A SIMPLE PROGRESSIVE TAX. vi | 
which the amount of the tax on the part derived from Personal 
Exertion under the scale given in Schedule IT. exceeds that under 
the scale given in Schedule I. 
The second schedule given above is obtained in the same 
way as the first schedule. 
The first pound pays (3 + =) pence. 
The second pound pays (3 + = ) pence. 
15 
400 
And so on, up to the 3800th pound. 
The third pound pays (3 + ) pence. 
A simple calculation will show that a total of £x would pay the 
sum named in the schedule. Also it will be noticed that the pro- 
gression stops at the 3800th pound, which pays (60 — ) pence, 
and that every pound over £3800 is to pay 60 pence. Further, 
an income of £3800 pays the sum of £498 15s. 
A comparison between the proposed schedule and the 
corresponding schedule of the present Act can most easily 
be effected by calculating under each the value of the 
average rate in pence per £& on an income of £x. By the 
term average rate is meant the amount of the tax in pence 
divided by the income in pounds—that is, T/x, in the 
notation of this paper. 
In the following table these rates are given at intervals 
sufficiently close for our purpose, up to £40,000. It will 
be seen that up to about £1,000 the rate in the new scheme 
is Slightly higher than the old; from £1,000 to about £3,300 
slightly lower; and from about £3,300 onward slightly 
higher. 
