Consider the labor-leisure choice model. Which of the following is a correct statement about the Marshallian demands:

Question

BlackTom AI · Accepted Answer

In tackling the labor-leisure choice model, we first recall the core idea: individuals maximize utility subject to a budget constraint that ties consumption to labor income, and they choose both consumption and leisure (or equivalently labor) as part of the optimization problem.
Option 1: 'The individual chooses the amount of consumption and leisure to demand, during the optimization problem. One minus the Marshallian demand for leisure gives the labor supply.' This aligns with the standard setup: consumers decide on C and L (consumption and leisure) to maximize utility, with leisure L and labor H related by L = T − H, so labor supply is determined as H = T − L, i.e., one minus the leisure chosen in the sense of time endowment. Since the Marshallian (ordinary) demand for leisure is the amount of leisure demanded as a function of prices and income, subtracting that from total time gives labor supplied; this option correctly reflects the relationship between leisure and labor supply in the Marshallian framework.
Option 2: 'The individual chooses the amount of labor and leisure to demand, during the optimization problem. The Marshallian demand for labor gives the labor supply.' This wording is inconsistent: in consumer theory, we do not simultaneously choose 'labor and leisure' as primary goods; the standard model focuses on consumption and leisure with labor as the time/feasible choice tied to leisure. Moreover, the labor supply is not given by Marshallian demand for labor; rather, labor supply derives from the chosen leisure via H = T − L. So this option confuses the role of labor in the optimization and misstates how labor supply is determined.
Option 3: 'The individual chooses the amount of consumption and leisure to demand, during the optimization problem. One minus the Marshallian demand for leisure gives the labor supply.' This is very close to Option 1 but differs only in punctuation or emphasis; structurally, it expresses the correct idea: C and L are chosen, and labor supply equals total time minus leisure. If interpreted within the standard framework, it is correct. The content matches the conventional derivation where labor supply is T − L, with L being the Marshallian demand for leisure.
Option 4: 'The individual chooses the amount of labor and leisure to demand, during the optimization problem. The Marshallian demand for labor gives the labor demand.' Similar to Option 2, this misidentifies the basic goods and misstates the linkage between labor and leisure in the optimization. In usual theory, the agent does not choose 'labor and leisure' as if both are independent demand goods for a consumer; instead, leisure and consumption are chosen subject to time and budget constraints, and labor supply is derived from leisure as H = T − L. The claim that Marshallian demand for labor directly gives labor demand is not how the model works.
Overall, the most accurate statement is the one that emphasizes choosing consumption and leisure within the optimization and identifies labor supply as the remaining time after leisure, i.e., labor supply equals total time minus the chosen leisure. The remaining options either misstate which variables are chosen in the optimization or misattribute the source of labor supply to the labor demand demanded by Marshallian theory.

Consider the labor-leisure choice model. Which of the following is a correct statement about the Marshallian demands:Single choice

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