Equation to Determine the Hypothetical Income (J) in Figure E3.4
To calculate the amount of hypothetical unearned income, J, that would allow an individual to reach the utility level of point D while facing the original wage (w=$96), an equation must be solved. This equation sets the utility at the hypothetical point C equal to the utility at the final point D. For the specific model in Figure E3.4, this relationship is expressed as $96t_C^2 = 150t_D^2t_Ct_D$).
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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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Equation to Determine the Hypothetical Income (J) in Figure E3.4
An individual initially earns a wage of $15 per hour and chooses to have 16 hours of leisure per day. The wage then increases to $20 per hour, and the individual adjusts their choice to 15 hours of leisure per day. To understand this change, an economist constructs a hypothetical scenario where the wage remains at the original $15 per hour, but the individual receives a hypothetical cash payment just large enough to make them as well-off as they are with the $20 per hour wage. In this hypothetical situation, the individual chooses to have 17 hours of leisure. Based on this analysis, what does the change from 16 hours of leisure to 17 hours of leisure represent?
Rationale for Isolating the Income Effect
In an analysis of a consumer's response to a wage increase, the thought experiment used to isolate the income effect involves constructing a hypothetical budget constraint. This hypothetical constraint has the same slope as the new budget constraint (reflecting the higher wage) and is tangent to the original indifference curve (reflecting the initial level of satisfaction).
Isolating the Income Effect
Analyzing a Policy Change for Gig Economy Workers
An economist is analyzing the effect of a wage increase on an individual's choice of leisure hours. To isolate the pure income effect, the economist constructs a hypothetical scenario where the individual's purchasing power increases, but the wage rate is held constant at its original level. Arrange the following steps in the correct logical order to graphically determine the income effect using this specific method.
An individual experiences a wage increase, which changes their optimal choice between work and free time. To understand this behavioral change, a hypothetical scenario is constructed where the wage rate is held at its original level, but the individual is given just enough extra unearned income to reach the new, higher level of satisfaction. Match each analytical component of this scenario with its corresponding description.
In the thought experiment designed to isolate the pure income effect resulting from a wage change, an individual's wage rate is held constant at its original level. To enable the individual to reach the new, higher level of satisfaction, their ______ is hypothetically increased.
Evaluating the Practicality of an Economic Thought Experiment
Critiquing a Method for Economic Analysis
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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.