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A1.2 The 1917 ‘war-time’ tax structure

The tax structure described above also applied in 1917, with an exemption of £300 available to all taxpayers with incomes below £600. Thereafter the exemption was withdrawn at a rate of £1 each additional £1 earned; ie, the exemption is zero for incomes above 900. (For other years there were different withdrawal regimes, sometimes involving more than one withdrawal or abatement rate).

The marginal tax rate, from (1), now needs to reflect that d(y - a) ≠ dy, hence:

τ = dT/dy = τ*(d(y - a)/dy) + (y - a)(dτ*/dy)         (A7)

Allowing for the abatement range of incomes (600 to 900), this gives:

τ = τ* + (y - a)(dτ*/dy)         y ≤ 600              where d(y - a)/dy = 1

τ = 2τ* + (y - a)(dt*/dy)       600 < y ≤ 900    where d(y – a)/dy = 2                 (A8)

τ = τ* + y(dτ*/dy)                 y > 900                where a = 0; d(y - a)/dy = 1

For 300 ≤ y ≤ 400, the tax schedule specified a tax rate of 6 pence per pound (0.025) plus a ‘war tax' rate of 9 pence (0.0375). The combined marginal tax rate is given by:

τ = τ* = 0.0625 (6+9 pence per pound)

For 400 ≤ y ≤ 600, the 6 pence per pound tax rate is increased by 1/200th of a penny per pound and the special war tax rate is increased at 3/400ths of a penny per pound. This gives:

τ* = 0.041667 + 0.000052083y         (A9)

yielding: τ* = 0.0625 at y = 400, and τ* = 0.0729 at y = 600. Using (A2) and (A9) it can be shown that t = 0.02604 + 0.00010417Y, and hence t = 0.0677 at y = 400, and τ = 0.0885 at y = 600.

For 600 ≤ y ≤ 900, the abatement of the £300 exemption begins; therefore using (A8) and the previous definition of τ* yields:

τ = 0.03646 + 0.00020833Y         (A10)

In this case: τ* = 0.0729 and τ = 0.1615 at y = 600, while τ* = 0.0885 and τ = 0.2237 at y = 900.

For 900 ≤ y ≤ 6,400, t* is given by the last line of (A8) such that, with no exemptions,

τ = 0.1354 at y = 900 and τ = 0.7083 at y = 6,400. Thereafter, for incomes in excess of 6400 there is no longer any increase in τ* as incomes increase, That is, dτ*/dy = 0 and this element of the MTR calculation in drops out. The marginal tax rate is now simply τ = τ* = 0.375, implying a large drop in the MTR at y = 6,400 (from 70.8% to 37.5%) which remains constant at higher income levels; see Figures A1a and A1b.

Figure A2- Marginal and average tax rates in the 1917 tax structure

A2(a) Individual incomes up to £1200
A2(a) Individual incomes up to £1200   .
A2(b) Individual incomes up to £7000
A2(b) Individual incomes up to £7000 .
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