By David Romer
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Additional info for Advanced Macroeconomics Solution Manual
Again, there would be no way for c to jump up by (GH - GL ) at t1 and still put the economy on the original saddle path. In summary, the capital stock and the real interest rate are unaffected by the temporary increase in G. At the instant that G rises, consumption falls by an equal amount. It remains constant at that level while G remains high. At the instant that G falls to its initial value, consumption jumps back up to its original value and stays there. © 2012 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use.
Thus the proposed price path cannot be an equilibrium. (b) Consider the social planner's problem. 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.
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. However, if the economy ends at some date T, the planner cannot do this. Taking anything from the young at date T would make them worse off since the planner cannot give them anything in return the next period; there is no next period.
Advanced Macroeconomics Solution Manual by David Romer