Evaluating an Economic Interpretation
An economist is studying a worker whose daily satisfaction is modeled by the expression U = w × t², where U is the satisfaction level, w is the hourly wage, and t is hours of free time. The worker's wage increases from $25/hour to $36/hour. At the new, higher wage, the worker chooses 10 hours of free time.
The economist calculates a hypothetical amount of free time (t_H) that would provide the same level of satisfaction as the final choice, but if the worker were still facing the original wage. They solve the equation $25 × t_H² = $36 × 10² and find that t_H = 12 hours.
Based on this, the economist concludes: "The fact that the worker now chooses 10 hours of free time instead of the hypothetical 12 hours proves that the pure effect of their increased purchasing power has led them to consume less free time."
Critically evaluate the economist's conclusion. Is their interpretation of the comparison between the 10-hour and 12-hour figures correct? Explain your reasoning.
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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
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