using 1=L+l: + = P c  W∙(1-l) (this is in 'nominal' terms: divide by P to put it in real terms) - Crusoe's consumer problem: max U(c,l) s.t. + = P c  W∙ (1-l) <c,l> - The Lagrangian for the consumer problem is: (c,l,)= U(c,l) + [ W(1-l) + P c ]   – = Lagrange multiplier  - maximizing this WRT c, and gives the  l f.o.c’s: c: = Uc =0 P ∂/∂c – = Ul - W=0  l: ∂/∂l : = -Pc = 0   ∂/∂ W∙(1-l)+ - combine first two foc's: = W/P Ul/Uc using this and the budget constraint (f.o.c. for implies ) solutions for: Output demand: c*=c(w/P, parameters) Leisure demand: parameters) l*=l(w/P,
using 1=L+l: W∙(1-l) +  = P c (this is in 'nominal' terms: divide by P to put it in real terms) - Crusoe's consumer problem: max U(c,l) s.t. W∙ (1-l) +  = P c <c,l> - The Lagrangian for the consumer problem is: (c,l,)= U(c,l) +  [ W(1-l) +  – P c ]  = Lagrange multiplier - maximizing this WRT c, l and  gives the f.o.c’s: c: ∂/∂c = Uc – P =0 l: ∂/∂l = Ul -  W=0  : ∂/∂ = W∙(1-l)+  -Pc = 0 - combine first two foc's: Ul/Uc = W/P using this and the budget constraint (f.o.c. for ) implies solutions for: Output demand: c*=c(w/P, parameters) Leisure demand: l*=l(w/P, parameters)