# A2 Theoretical Considerations

## A2.1 Evaluation of Government Spending

The basic model is the standard infinite-horizon model where individuals act as though they are infinitely lived. The agent has time-separable preferences over private consumption, C, and the size of government spending, G; namely the goods and services flowing from the government sector, GE, plus government transfer payments to individuals, TR. Thus, G = GE + TR.

Specifically, the individual’s utility function is given by

where 5 is a constant rate of time preference and U() is a time-invariant, concave momentary utility function. C* = C + 0G denotes the level of “effective” consumption. A unit of government expenditure yields the same utility as 0 units of private consumption.

The index of the private sector’s evaluation of government,0, reflects the private sector’s evaluation of how the size of government spending is beneficial to the private sector. In a strict sense, the evaluation of government purchases is different from that of transfer payments. For example, if government consumption is perfectly substitutable with private consumption, the evaluation of government consumption is unity (0 = 1). In contrast, if individuals are perfectly identical, the private sector would be concerned only with net transfer payments (transfer payments TR minus taxes T), not with total transfer payments TR. In such an instance, the evaluation of transfer payments is zero (0 = 0). In a real economy, individuals are not identical, and the private sector does not distinguish between negative transfer payments and taxes. Here, the evaluation of transfer payments reflects some sort of beneficial externality.

It would be more desirable to allow for the possibility that the evaluation of government purchases is different from that of transfer payments. However, with respect to the fiscal reconstruction movement in recent years, it seems that the size of government spending is the primary concern. Thus, for a first approximation, it is assumed that individuals are concerned with the size of government spending including total transfer payments.

In the perfect capital market, the representative individual may accumulate or deccumulate assets at the assumed constant real rate of interest r. Her or his budget constraint in period t is given by

where W is beginning-of-period holdings of one-period assets (which include government debt), Y is labor earnings, T is tax payments, and TR is transfer payments. Under the solvency condition, forward substitution in (3.A2) yields

Here, the left-hand side of Eq. (3.A3), the present discounted value of private consumption, is equal to the right-hand side of Eq. (3.A3), the initial asset holdings plus the present discounted value of after-tax labor earnings (net of transfers).

The government budget constraint in period t is

where B is beginning-of-period outstanding government debt of one-period maturity and GE is government purchases. Under the solvency condition, government budget constraint (3.A4) may be utilized to produce, in terms of present values,

Here, the left-hand side of Eq. (3.A5), the present discounted value of tax revenue is equal to the right-hand-side of Eq. (3.A5), the initial government debt plus the present discounted value of government spending. The representative individual is assumed to be forward-looking with regard to the fiscal variables of the government. He or she recognizes the future tax obligations implicit in current debt issuance, which allows an equivalence between tax and debt finance of a given government expenditure stream.