Preference sS is altruistic towards her children (also skillful) in the following generations, so as U. Therefore, S and u in the first two generations would like to leave bequest to the their own children in the following generations 复9大学经学院
Preference ❖ S is altruistic towards her children (also skillful) in the following generations, so as U. Therefore, S and U in the first two generations would like to leave bequest to the their own children in the following generations
Capital, Technology and Policy Capital: The first generation is born with certain level of capital Their bequests form the capital held by the second generation whose bequest consequently form the capital held by the last generation ss Technology: Assume small open i economy so that interest rate and 3 wage rate are both exogenously x gIven o Policy Set: Flat-rate capital income tax is collected to balance 学经学院 the transfer payment, which is
Capital, Technology and Policy ❖ Capital: The first generation is born with certain level of capital. Their bequests form the capital held by the second generation, whose bequest consequently form the capital held by the last generation. ❖ Technology: Assume small open economy so that interest rate and wage rate are both exogenously given. ❖ Policy Set: Flat-rate capital income tax is collected to balance the transfer payment, which is equally distributed between S and
Backward Solution: 1 9 The Third Generations Programming maX c3) st 23-k=M4+(-x3)k3+xyk3 yields The Second Generations Programming max n(2)+A(2) st c2+k-k2=+(1-2)yk2+z2rk2 yields: C2=C22,k2,T2, t3 复9大学经学院
The Third Generation’s Programming max ( ) . . 3 u c st i ( ) 3 3 3 1 3 3 3 c k w rk rk i i i i − = + − + yields: ( ) 3 3 3 3 3 c c k ,k , i i i = The Second Generation’s Programming max ( ) ( ) . . 2 3 u c u c st i i + ( ) 2 2 3 2 2 2 2 c k k w 1 rk rk i i i i i + − = + − + yields: ( ) 2 2 2 2 2 3 c c k ,k , , i i i = ( ) 3 3 3 3 3 c c k ,k , i i i = Backward Solution: 1
Backward Solution: 2 The First Generations Programming max ulC+ Bulc2 +Bul st +k2k1=+(1-c1)k+k k 252423 y、0m121,z2,z2)经
max ( ) ( ) ( ) . . 3 2 1 2 u c u c u c st i i i + + ( ) 1 1 2 1 1 1 1 1 c k k w rk rk i i i i i + − = + − + The First Generation’s Programming ( ) 2 2 2 2 2 3 c c k ,k , , i i i = ( ) 3 3 3 3 3 c c k ,k , i i i = yields: ( ) 1 1 1 1 1 2 3 c c k ,k , , , i i i = Backward Solution: 2
Backward Solution: 3 Note that in order to mimic the competitive equilibrium, we assume there is no strategic behavior between S and U in each period The model is closed by k.= S +h Finally, we can get three generations indirect utility functions (k1,k 1515233 22253 k3,k3 复9大学经学院
( ) 2 2 2 2 2 3 v v k ,k , , i i i = ( ) 3 3 3 3 3 v v k ,k , i i i = ( ) 1 1 1 1 1 2 3 v v k ,k , , , i i i = u t s kt = kt + k Backward Solution: 3 • Note that in order to mimic the competitive equilibrium, we assume there is no strategic behavior between S and U in each period. • The model is closed by: • Finally, we can get three generations’ indirect utility functions: