Evaluation of the Public Sector

Substitutability

So far, we have not investigated the benefit of government spending in the utility function. In Keynesian economics, even wasteful public spending can be useful in stimulating aggregate demand. If we include the benefit of government spending in the model, how is the neoclassical framework altered?

For simplicity, let us denote by 0 the degree of substitutability between private consumption C and public spending G. Thus,

Here, effective consumption C* appears in the utility function. Hence,

So far, we have assumed that 0 = 0. In terms of 0 > 0, we may add two channels to the analytical results.

One is the direct effect on private consumption. If the government raises public spending to almost the same level as private consumption, the latter directly declines. For example, if public education is very similar to private education, households reduce spending on private education when public spending on education increases. If a unity unit of government spending is the same as a 0 unit of private spending, private consumption declines by the 0 amount. This direct crowding out occurs if government spending actually increases. Further, the crowding out directly reduces private consumption at a given level of C*. This is the direct substitution effect.

Another effect is on permanent income. If government spending is useful, it raises households’ effective income, Yp — Gp + 0Gp. The degree of 0 refers to how useful government spending is for households. A unity increase in government spending raises permanent income by 0 amount, raising private consumption by 0 amount. This effect occurs if permanent government spending increases.

Considering Eq. (3.22), private budget constraint is rewritten as

Then, from the optimizing behavior we have

which is the consumption function in this section. Effective consumption is equal to permanent effective disposable income.

An increase in Gp raises permanent effective disposable income by the amount of 0Gp, which is the third term in the right-hand side of the equation. This stimulates private consumption by the amount of 0Gp. This is the permanent income effect.

 
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