Preference sS is altruistic towards her children (also skilful) 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 s Technology: Assume small open i economy so that interest rate and a 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 e2) st c3-k=M+(1-x)k3+乙yk3 yields The Second Generations Programming max u 2 A() st C,'+k-k,=w+(1-t)rk,+r,rk2 k3,k,) 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 )A(2)+m) st c1+k2k1=w+ K,+tr k 252253 yieldsaic1 (15 /17154273 k旦大学经济学院
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 tk Finally, we can get three generations indirect utility functions (k1,k1 1515233 22253 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: