Jeff's Retraction, with Equations! was Re: Taxes: Taxonomy and Evaluation

From: Jeff Bone (
Date: Thu Mar 29 2001 - 13:34:01 PST

Okay, I was wrong, and I'm about to prove it. ;-) Dave and I agree on the
following point:

  - We do not want the tax system to affect the wealth distribution.

This is actually a pretty good analytical tool. When I've been fumbling around
talking about "FAIR," I've been missing an opportunity for factoring; I've
been confusing the notion of fairness in provisioning of services and fairness
in the collection process and the effect it has on wealth accumulation. So
let's forget my half-ass notion of FAIR for now. Let's call a tax system with
the above characteristic "EQUITABLE," and stipulate that it's a required
characteristic of any acceptable tax system.

 Actually, the above statement needs a little more rigor. Here we go.

EARNING (E) is the pre-tax accumulation of economic benefit or value through
the exercise of capitalism --- it's income, interest, ROI, whatever, all of
these things lumped into one figure.

We will define the relative economic PRODUCTIVITY (Pxy) of one party relative
to another as

  For all x, y such that Ex > Ey: Pxy = Ex / Ey

WEALTH ACCUMULATION is the amount of economic value one has left after some
period during which one both pays taxes and consumes, i.e. "burns" some amount
of economic value in a nonrecoverable manner, for example in maintaining some
standard of living. Each tax system has a unique WEALTH ACCUMULATION FUNCTION,

An EQUITABLE tax system is one where, given two parties x, y such that Ex > Ey,
all other things being equal, the relative wealth accumulation of the two
parties is equivalent to the relative productivity of the two parties. The
following relation must hold:

   Wx / Wy = Pxy

We need two additional quantities in order to define the wealth accumulation
function for our discussion. CONSUMPTION (C) is defined as the amount of
nonrecoverable burn a person expends to maintain some standard of living. The
TAX RATE (T) is defined to be the percentage of some basis that is spent on
taxes, and for a consumption tax this is a percentage of C. Given these
quanties, W for a consumption-based tax is:

   W = E - C - (T * C)

THEOREM: A straight consumption tax is not EQUITABLE. PROOF:


   Er = 10 (Ritchie earns $10)
   Ej = 2 (Joe earns $2)
   Cr = Cj = 1 (Cr and Cj must be equal for our comparison)
   T = .5 (50%, or whatever...)


   Wr = 10 - 1 - .5 = 8.5
   Wj = 2 - 1 - .5 = .5
   Wr / Wj = 8.5 / .5 = 17

   Prj = 10 / 2 = 5

   17 != 5
   Wr / Wj != Prj

.: A straight consumption tax is not EQUITABLE.


I've been convinced by Dave's arguments and this analysis that a straight consumption tax is "regressive" in that it encourages the additional accumulation of wealth by higher earners outside of the conduct of ordinary capitalist activities. The relative wealth accumulation is very out of scale with respect to the relative economic productivity. That can't be a good thing.

Note that this isn't a very good model of FairTax, though. FairTax has some "progressive" features in the form of vouchers and rebates, etc. to lower earners. I not sure whether those compensate or not, I'm going to have to model it in a bit more detail to know.

But anyway, I yield on my position that pure consumption-based taxes are a desirable thing. The construction of the system itself leads to an accumulation of wealth by the higher earner which is greater than the relative economic productivity of the higher earner.


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