- The five first order conditions imply implicit solutions for the endogenous variables: c1, c2, b1 , and in terms of the exogenous variables   (r, b0, y1, y2, and the form of the utility function). - Comparative statics: Outcome is described by the optimality condition and the constraints (here they are combined into one intertemporal constraint): -U'(c1) + = 0 U'(c2)(1+r) - take derivatives of these conditions WRT c1, c2 and the desired exogenous variable e.g. b0 then solve for dc1/db0 and dc2/db0 (see Williamson p.678 a version of this model with taxes) – - Take an example: Say U = ln(c1) + ln(c2) so: /c2 ∂/∂c1=U'(c1)=1/c1 ∂/∂c2=U'(c2)= Euler equation becomes: =1 c1(1+r) c2 - notice: rise in r or means c1/c2 falls ;  if: then c1=c2 (1+r) Exact solution:
- The five first order conditions imply implicit solutions for the endogenous variables: c1, c2, b1 ,  and  in terms of the exogenous variables (r, b0, y1, y2, and the form of the utility function). - Comparative statics: Outcome is described by the optimality condition and the constraints (here they are combined into one intertemporal constraint): -U'(c1) + U'(c2)(1+r) = 0 - take derivatives of these conditions WRT c1, c2 and the desired exogenous variable e.g. b0 then solve for dc1/db0 and dc2/db0 (see Williamson p.678 – a version of this model with taxes) - Take an example: Say U = ln(c1) + ln(c2) so: ∂/∂c1=U'(c1)=1/c1 ∂/∂c2=U'(c2)= /c2 Euler equation becomes: c1(1+r) =1 c2 - notice: rise in r or  means c1/c2 falls ; if: (1+r) then c1=c2 Exact solution: