4 
A SIMPLE PROGRESSIVE TAX. 209 
For example, the First Schedule for Income Tax (Finance 
Act, 1917, p. 32) contains the following clauses :—— 
(a) Where the income on which tax is payable does not exceed 
£400 the rate shall be 6d. for every £1 thereof. * 
(6) Where such income exceeds £400 the rate shall be 6d. for 
every £1 thereof increased by one two-hundredth part of 1d. for 
every £1 in excess of £400, but so as not to exceed in any case 
the rate of 3s. in the £1. 
It will be seen that each £1 over £6400 pays 36 pence, 
whereas each of these pounds should pay 68 pence. 
§ 6. In dealing with incomes derived from property, it is 
usual to exact a higher rate than when dealing with 
incomes derived from personal exertion. It is unfortunate 
that the Commonwealth of Australia, in the Income Tax 
Acts of 1915—1917, adopted for incomes from property a 
system far more complicated than the simple progressive 
tax described in §4. 
The reader is referred to the Appendix for the full 
statement of the matter as given in the Income Tax Act, 
1917, but using the language of the Calculus, the Schedule 
may be summed up in the following terms:— 
Let the income be £x and the amount of the tax 7’ pence. 
Then 7’ is a continuous function of «x, such that 
(a) T= (3+ ¥ ) #, when « =< 546. 
181-058 
92.9 9 
Q) CE ee 8 ch ee SO. 
ie ie 10 = | 
Cy a 2 OL Mi 192) Wass Or BB to 
ere ca” 1 foe One oe 
when 2000 <a < 6500. 
(d) : = 6, wisn > a500 
x 
‘ This clause is a little misleading, as there is a rather complicated set 
of exemptions. 
N—July 3, 1918. 
