104A_Preferences - Preference Theory Consumption quantities...

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Preference Theory. Consumption quantities : X i = quantity consumed per time pe- riod of commodity i , i = 1 , . . . , n . Assumption 1 (perfect divisibility): X i can be any nonnegative (real) number for all i . Consumption bundle : X = [ X 1 , . . . , X n ]. Assumption 2 (Completeness of preferences): For any pair of bundles, ¯ X and ˆ X , the consumer prefers ¯ X to ˆ X or prefers ˆ X to ¯ X or is indi ff erent between the two.
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Assumption 3 (transitivity of preferences): (a) ¯ X preferred to ˆ X and ˆ X preferred to X implies that ¯ X preferred to X . (b) ¯ X indi ff erent to ˆ X and ˆ X indi ff erent to X implies that ¯ X indi ff erent to X . Assumptions 2 and 3 imply a complete (preference) ordering of consumption bun- dles. Assumptions 1–3 imply the existence of an indi ff erence map . Every consumption bundle lies on one and only one indi ff er- ence surface (indi ff erence curve in two di- mensions).
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Assumption 4 (fixed income and prices): The consumer is endowed with fixed nonneg- ative income, I, and faces fixed positive
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