interdependencies. - Expectations of future values of key variables are important to current decisions. - MaCurdy (1981) a key paper: Rt = discount rate e.g. 1/(1+r)t assuming r is a constant interest rate. Nt = T* - (labour supplied) T* = total time available to allocate in a period, lt A0 = initial wealth Ct = consumption in time t = leisure in time t time preference parameter = lt Wt = wage rate in period t (some time path of wage rates is expected at time 0). - first term: present value of lifetime utility - constraint: - lifetime budget constraint - present value of resources (wealth, income) = present value of consumption - constraint assumes ability to borrow and lend at rate “r” (note: if borrow and lend model reverts to static model!) can’t f.o.c.: (where = Lagrange multiplier: Marginal Utility of initial wealth)  Ct: {1/(1+)t} Uct - Rt = 0 Uct= U/Ct  {1/(1+)t} Ult - RtWt 0 (inequality if Ult= U/lt lt:  l=T) this can be solved for the Frisch demand functions: Ct = C( Rt (1+)t Wt ) = Rt (1+)t Wt ) lt l( replace leisure demand with labour supply: Nt=T*-lt = N( Rt (1+)t Wt ) labour supply as a function of wage, interest and )  (Frisch labour supply function) - Effects of the two arguments on labour supply in time t: Wt - substitution story
interdependencies. - Expectations of future values of key variables are important to current decisions. - MaCurdy (1981) a key paper: Rt = discount rate e.g. 1/(1+r)t assuming r is a constant interest rate. Nt = T* - lt (labour supplied) T* = total time available to allocate in a period, A0 = initial wealth Ct = consumption in time t lt = leisure in time t = time preference parameter Wt = wage rate in period t (some time path of wage rates is expected at time 0). - first term: present value of lifetime utility - constraint: - lifetime budget constraint - present value of resources (wealth, income) = present value of consumption - constraint assumes ability to borrow and lend at rate “r” (note: if can’t borrow and lend model reverts to static model!) f.o.c.: (where  = Lagrange multiplier: Marginal Utility of initial wealth) Ct: {1/(1+)t} Uct -  Rt = 0 Uct= U/Ct lt: {1/(1+)t} Ult -  RtWt 0 (inequality if l=T) Ult= U/lt this can be solved for the Frisch demand functions: Ct = C( Rt (1+)t Wt ) lt = l( Rt (1+)t Wt ) replace leisure demand with labour supply: Nt=T*-lt = N( Rt (1+)t Wt ) labour supply as a function of wage, interest and  ) (Frisch labour supply function) - Effects of the two arguments on labour supply in time t: Wt - substitution story
GLAB14b.docx