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A3.3 Macro IS Balance
Let us denote by © the private saving/GDP ra (s/f). Then, Eq. (6.A12) is rewritten as
which is the so-called macro IS balance equation. 1 — X — у is the private invest- ment/GDP ratio. In order to discuss the policy implications of optimal deficits, Eq. (6.A12) is more useful than Eq. (6.A13). When the propensity to save, a, is given, Eq. (6.A12) can determine the optimal level of deficits.
A3.4 Comparative Dynamics
With these tools, we analyze the dynamic effects of exogenous changes in a, a, and p. Note that the Dk = 0 and Dc = 0 loci are independent of a or a. A change in a does not affect the optimal time paths of X and y. Thus, from (6.A12) an increase in a raises the optimal level of Ф during transition. If an exogenously given a is increased, the government deficit should be increased. A change in a will affect у so as to maintain the original optimal time path of gc. Thus, an increase in a will raise у, and hence the optimal level of Ф, during transition.
Figure 6.A2 illustrates the situation where p is increased. An increase in p moves the Dc = 0 curve to the left. At t = 0, consumption must jump from point A to B so as to move the economy toward a new long-run equilibrium point E1. X and у are increased so that the optimal level of Ф is increased during transition.
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