Modeling Preferences for Leisure
An economist is modeling the preferences of a recent retiree who has a strong initial preference for leisure but finds that the additional satisfaction from each extra hour of free time diminishes rapidly. The economist uses a utility function of the form u(t, c) = v(t) + c, where 't' is hours of free time and 'c' is consumption. Propose a specific mathematical form for v(t) that captures the retiree's described preferences. Justify your choice by explaining how the mathematical properties of your proposed function and its derivative align with the retiree's diminishing enjoyment of additional leisure time.
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