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

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BlackTom AI · Accepted Answer

In tackling the labor-leisure choice model, we need to examine what each option says about the choice variables and how labor supply is derived.
Option 1: The claim that the individual chooses the amount of consumption and leisure to demand during the optimization problem is correct in spirit, since the standard two-good choice in this model is consumption and leisure (with labor being the complement of leisure given a fixed total time). However, the statement that one minus the Marshallian demand for leisure gives the labor demand is inaccurate. Labor supply is the amount of labor actually supplied, which equals total available time minus the chosen leisure, i.e., Labor = Total Time − Leisure. Simply using 1 − Marshallian leisure is not the correct mapping unless total time is normalized to 1, which is not generally the standard parameterization. Thus this option mixes the correct idea (consumption and leisure chosen) with an incorrect articulation of how labor is derived from leisure.
Option 2: This option says the individual chooses the amount of labor and leisure to demand, and that the Marshallian demand for labor gives the labor demand. In the usual framework, the optimization problem centers on choosing consumption and leisure, not labor directly. Labor is endogenous and determined by the constraint Total Time = Leisure + Labor. Therefore treating labor as a primitive choice and referencing a Marshallian demand for labor as the output of the problem misstates the setup, making this option incorrect.
Option 3: Here, the individual chooses the amount of consumption and leisure to demand during the optimization problem, which aligns with the standard labor-leisure model where leisure (and hence consumption via the budget constraint) are the primary decision variables. Crucially, one minus the Marshallian demand for leisure yields the labor supply, since Labor = Total Time − Leisure. This matches the conventional interpretation and the mathematical relationship that connects leisure demand to labor supply, so this statement is consistent with the theory.
Option 4: This option asserts that the individual chooses the amount of labor and leisure to demand, and that the Marshallian demand for labor gives the labor supply. This is inconsistent with the typical formulation, which centers on consumption and leisure as the choice variables and treats labor as the residual from total time after choosing leisure. Also, the Marshallian demand for labor is not the standard mechanism by which labor supply is determined. Consequently, this option misrepresents both the choice variables and the labor-supply mapping.

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

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