Utility function: U = U( Y, l) Y = spending on goods (= Income i.e. ignore saving) = hours of leisure l - represents well-being from Y, le combinations, i.e. ranking of possible (Y, choices in terms of well-being. l) - marginal utilities positive: U/l >0 Uy ≡ U/Y>0 , Ul ≡ - assume diminishing marginal utility : Uyy = Uy/Y <0 , Ull = Ul/l <0 (also for later define: Uyl = Uy/l =Ul/Y ) - Utility in graphs? - indifference curve U* = U( Y, combinations of Y, that give some fixed l) l level of utility U*. - an indifference curve goes through each point in Y, space. l - a higher indifference curve means higher U. - indifference curves are downward sloping on an indifference curve: dU* = 0 = UydY + Ul dl slope = dY/dl = -Ul/Uy <0 Ul/Uy = Marginal rate of substitution between leisure and income (MRS). `i.e. value of an extra bit of leisure in terms of extra income. (dollar value of extra bit of l)
Utility function: U = U( Y, l) Y = spending on goods (= Income i.e. ignore saving) l = hours of leisure - represents well-being from Y, le combinations, i.e. ranking of possible (Y, l) choices in terms of well-being. - marginal utilities positive: Uy ≡ U/Y>0 , Ul ≡ U/l >0 - assume diminishing marginal utility : Uyy = Uy/Y <0 , Ull = Ul/l <0 (also for later define: Uyl = Uy/l =Ul/Y ) - Utility in graphs? - indifference curve U* = U( Y, l) combinations of Y, l that give some fixed level of utility U*. - an indifference curve goes through each point in Y, l space. - a higher indifference curve means higher U. - indifference curves are downward sloping on an indifference curve: dU* = 0 = UydY + Ul dl slope = dY/dl = -Ul/Uy <0 Ul/Uy = Marginal rate of substitution between leisure and income (MRS). `i.e. value of an extra bit of leisure in terms of extra income. (dollar value of extra bit of l)
GLAB14b.docx