Evaluating the Analysis of a Non-Monotonic Utility Function
An economics student analyzes a consumer's preferences for consumption (c) and free time (t) using the utility function u(t, c) = 20t - t² + c. After finding that the second derivative of the indifference curve (d²c/dt²) is a positive constant, the student concludes: 'The indifference curves are convex, which implies a diminishing marginal rate of substitution for all possible amounts of free time.'
Critique the student's conclusion. Identify the flaw in their reasoning and provide the correct economic interpretation, specifying any limitations on the range of free time.
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Evaluating the Analysis of a Non-Monotonic Utility Function