By David Romer
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Additional resources for Advanced Macroeconomics Solution Manual, 4th Edition
For the old at date t, Qt+1 is irrelevant. They based their decision of how much to trade when old on Qt /Qt-1 which was equal to x. Thus each old individual was not planning to buy or sell anything. Thus aggregate demand exceeds aggregate supply and the market for the good will not clear. 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.
At time t0 , the tax is announced. Consumption must jump up so that the economy is at a point like A. c 0 [between time t1 and t2 ] c B A c 0 [before time t1 and after time t2] E C k 0 k At A, the economy is still on the c 0 locus but is above the k 0 locus and so k starts falling. The economy is then to the left of the c 0 locus and so c starts rising. The economy drifts off to the northwest. At time t1 , the tax is implemented, the c 0 locus shifts to the left and the economy is at a point like B.
The economy drifts off to the northwest. At time t1 , the tax is implemented, the c 0 locus shifts to the left and the economy is at a point like B. The economy is still above the k 0 locus but is now to the right of the relevant c 0 locus; k continues to fall and c stops rising and begins to fall. Eventually the economy crosses the k 0 locus and k begins rising. Households begin accumulating capital again before the actual removal of the tax on capital income. Point A must be chosen so that given the dynamics of the system, the economy is right at a point like C, on the original saddle path, at time t2 when the tax is removed.