By deduction, one can obtain (1-x,O)k,S B0(1-r1 1-x1O+B(1-+1)-s12 0 It is clear that future taxation affects current 9osaving decision. Specifically, at time t, government takes into consideration the impact of tt+ upon k++. However, at time t+l optimal taxation plan would change since k +1 is fixed and the impact of tt+1 disappear Maximizing value function(static problem?) yields TC solution. Precommitment(Ramsey) Solution can't be solved analytically(bellman problem?) Next we consider proportional income tax &t=t By the same procedure. one can obtain r(k)=U(a7MR/=(-)0 k2=B0=)-x=0k 1-x76+B O(1-x) 复9大学经学院 Note that by proportional income tax, there is F no distortion in marginal returns of capital• By deduction, one can obtain: ( ) ( ) , 0 1 1 1 1 1 1 1 = − + − − − = + + + + T t t t t t s s s         ( ) t t t t k = s −  k +1 1 • It is clear that future taxation affects current saving decision. Specifically, at time t, government takes into consideration the impact of τt+1 upon kt+1. However, at time t+1, optimal taxation plan would change since kt+1 is fixed and the impact of τt+1 disappear. • Maximizing value function (static problem?) yields TC solution. Precommitment (Ramsey) Solution can’t be solved analytically (bellman problem?). • Next we consider proportional income tax:   t t t g = k ( ) ( ) ( ) ( ) ( ) T T T t T T T T k k V k U c MR k     = − − = = 1 1 ' ' ( )( ) ( ) 1 1 1 1 1 1 − − − + − − −  = T T T T T T k k           • By the same procedure, one can obtain: • Note that by proportional income tax, there is no distortion in marginal returns of capital