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Punchline up front: I was sloppy. It's equitable. The math was

sound, but I plugged the wrong numbers. Kudos to Russell for keeping

me honest.

TRANSACTION TAX SYSTEM

W = E - C - T(I+C) (Eq. 1)

EQUITABLE-3

Definition 2: (D2) An EQUITABLE-3 tax system is one where,

given two parties x, y such that Ex > Ey, independent of the

absolute allocations of earnings between consumption,

savings, or investment but assuming that the individual

ratios of these components over earnings are equal:

for x, y such that Ex > Ey:

Cx/Ex = Cy/Ey & Ix/Ex = Iy/Ey & Sx/Ex = Sy/Sy ---> Wxy =

Pxy

THEOREM: A flat universal transaction tax is EQUITABLE-3

Given:

W = E - C - T(I+C) (Eq. 1)

Wxy = Wx / Wy (Eq. 2)

Pxy = Ex / Ey (Eq. 3)

Er = 10 (Ritchie earns $10) (G1)

Ej = 2 (Joe earns $2) (G2)

Cr = 5, Ir = 2.5, Sr = 2.5 (G3)

Cj = 1, Ij = .5, Sj = .5 (G4)

Cr / Er = Cj / Ej etc. (satisfying D2)

T = .5 (50%, or whatever...) (G5)

Analysis:

Wr = 10 - 5 - .5(2.5 + 5) = 1.25 (A1, from Eq. 1, G1, G3, G5)

Wj = 2 - 1 - .5(.5+1) = .25 (A2, from Eq. 1, G2, G4, G5)

Wrj = Wr / Wj = 1.25 / .25 = 5 (A3, from Eq 2, A1, A2)

Prj = 10 / 2 = 5 (A4, from Eq. 3, G1, G2)

5 = 5, Wrj = Prj (A3, A4)

D1 is TRUE

.: A flat universal transaction tax is EQUITABLE-3.

DISCUSSION

Grr...

jb

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