Activity (Process)

Derivation of the Change in Output from an Investment Shock

The change in equilibrium output (ΔY\Delta Y) resulting from a change in investment (ΔI\Delta I) is derived by calculating the difference between the new and original equilibrium output levels. Starting with the equilibrium equation Y=k(c0+I)Y = k(c_0 + I), the change is expressed as ΔY=k(c0+I+ΔI)k(c0+I)\Delta Y = k(c_0 + I + \Delta I) - k(c_0 + I). By simplifying this expression, the terms k(c0+I)k(c_0+I) cancel out, leaving the final relationship: ΔY=kΔI\Delta Y = k \Delta I.

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Updated 2026-05-02

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