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Exercise 1.pdf - Practice Questions 1 1 An increasingly...

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Practice Questions 1 1. An increasingly common utility function used in macroeconomic applica- tions is one in which period-t utility depends not only on period-t consumption but also on consumption in periods earlier than period t. This idea is known as “habit persistence,” which is meant to indicate that consumers become “ha- bituated” to previous levels of consumption. To simplify things, let’s suppose only period-(t-1) consumption enters the period-t utility function. Thus, we can write the instantaneous utility function as u ( c t - 1 , c t , n t ) . When a consumer arrives in period t, c t - 1 of course cannot be changed (because it happened in the past). Now, Consider a representative consumer at time t=0 seeking to maximize the sum of discounted lifetime utility from t=0 on, t =0 β t u ( c t - 1 , c t , n t ), subject to the infinite sequence of flow budget constraints P t c t + S t a t = S t a t - 1 + D t a t - 1 + P t w t n t , where the notation is as in class: a t is holdings of a real asset (a “stock”) at the end of period t, S t is its nominal price in t, D t is the nominal dividend that each unit of assets carried into t from period t-2 pays out, P t w t n t
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