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The trick is to apply the total derivative. Going from $Y = C(Y-T(Y)) + I(r) + G + NX(Y)$, we have: $$ \operatorname{dY} = \underbrace{\frac{\partial C(\cdot)}{\partial Y}}_{\equiv C_Y > 0} \cdot \operatorname{dY} + \underbrace{\frac{\partial I(\cdot)}{\partial r}}_{\equiv I_r < 0} \cdot \operatorname{dr} \therefore \operatorname{dY} - C_Y \cdot \...


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