Atomistic Assumption wIthout loss of generality, we can write down a"semi-indirect utility function?" for the ith household vlk.KT Precommitment Solution(the first equation is the households behavior and the second is the government's choice) ay ak av 0 0 Time Consistent Solution(the first equation is the households behavior and the second is the government's choice) 0 ak 0∑ l aT Clearly the discrepancy lies in atomistic i agents, or similarly, the externality of F aggregate capital KAtomistic Assumption ❖ Without loss of generality, we can write down a “semi-indirect utility function” for the ith household: v (k ,K, ) i i • Precommitment Solution (the first equation is the households’ behavior and the second is the government’s choice): 0 = 0           +     =   i i i i i K v K v k v   • Time Consistent Solution (the first equation is the households’ behavior and the second is the government’s choice): 0 = 0   =   i i i i v k v  • Clearly the discrepancy lies in atomistic agents, or similarly, the externality of aggregate capital K