Homothetic/ Quasilinear Preference

Homothetic Preference

A monotone preference relation such that if x ∼ y, then αx ∼ αy for any α ≥ 0.

Quasilinear Preference (with respect to commodity 1)

A preference relation such that

1. if x∼y, then (x+αe1)∼(y+αe1) for e1 = (1,0,...,0) and any α ∈ R.

2. Good1 is desirable; that is,x+αe1 ≻x for all x and α>0.

Note that commodity 1 can be negative (commodity 1 ∈ R).

Mas-Colell, Whiston and Green "Microeconomic Theory" (p.45)