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In the short term, budgetary cuts that are used to reduce the deficit will result in higher unemployment and lower consumption spending because less money will be in the system. In the long run, the reduced inflation rate, lower interest rates, and lower taxes needed to support the size of government or pay for the government’s debt will more than compensate for the reduced government spending.

Conceptually, it isn't that much different from looking at an individual who spends far more than they earn; if they maintain their current path the amount they spend on covering the interest payments on past consumption will be large enough that they will have to continue to spend far more than they earn to maintain a standard of living far lower than if they didn't have any debt in the first place.