By David Romer
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Extra resources for Advanced Macroeconomics Solution Manual
Aw t T 1 rt 1 (1 rt 1) Rearranging, we get the intertemporal budget constraint: C 2 ,t 1 ( rt 1 n) Aw t T. (6) C1,t (1 rt 1 ) 1 rt 1 We know that with logarithmic utility, the individual will consume fraction (1 + )/(2 + ) of her lifetime wealth in the first period. Thus rt 1 n 1 (7) C1,t T . Aw t 2 1 rt 1 To solve for saving per person, substitute equation (7) into equation (2): rt 1 n 1 (8) S t Aw t T T Aw t 2 1 rt 1 Simplifying gives us 1 r n 1 t 1 (9) S t 1 Aw T , t 1 2 2 1 rt 1 or (2 )(1 rt 1 ) (1 )( rt 1 n) (10) S t 1 2 Aw t T .
6) Dividing equation (6) by equation (5) yields Pt 1 Pt 1 (1 n) Pt 1 Pt (1 n) . This analysis holds for all time periods t 0 and so Pt+1 = Pt /(1 + n) is an equilibrium. This shows that if money is introduced into a dynamically inefficient economy, storage will not be used. The monetary equilibrium will thus result in attainment of the "golden-rule" level of storage. 18 for an explanation of the reason that zero storage maximizes consumption per unit of effective labor. (c) This is the situation where Pt /Pt+1 = x; the return on money is equal to the return on storage.
The planner can divide the resources available for consumption between the young and the old in any matter. The planner can take, for example, one unit of each young person's endowment and transfer it to the old. Since there are the same number of old and young people in this model, this increases the consumption of each old person by one. With x < 1, this method of transferring from the young to the old provides a better return than storage. If the economy did not end at some date T, the planner could prevent this change from making anyone worse off by requiring the next generation of young to make the same transfer in the following period.
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