Anticipation under lack of commitment leads to excess growth

We study a simple asset accumulation problem in which instantaneous utility depends not only on current consumption but also on anticipated future consumption. This feature of the preferences renders them dynamically inconsistent. We solve the model under the assumptions that the decision maker (i) is aware of the dynamic inconsistency and (ii) lacks commitment power (sophisticated approach). It is shown that asset growth under these assumptions always exceeds the corresponding growth rate under commitment.