Tax Policy Noodlings

George Rebane

The newly proposed GOP tax cut has everyone talking.  A couple of its main features are supposed to include switching from sequential taxing to concurrent taxing of earnings.  Also discussed is the removal of certain deductions like mortgage interest paid from taxable earnings.  I was interested in the impact of these two policy changes so I pushed a few squigglies, and I’ll share with you here some of the results without taking you through the weeds – BTW, nothing higher than your high school algebra is required to derive these formulas.

In sequential taxing, the taxing jurisdictions calculate the taxes due in sequence, the later jurisdictions applying their tax rate to the remaining earnings after you’ve paid the earlier jurisdictions.  As an example, say, jurisdiction J1 (e.g. California) taxes at rate r₁, and J2 (e.g. the feds) then tax the remainder at rate r₂.  The overall tax rate r_S  you pay on earnings E is given in formula (1) in the panel below.

In concurrent taxing, the jurisdictions all compute their tax take on your taxable earnings E.  The overall tax rate r_C you pay is then given in formula (2) above.  This rate is always higher than the overall rate for sequential taxing, and the switch from sequential to concurrent is an effective tax increase R_SC given by formula (3).

Say, that r₁ = 0.1 (10%) and r₂ = 0.2.  Then from formula (1) r_S  = 1 – (1 – 0.1)(1 – 0.2) = 0.28 = 28%.  And similarly, from formula (2) r_C  = 0.1 + 0.2 = 0.3 = 30%.  From (3) we calculate the increase in effective tax rate as 0.1*0.2/(0.1 + 0.2 - 0.1*0.2) = 0.0714 = 7.14%.

For calculating the effective tax rate for deductions, assume that to compute your taxable earnings you can deduct a fraction f of your earnings E before applying the relevant tax rate r.  Then your effective tax rate r_f  is given by formula (4).  Now suppose that a deduction, say Δf, is no longer allowed.  This reduces the fractional amount of E you can deduct to (f – Δf).  Your effective tax rate is now given by formula (5).  Finally, the percentage of your tax increase R_fΔf through the denial of such a deduction is given by formula (6).

As an example, let f = 0.35 = 35% and Δf = 0.25, then R_fΔf  = 0.25/(1 – 0.35) = 0.385 = 38.5%.

You may want to enter the formulas into a spread sheet and play with the numbers to understand the real damage that such tax policy changes will deliver.

Comments

[Walt]

Really? You had to write it up that way? All scientific and stuff?
This knuckle dragger says,, "It's all Greek to me,"

So... is it good,,or bad??
Does it say that the days of the few, paying the most are going away? Now most will pay some?
The Left demands "fairness",, so , give it to them. They pay their fair share.

[Russ]

Where do we apply the saving of not having to employ at CPA to prepare our taxes, when we use the postcard tax return?

[Barry Pruett]

Did I read also that they are contemplating eliminating the deductions for local property tax deduction and the state and local income tax paid?

If so, living in California, Illinois, or New York all of the sudden does not seem so fiscally appetizing...