical amount of free time (t_H) that would have provided this same level of satisfaction at the original wage, one must solve the equation:$64 × t_H² = $49 × 7². Is the analyst's statement correct?An economist is studying how a wage change affects an individual's choice of free time. The individual's daily satisfaction is modeled by the expression
U = w × t², wherewis the hourly wage andtis hours of free time. The wage increases fromw_initialtow_final, and the individual is now observed choosingt_finalhours of free time. The economist sets up the following equation to solve for a hypothetical amount of free time,t_hypothetical:w_initial × (t_hypothetical)² = w_final × (t_final)²What does the value of
t_hypotheticalrepresent in this context?An individual's daily satisfaction is modeled by the expression
U = w × t², whereUis the satisfaction level,wis the hourly wage, andtis hours of free time. This person's wage increases from $36/hour to $64/hour. At the new, higher wage, they choose to have 9 hours of free time. To analyze this change, an economist sets up the following equation to find a hypothetical choice of free time (t_H):$36 × t_H² = $64 × 9². Match each mathematical expression from the equation to the concept it represents.An economist wants to analyze the impact of a wage increase on an individual's choices. The individual's daily satisfaction is modeled by the expression
U = w × t², wherewis the hourly wage andtis hours of free time. The wage increases fromw_initialtow_final, and at the new wage, the individual choosest_finalhours of free time. The economist needs to find the hypothetical amount of free time (t_hypothetical) that would provide the same level of satisfaction as the final choice, but if the individual were still facing thew_initial. Arrange the following steps in the correct logical order to solve fort_hypothetical.Evaluating an Economic Interpretation
An economist is analyzing an individual's response to a wage change, where daily satisfaction is modeled by the expression
U = w × t²(w= hourly wage,t= hours of free time). After the individual's wage increased to $72/hour, they were observed to choose 10 hours of free time. The economist calculated that to achieve this same level of satisfaction at the original wage, the individual would have needed 12 hours of free time. Based on this analysis, what was the individual's original hourly wage?An individual's satisfaction from their daily choices is modeled by the expression
w × t², wherewis their hourly wage andtis the hours of free time they enjoy. This individual's wage increases from $50/hour to $72/hour. At the new, higher wage, they are observed to choose 10 hours of free time. To find the hypothetical amount of free time (t_H) that would provide this same level of satisfaction if they were still earning their original wage, the following equation must be solved:50 × t_H² = ____ × 10².
Learn After
A worker's hourly wage increases, leading them to choose a new combination of goods and leisure that provides a higher level of overall satisfaction. To understand this behavioral shift, an economist identifies a hypothetical choice: the bundle of goods and leisure the worker would select if they faced the original, lower wage rate but were given a lump-sum payment just large enough to reach the new, higher level of satisfaction. What is the primary purpose of identifying this hypothetical bundle?
A freelance writer's hourly rate increases. As a result, they adjust their work hours and are able to achieve a higher level of overall satisfaction (utility). To isolate the pure 'price' effect of this wage change on their choice between leisure and income, an economist constructs a hypothetical budget constraint. What are the two defining characteristics of this hypothetical budget constraint?
An economist analyzes a worker's response to a wage increase. To do this, they identify a hypothetical choice ('Point C') which represents the bundle of goods and leisure the worker would choose if they were paid their original, lower wage rate but received a lump-sum income payment just large enough to make them as satisfied as they are after the wage increase. If this hypothetical choice at 'Point C' involves the worker taking more leisure time than they did at their initial position ('Point A'), what can be concluded?
Decomposing the Effect of a Wage Change
Analyzing a Change in Work Hours
An individual's wage rate increases, resulting in a new combination of goods and leisure that provides a higher level of overall satisfaction. To analyze this change, a hypothetical scenario is constructed where the individual is given just enough income to reach this new, higher satisfaction level, but at their original, lower wage rate. The statement is: The amount of leisure the individual chooses in this hypothetical scenario will be identical to the amount of leisure they choose in their final situation after the actual wage increase.
An economist is analyzing how a worker's choice between leisure and consumption goods changes after an increase in their hourly wage. To do this, they identify three key bundles (combinations of leisure and goods) in their model. Match each description of a bundle to its role in the analysis.
An individual's hourly wage increases. To analyze the effect of this change on their choice between work and leisure, an economist constructs a hypothetical scenario. In this scenario, the individual is given just enough additional income to make them as well-off as they are after the wage increase, but they are hypothetically still facing their original, lower wage rate. At the optimal bundle of goods and leisure identified in this hypothetical scenario, what is the individual's marginal rate of substitution between consumption goods and leisure equal to?
Purpose of a Hypothetical Budget Constraint
Critiquing an Economic Analysis of a Wage Change