# Annex

## The differences between a CFT and a tax on economic income

This Annex sets out in some detail the economics taxes on economic income and a CFT. First to be presented is a discussion on why a CFT is equivalent to a consumption tax. Then the discussion turns to the economic differences between a CFT and an income tax. It does so by examining the “neutrality” properties of each tax, being the circumstances in which each tax will not distort the decision making of taxpayers.

## Cash flows and the consumption base

One way to see why a consumption tax is equivalent to a CFT is to express an individual’s consumption as follows[24]:

(1)

where C is current consumption, W current wage income, R current net (of depreciation) capital income and S current net savings. S can be positive (purchasing assets or repaying debt) or negative (selling assets or acquiring debt). The right-hand side of the expression (2) can be disaggregated by asset type, 1,…,n:

(2)

In the case of a comprehensive income base, the capital income accruing from each type of asset Ri, i = 1,…..,N would have to be measured with all the problems we have seen that that would entail for at least some asset types.

For the consumption base, however, it is not necessary to measure Ri and Si separately, only to measure (Ri - Si) and this is simply the cash flow to or from the individual with respect to asset i. For example, suppose asset i earns income in the form of an unrealised capital gain. Then Ri = Si and the cash flow is zero. As another example, suppose an asset accrues \$100 of income and the individual dissaves \$25. Again, the two values do not have to be separately observed and measured to reach the figure of \$125 for Ri - Si. It is sufficient to observe that the individual withdraws \$125 in cash from his or her stake in asset i. Indeed the same observed cash flow event is consistent with an accrual of \$200 and net saving of \$75 or any other number of combinations.

There is one exception to the nice property that the consumption base can be observed and taxed by focusing solely on cash flows - the case of imputed rental income when income accrues and is then consumed in-kind without the interposition of a cash flow. A possible solution is to apply yield-exemption treatment to assets that earn imputed rental income, i.e. purchases of these assets would not be deductible but the imputed rentals would then not be assessable[25].

Equation (1) neatly depicts the differences between an income tax (base = W + R), a wage tax (base = W) and a consumption tax (base = W + R - S). The difference between the latter two taxes is primarily a matter of the their treatment of existing assets. The consumption tax, by including a CFT on assets (the R-S term) essentially imposes a capital levy on existing assets. On the other hand the normal returns on new assets escape tax since the discounted values of normal-return cash flows are zero over the life of an asset. A wage tax (or equivalently the yield exemption form of expenditure tax) does not impose such a one-off levy on existing assets.

#### Notes

• [24]This representation is based on Auerbach (1996).
• [25]Note that this tax treatment is strictly equivalent to cash-flow treatment only if we ignore existing assets and supernormal returns and we assume the tax rate stays constant.
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