Evaluating a Constrained Optimization Solution
An individual's satisfaction from leisure (t, in hours) and consumption (c, in dollars) is described by the utility function u(t,c) = t³c. They earn an hourly wage of $25 and have 24 hours per day to allocate between work and leisure. A classmate attempts to solve for the optimal amount of leisure and consumption and begins their work with the following steps:
- Calculate the marginal utility of leisure (MUt) and the marginal utility of consumption (MUc).
- Set the marginal utility of leisure equal to the marginal utility of consumption (MUt = MUc).
- Use this equality to find a relationship between c and t, and substitute it into the budget constraint to solve for t.
Critically evaluate this proposed method. Is this approach correct? If not, identify the specific conceptual error in the classmate's reasoning and explain the correct principle that should be applied to find the optimal choice.
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Science
Economy
CORE Econ
Social Science
Empirical Science
Economics
Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
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