By David Romer

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**Extra info for Advanced Macroeconomics Solution Manual**

**Example text**

Thus, for the economy to return to a balanced growth path, we must be somewhere on the original saddle path right at time t1 . Before the tax is put in place – until time t0 – and after the tax is removed – after time t1 – the equations governing the dynamics of the economy are c( t ) f k ( t ) g , and (2) k ( t ) f k ( t ) c( t ) ( n g) k ( t ) . (1) c( t ) The condition required for c 0 is given by f ' (k) = + g. The capital-accumulation equation, and thus the k 0 locus, is not affected by the tax.

Using equation (14) to substitute for the wage yields (29) k t 1 1 1 n 1 2 (1 ) k t . Thus the fully-funded social security system has no effect on the relationship between the capital stock in successive periods. (b) (ii) Since there is no effect on the relationship between kt+1 and kt , the balanced-growth-path value of k is the same as it was before the introduction of the fully-funded social security system. (Note that we have been assuming that the amount of the tax is not greater than the amount of saving each individual would have done in the absence of the tax).

Thus 1 (2 ) (1 ) k t 1 (11) s (1 ) . 2 k t Thus equation (10) can be rewritten as s 1 t sk (12) k t 1 f (k t ) . (1 n)(1 g) (1 n)(1 g) Note that this is exactly the same as the expression for kt+1 as a function of kt in the discrete-time Solow model with = 1. 15 with set to one. Thus that version of the Solow model does have some microeconomic foundations, although the assumption of 100% depreciation is quite unrealistic. 17 (a) (i) The utility function is given by (1) ln C1,t 1 1 ln C 2,t 1 .