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the principle of equal sacrifice imparts the rule of proportional taxation. If it errs in underestimating the sacrifice incurred by a poor man we get the rule of progressive taxation. How much and in what manner does the principle err ? It is not unreasonable to suppose that to take any small sum of money from a man on the verge of starvation would cause more suffering than to take half the wealth of a millionaire. It has therefore been suggested that we should allow a minimum income (free from taxation) to every one and then levy a proportional tax upon the residue. Thus in the example given above, suppose that £30 was the minimum income which a man should enjoy free from taxation. Then if we tax A. £2 (that is 10 per cent. on the residue of his income after subtracting £30) we should have to tax B. £47 and C. £197 in order to be fair. To some extent this principle appears to be adopted in the English income tax, and it was adopted in the income tax for the United States 1 which was declared illegal by the Supreme Court. This tax was at the rate of 2 per cent. on all incomes after a deduction of $4,000.

Let us apply these hypotheses to our facts. The working classes with an income of 700 million £ are taxed 41.5 million £, or 5-7 per cent. The other classes with an income of 1000 million £ are taxed 85.2 million £, or 8.5 per cent. On the principle of equal sacrifice combined with Adam Smith's form of Bernoulli's hypothesis we conclude that the upper and middle classes of the United Kingdom bear too large a share of the public burdens. Next let us try the modified form of Bernoulli's hypothesis and assume that £10 per head of income should be free from taxation ; that is, that roughly £l a week per family is necessary to enable them to live without positive suffering. We then find that 41.5 million £ are paid out of a working class income of 426 million £ (the residue of 700 million £after subtracting 274 million £ obtained by multiplying £10 by 27:4 millions the number of the working class population), or rather less than 10 per cent., and that 85:2 million £ are paid out of an income of 883 million £ (1,000 minus 11.7 multiplied by 10), or again rather less than 10 per cent. So that if Bernoulli's hypothesis is true when we have subtracted £10 per head from each class we find that, adopting the principle of equal sacrifice, the system of public burdens in the United Kingdom is substantially fair. If more than £1 a week is really necessary to the average family it is rather unfair to the working classes, if less it is rather unfair to the upper and middle classes.

1 "An Act to reduce taxation, to provide revenue for the Government and for other purposes.” Act of August 24, 1894. Sections 27—36.

If, on the other hand, Bernoulli's hypothesis (even in the modified form) is untrue, and the true view is that the loss of a certain portion (say 10 per cent.) of his income is felt much less by a rich man than by a poor man, then the principle of equal sacrifice would give us the rule of progressive taxation. It has, for instance, been suggested that to subtract amounts of money varying as the squares of each income would cause equal sacrifices. In most countries incomes vary according to a law formulated by Professor Pareto, so that it would be possible to apply this test to the English system ; but as the initial hypothesis is very doubtful, and the calculations involve some

use of mathematics, it is not worth while to apply this test here. But it is by no means certain that the English system would be completely found wanting if tested by some such hypothesis.

It has also been suggested that Bernoulli's hypothesis is true for high incomes (which should therefore be taxed proportionally if we adopt the equal sacrifice principle), but that for low incomes the true hypothesis is one which would lead us to progressive taxation of such incomes. The result of this is that we conclude in favour of degressive taxation; that is a system in which the tax is at first graduated, but becomes proportional when the incomes exceed a certain limit. This is substantially the result arrived at by the system of deductions allowed in the English Income Tax ;and it is also suggested in the English Estate Duty wbich ceases to be graduated when the property passing on a death exceeds £1,000,000.

Tested by this principle the English system would probably be found to be unfair to persons with incomes as low as 255. a week. But almost any system of public burdens which involves the taxation of alcohol and tobacco is liable to this defect.

The principle of proportional sacrifice almost inevitably leads to the rule of progressive taxation. First let us assume Bernoulli's hypothesis to be true, and take the example given above. Then a tax of £l on A., causes the same sacrifice as a tax of £10 on B., or of £100 on C. If, therefore, the sacrifices are to be proportional to the income and C. is taxed £100, B. should be taxed only onetenth of £10 (because his income is one-tenth of A.’s) and C. only one-hundredth part of £1.2 The result is progressive taxation, and | The rates (pence in the £) will work out for the present year as follows :Incomes above.

£150 £400 .£500 £600 £700 Pay pence in the £... 4.8 5.6 6.4 7.2 8.0 ? This statement is not strictly accurate, but the correct working would involve mathematics, and the principle is sufficiently ill ated in this way. For illustra. tion of progressive taxation, see an article by Mr. Cohen Stuart : ECONOMIC JOURNAL, vol. viii., p. 325.


if Bernoulli's hypothesis is untrue the result is still progressive taxation only with a steeper scheme of graduation. The figures quoted above tell us that roughly an income of £127 10s. pays a tax of 5-7 per cent., whereas one of £427 10s. pays a tax of 8:5 per cent., and indicates, therefore, that the English system is scarcely sufficiently progressive if we adopt the principle of proportional sacrifice.

We may, therefore, say that the working classes of the United Kingdom do not bear an obviously excessive amount of the public burdens, but that tested by the modified Bernoullian hypothesis, the share that they bear is fair and reasonable. Further, the slight alterations that have been made in the English system during the past three years have on the whole been in favour of persons with small incomes. The real inequalities and difficulties arise when we consider the differences in the burdens laid upon classes which differ inter se either in the source from which their income comes or in the manner in which they spend their in

As to the source of the income the main distinction is whether the income is derived from real or personal property. At the present time a Royal Commission is considering the equity of the system of public burdens from this point of view.

As to the way in which the income is spent the chief difficulty arises from the very heavy taxation of alcohol and tobacco. The heavy taxation of alcohol is defended as being both financially productive and morally beneficent. These two grounds are to a great extent contradictory. If alcohol were so heavily taxed that (putting aside the probability of illicit distillation) very little were drunk, the tax would be unproductive. At present, however, we do not appear to have reached the maximum limit of productiveness. Yet the tax presses heavily on persons with small incomes, and is one of the causes of the difficulties that attend the Financial Relations of Great Britain and Ireland. The duty on tobacco is also extremely heavy and extremely productive. A slight reduction has recently taken place, but if it were not that the habit of smoking was almost universal, smokers would have a very legitimate grievance.

It may now be interesting to see in what direction the changes which have occurred in the last fifty years in the English system have been. Several authorities have made estimates of the incidence of English taxation at different times. And although their results are not strictly comparable with the figures quoted above or with one another, they do afford us some indication of the direction and amount of the change of incidence.

Of such estimates Professor Leoni Levi's are perhaps the best known; his figures for the Imperial Public Burdens (in millions of £) are as follows :

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For the year 1882 he takes the Local Public Burdens to be thirteen million £ for the working classes and twenty-six million £ for the higher and middle classes, so that for that year we have

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Mr. Dudley Baxter's figures for the year 1869 are :

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So that even with Mr. Sargent's and Mr. Baxter's excessive estimates for the amount of rates paid by the upper and middle classes we see that the proportion of public burdens borne by the working classes has been decreasing during the last thirty years ; and the tendency of recent fiscal legislation has been in the same direction ; on the one hand death duties have been increased, on the other the taxes on tea and tobacco diminished. The question for Chancellors of the Exchequer of the near future will be.—“Is it fair to continue to make alterations of the fiscal system in this sense ?” The answer, if the figures above given are fairly correct, would seem to be that, if we except the principle of equal sacrifice and a moderate hypothesis as to the weight of a given burden, the process of decreasing the burdens of the working classes should now cease. But if, on the other hand, we believe in proportional sacrifice it is reasonable to continue this process still further. At any rate the time has come for the financial authorities of the United Kingdom to consider whether or not they have abandoned, or intend to abandon, the propositions stated by Adam Smith in his first maxim.


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