The Taxation Equation

Posted on 28/09/2011 by


Read part 5 here.

This post is a technical analysis of the taxation policy which I presented previously. The analysis will be in a Keynesian/Galbraithian manner, involving formulae and discussion of the various components thereof. I will try to make this as painless as possible.

In a nutshell, my taxation policy is designed to limit the growth of businesses and profits beyond a community scale. The most advantageous business model, if my policy were implemented, would be a sole-proprietorship. Businesses involving employees in their businesses would be taxed according to 1) the number of employees and 2) the profitability of the venture.

The reason to make this division is relatively simple: a sole-proprietor is entitled to the entirety of their income, because its source is unambiguous. All profits arise solely through their own efforts.

Once employees are involved in the production of profits for the owner, the nature of those profits are no longer clear-cut. Their production involved the expropriation, in Marxist terms, of a percentage of the value of the employee’s labour. This is simply business; however, the profits are no longer solely the result of the owner’s efforts. The profits, although perhaps not the employee’s, are also not the owner’s. The economic arrangement owes the larger social sphere a ‘rent’ due to the latter facilitating and protecting the former.

Obviously small-scale industry and employment is not to be discouraged. Less obviously, but no less important, is that large-scale industry and employment is to be discouraged. Businesses which grow beyond a certain size are, quite simply, difficult to hold responsible to the actions of the owners and the institution itself. By putting downward pressures on the size of business ventures, employment rates are elevated and businesses can be held responsible for their activities.

In order to facilitate that general concept, the graphical shape for the taxation rate is sharply progressive, evocative of a standard x^2 algebraic function. The taxation rate increases slowly on the low end of profits and employees, and then steepens quickly as profitability and employment numbers increase. Where that steepening begins is a matter of public policy; however, I will endeavour to provide some crude examples for illustrative purposes.

Now for the nasty algebra part. The tax rate of a given business (T) is the function of number of employees (n) multiplied by profits (P) divided by wages (w). Hence:

T = f(nP/w)

This is a very basic description of the actual equation desired. The final equation involves five parts, three of which we have already seen: number of employees (n), profits (P), and wages (w). These three numbers are variable, from business to business. However, they are relatively objective, and business specific. In other words, they’re entrepreneur-focused, not society-focused.

The remaining two unknowns — let us call them (x) and (k) — are the society-focused facets of the equation. They are the limits upon the size of profits and employment in any given business, regardless of the nature of the venture. These two numbers will be constants across the entire economy; every business will have the same taxation standards applied to them.

This, as an aside, avoids any decisions upon the relative merits of one business over the other. Each employing business is considered equivalent to any other, and avoids the serious moral hazard which arises from taxation policy picking ‘winners’ and ‘losers’.

Continuing, (x) is the policy adjustment for how large a business may grow, employment-wise, before incurring taxation penalties. Lower x numbers encourage larger numbers of employees.

(k) is the policy valuation placed upon how much profit a business may derive from its employees, before incurring taxation penalties. Lower k numbers encourage higher profitability.

Both (x) and (k), therefore, are constants in terms of the equation. Their exact values are matters of public policy. Generally, (x) and (k) should be kept at such values which work to suppress profit-seeking and keep business sizes at a community level. Careful and sensitive economic policy-making can arrive at values for (x) and (k) which are therefore revenue-neutral and best support the flourishing of a sole-proprietor and small-workshop economy.

(x) involves employment, so it is the exponent upon the number of employees which a given business has. That represents the interaction of the economic policy with the business itself. (k) is the multiplier upon profits, as it involves the policy decision regarding what portion of profits are due as ‘rent’ to the wider public sphere.

Expanding the function, we finally arrive at the only equation which one would need to see on one’s tax return:

T = n^x * kP/w

At this point, I will provide some crude values for (x) and (k), to give a general idea of how this equation operates. Let us suppose a business with 10 employees, with wages around $25,000 for each employee. Profits let us suppose are $50,000 (ie what the owner receives after all business expenses are paid). Therefore:

T = 10^x * 50,000k/(10 * 25,000)

Let x = 2 and k = 0.01

T = 10^2 * 50,000(0.01)/(10 * 25,000)
T = 0.2 or 20%

With these (x) and (k) values, this particular business’ tax payment is 20% of the profits, or $10,000.

Taking the same business, let x = 2 and k = 0.005

T = 10^2 * 50,000(0.005)/(10*25,000)
T = 0.1 or 10%

A lower (k) value obviously encourages greater profitability. Let us increase profits to demonstrate. P = 100,000

T = 10^2 * 100,000(0.005)/(10*25,000)
T = 0.2 or 20%

The business in question is able to safely double its profits without any other structural changes, and incur the same tax penalty as when k = 0.01

Let us increase the business’ employment to, say, 15.

T = 15^2 * 100,000(0.005)/(10*25,000)
T = 0.45 or 45%

Obviously increasing employment is not encouraged under this model. Profits can be safely increased, however, under smaller (k) values.

Returning to the original business — n = 10, P = 50,000, w = 10*25,000 — let x = 1.5 and k = 0.01

T = 10^1.5 * 50,000(0.01)/(10*25,000)
T = 0.06 or 6%

Now, doubling profits to $100,000:

T = 10^1.5 * 100,000(0.01)/(10*25,000)
T = 0.12 or 12%

With this profitability, let us assume more employees are hired; there are now 15.

T = 15^1.5 * 100,000(0.01)/(10*25,000)
T = 0.11 or 11%

This taxation reduction obviously encourages higher employment for a given profit and wage level.

Now let us look at a larger, more profitable business. Employment is 100 people, wages are $25,000 each, and profits are $1,000,000. For the purposes of clarity I will keep (x) equal to 2 and (k) equal to 0.01

T = 100^2 * 1,000,000(0.01)/(100 * 25,000)
T = 40, or 4,000%

Obviously a taxation cap is needed at some point. Although this is outside the bounds of the equation, I modestly propose a 90% cap. In the above case, this would mean the business would pay $900,000 in taxes.

Keeping the employment, let us say the owners had a change of heart and vastly reduced their profit expectation. Employment is still 100, wages are $25,000 each, but profits are now $100,000.

T = 100^2 * 100,000(0.01)/(100*25,000)
T = 4, or 400%

The arbitrary 90% tax cap I made again comes into play. The point is, however, the business is simply too large. Even if profits were reduced to $25,000 — the wage of the employees — the theoretical tax rate would still be 100% (or, more accurately, the 90% cap). This business as it stands is simply too large. The taxation benefits which would come from breaking up this venture are too attractive for any sensible owner to resist.

Such breaking up would have the much-desired outcome of increasing employment whilst lessening the tax burden of the owner in question. Eventually the taxation policy would push the average size of taxable businesses to a very manageable size, and simultaneously increasing the number of businesses.

In closing, I would like to once again state that the precise form of the taxation equation (ie the values of the [x] and [k] constants) are matters of public policy. The establishing of these values warrant both careful study and vigourous conversation. However, this taxation policy would help foster and strengthen a social structure which would more closely realise a stable, resilient, and human-scaled full-employment economy.

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Posted in: Distributism, Reform