Comparing Willingness to Substitute Across Different Preference Structures
An individual's satisfaction is derived from two sources: their annual income (y) and the number of vacation days they take (d). Consider two individuals with different preferences:
- Individual A's satisfaction: U_A(y, d) = y + 200d - 2d²
- Individual B's satisfaction: U_B(y, d) = y + 120d
For both individuals, the Marginal Rate of Substitution (MRS) represents the amount of income they are willing to give up for one additional vacation day. Analyze and compare how the MRS for Individual A and Individual B changes as the number of vacation days they take increases. Based on your mathematical analysis, explain the economic intuition behind the difference in their preferences for vacation days.
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