An increase in G reduces the budget balance and BB drops to , increasing the deficit from D1 to D2. The higher autonomous G increases AE to and real GDP increases to YP, eliminating the output gap. That increase in Y increases tax revenue and offsets some of the initial increase in the deficit such that the final budget deficit is D3.
A cut in government expenditure to reduce the budget deficit D0 at Y0 shifts the BB line up to BB1. The deficit is reduced but the austerity policy lowers autonomous aggregate expenditure and equilibrium national income from Y0 to Y1. The net reduction in the deficit is less than the cut in G.
The structural budget balance
Structural budget balance SBB0=t0YP–G0. Actual budget balance BB1=tY1–G0.