By deduction, one can obtain (1-x,O)k,S B0(-r1+1 T 0 1-tt+1 +B(1-r 1+1)-S t+1 It is clear that future taxation affects current 9osaving decision. Specifically, at time t, government takes into consideration the impact of t+ upon k+. However, at time t+1 optimal taxation plan would change since k+1 is fixed and the impact of t+ 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 By the same procedure. one can obtain VT(hr)=U(CT )MR(kr)= →k B(-x7)1 1-rO+B(1-r 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