Modeling Preferences with Utility Functions
An economist is modeling the preferences of two individuals, Maya and Liam, concerning their weekly free time (t, in hours) and consumption (c, represented by a consumption index). Maya is very career-oriented and is willing to sacrifice a significant amount of free time for a relatively small increase in her consumption. Liam prioritizes his work-life balance and requires a large increase in consumption to be convinced to give up even a small amount of his free time. The economist considers two possible utility functions:
- Function A: U(t, c) = t + 5c
- Function B: U(t, c) = 5t + c
Based on the descriptions, which function best represents Maya's preferences, and which best represents Liam's? Justify your reasoning for each choice by explaining what the structure of the function implies.
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