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If we look at the equation for national Savings = S(priv) + S(pub) = [Y-C+Tran-T] + [T-G-Tran] = Y - C - G . We see that Tax falls out of the equation. Therefore, does that mean changes in taxation policy don't directly affect the Supply of Loanable funds? If this is the case, and we assume consumption isn't constant, then giving individuals massive tax cuts should influence them to consume and/or save more money. This should increase total savings and shift the supply right and interest rates down, allowing for greater investment in capital, leading to growth in economy. Looking at this, why is it that tax cuts are seen as being bad for economic growth?

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Tax falls out of the equation.

Based on your model, tax can still be in the equation, but it is hidden inside of your $C$ and $G$.

First, as you mentioned, if consumption is not constant, then adjusting the tax rate will change $C$ (lower $T$ higher $C$).

But the tax rate is also imbued in your $G$- the government must have some budget. In a balanced budget, $G=T$, which can be a model constraint.

We may not impose $G=T$, but suppose revenue must be a tenth of government spending; $$G = \frac{T}{10}$$

Thus, lower taxes must lower government spending (thus lowering $Y$), or imply higher taxes in the future (See Ricardian equivalence)

giving individuals massive tax cuts should influence them to consume and/or save more money

This is true, but we must consider the effects on $G$ and a looming future $\tau$ due to massive tax cuts now.

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