[Your Nightmare]

Not at all, Nightie. The example in #88 illustraates cascading very well, indeed. As a tax cost from one level is passed to the next, that next level's numbers have within them the tax from the previous level and that is operated on by the multiplicative effect of the calculations.

If one level's "numbers have within them the tax from the previous level," that's an additive process, not multiplicative. In your example, Level 2 has $0.12 tax cost on $0.47 profit. For this to be a cascading effect, the $0.12 would have to higher because of the previous level than it would be without. It wouldn't. In your example, a business making $0.47 profit would pay $0.12 profit whether it was on the first level or the fiftieth.

To have a cascading effect, the tax on one level must be taxing the tax from another. That is most definitely not happening in your example. Each level's profits are being taxed and as the profits accumulate, so do the taxes. (Duh.)

The following is an example of a cascading turnover (sales) tax:

Level	1	2	3	4	5	6	7	8
Inputs	$ 1.00	$ 1.66	$ 2.76	$ 4.59	$ 7.64	$ 12.70	$ 21.11	$ 35.10
Profit	$ 0.33	$ 0.55	$ 0.91	$ 1.52	$ 2.52	$ 4.19	$ 6.97	$ 11.58
Total	$ 1.33	$ 2.21	$ 3.68	$ 6.11	$ 10.16	$ 16.89	$ 28.08	$ 46.69
Nominal 25% Sales Tax	$ 0.33	$ 0.55	$ 0.92	$ 1.53	$ 2.54	$ 4.22	$ 7.02	$ 11.67
Cumulative Tax	$ 0.33	$ 0.89	$ 1.80	$ 3.33	$ 5.87	$ 10.09	$ 17.12	$ 28.79
Effective Tax Rate	25%	40%	49%	55%	58%	60%	61%	62%
Ratio: Effective/Nominal	1.0	1.6	2.0	2.2	2.3	2.4	2.4	2.5

Notice how the effective rate quickly exceeds the nominal rate? This is the cascading effect. "As a rule of thumb, it is estimated that the effective rate of a cascade tax to the retail stage is approximately two and a half times the nominal rate."¹ In your example, the effective rate could never be greater than the nominal rate because even if every level was 100% pure profit (which it almost is in your example), the effective rate would still only be the nominal rate, 25%.

The table above is illustrating a cascading tax. Your's is not. The income tax is not a cascading tax.

1. Tait, Alan A. Value Added Tax: International Practice and Problems. Washington, D.C.: International Monetary Fund, 1988.

[pigdog]

Sorry, Nightie, but it IS a cascading of taxation. The example you present is quite different and is your same old trick of trying to squash all the levels into one so that the result is warped.

It is you who are adding the tax at each stage ("cumulative tax") and that is unrealistic as is the cumulative tax so derived to calculate a meaningless "effective tax rate". This is the same thing you tried with your earlier examples and it is not meaningful (despite Tait's comment in his VAT elucidation).

The example I have given shows the mechanism more clearly and the 12 cents you comment on which goes to the next level is then cascaded by appearing in the input costs to that stage and some part of it being multiplied (a tax being taxed) by the parameters there. The fact that is does not pile up as rapidly as your example doesn't concern me nor does its upper limit since it is the mechanism that is being illustrated and your example does not do that at all well.

Interesting, though, is the fact that you are now arguing that not only that there are, indeed, embedded taxes (and remember we have left off payroll/withholding and compliance costs) but you now are claiming that they are much, much higher after all. The Squirrels may start nibbling on you, Nightie.