The initial step in a comparative statics analysis of an individual's choice is to examine how the optimal amount of free time ($t^*$) is affected by a change in an economic parameter, like the wage rate ($w$) or unearned income ($I$). This involves differentiating the optimal free time function, $t^*(w, I)$, with respect to the parameter of interest, while holding other factors constant.

Analyzing the Effect of Parameter Changes on Optimal Free Time

A complete comparative statics analysis involves examining how the optimal consumption level ($c^*$) is affected by a change in an economic parameter. This is done by differentiating the optimal consumption function, $c^*(w, I)$, with respect to the parameter of interest. This same analytical method is applied to both the wage rate ($w$) and the amount of unearned income ($I$) to determine their respective impacts on chosen consumption.

Analyzing the Effect of Parameter Changes on Optimal Consumption

To determine how the optimal choice of consumption and free time responds to a change in an external factor, one can employ differentiation. This method of comparative statics involves differentiating the functions for the optimal choice (e.g., $t^*(w, I)$ and $c^*(w, I)$) with respect to the parameter of interest (e.g., wage, $w$), while holding other parameters (e.g., unearned income, $I$) constant.

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The utility-maximizing choice of consumption ($c^*$) and free time ($t^*$) is not a fixed value but rather a function of the economic parameters an individual faces. Specifically, the optimal bundle $(t^*, c^*)$ depends on the wage rate ($w$) and the amount of unearned income ($I$), meaning the solution can be expressed as $t^*(w, I)$ and $c^*(w, I)$.

Optimal Choice as a Function of Wage and Unearned Income

To cite the ebook, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/.

To cite a unit, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/ Unit [unit number] (url).

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