# Transaction tax equations... Re: So .. how does a transaction tax stack up?

From: Jeff Bone (jbone@jump.net)
Date: Fri Mar 30 2001 - 09:36:31 PST

Punchline up front: not equitable.

The analysis of a transaction tax is only somewhat more complex than
for a consumption tax, and that added complexity is really just for
completeness. We have to factor earnings (expenditures of earnings,
really) and our definition of equitable a bit further, into
consumption (C,) investment (I,) and savings (S). The difference
between the latter two is that presumably the latter is exempt from
the transaction tax.

E = C + I +S
C/E + I/E + S/E = 1

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 = Iy/Ey ---> Wxy =
Pxy

THEOREM: A flat universal transaction tax is NOT 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) = 1.5 (A1, from Eq. 1, G1, G3, G5)
Wj = 2 - 1 - .5(.5+.5) = .5 (A2, from Eq. 1, G2, G4, G5)
Wrj = Wr / Wj = 1.5 / .5 = 3 (A3, from Eq 2, A1, A2)

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

3 != 5, Wrj != Prj (A3, A4)
D1 is FALSE

.: A flat universal transaction tax is NOT EQUITABLE-3.

DISCUSSION

A flat universal transaction tax is not equitable because it gives
preference to one kind of (non-productive, btw) economic activity
(savings) over others. A modification that would make this type of
tax equitable would be to levy a transaction tax on deposits.

jb

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