Four Solutions First-Best Allocation maximize g households welfare subject to resource constraint o Cheating (Time-Inconsistent) Solution: government would like to deviate from her previous policy at the second period when k has been accumulated, because she always has incentive to reduce distortion by only taxing k &s Precommitment Solution: Open Loop Solution in the Stackelburghk Game Time Consistent Solution: Subgame, Perfect Equilibrium Welfare Comparison >2>3>Four Solutions ❖ First-Best Allocation: maximize household’s welfare subject to resource constraint. ❖ Cheating (Time-Inconsistent) Solution: government would like to deviate from her previous policy at the second period when k has been accumulated, because she always has incentive to reduce distortion by only taxing k. ❖ Precommitment Solution: Open￾Loop Solution in the Stackelburgh Game. ❖ Time Consistent Solution: Subgame Perfect Equilibrium. ❖ Welfare Comparison: 1 > 2 > 3 > 4