Preferences

# Preferences - Econ 452 Quasi-linear preferences Lecture III...

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Econ 452, Quasi-linear preferences Page 1 of 5 Lecture III: Special preferences Quasi-linear preferences - goods x and y (, ) () Uxy Bx y =+ '( ) 0 "( ) BB ⋅> > for x>0 - separable in goods - non-linear in one good (here,x), linear in other - Ex: ln Uxy x y α + = - Campbell's notation: Properties of demand? A. Individual optimum: Given (, , ) xy ppw , consumer problem is max x x yy p w Bx x PP +−

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Econ 452, Quasi-linear preferences Page 2 of 5 a) interior solution to consumer's problem: FOC for interior solution: '( ) x y p Bx p = - optimal amount independent of w (no income effect) - remainder of w spent on other good b) corner solutions to consumer problem: 1. only second good (linear) consumed: - if '(0) , x y p B p < then *0 x = and * y w y p = 2. only first good (concave) consumed: - if '( ) , x xy p w B pp > then 0 * y = and * x w x p = Pictures? IC's are vertically parallel (Horizontally parallel if U linear in x, and concave in y)
Econ 452, Quasi-linear preferences Page 3 of 5 B. fficient allocations? Simplify - let 1 y p = , so x ywp x =− is spending on all other goods.

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Preferences - Econ 452 Quasi-linear preferences Lecture III...

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