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From the closed economy equilibrium condition $I = S + (T - G)$, how does exactly a surplus (which I assume would be used for paying debt) increases investment in the same amount? I ask that because if the govt pays $(T - G)$ - assuming a surplus - to the public with a marginal propensity to consume equal to c, savings (and thus investment) would increase in $(1-c)*(T-G)$ and not $(T - G)$ (which is, of course, bigger). Am I losing something here?

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    $\begingroup$ I think this really needs to be cut down to a single question, and the title needs to be the question, so that people can see exactly what the question is from the title There’s too many embedded questions in the text, and so there’s no easy way to answer them. $\endgroup$ – Brian Romanchuk May 7 at 22:54
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    $\begingroup$ Thanks, Brian. I solved the first question by reading a few answers and a text-book but the second one still hangs. $\endgroup$ – Antônio Gabriel Zeni Landim May 8 at 22:56
  • $\begingroup$ I don’t understand the question fully, but in general, a federal government surplus takes money out of the pockets of citizens at high speed. How this could increase investment at all seems very unlikely to me. $\endgroup$ – aliteralmind May 11 at 11:59
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The increase in savings you described does happen, in the short-run. Remember, tho, investment and savings are flows. Accounting identities provide us truths about their ex-post behavior, not planned or desired savings.

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    $\begingroup$ I would add one point: a build up inventories counts as investment. So if we assume that the government raises taxes (for example), the drop in demand could lead to an inventory build up in the short term, hence higher investment. $\endgroup$ – Brian Romanchuk May 10 at 11:25

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