Talk:Marginal tax rate

Major Edits April 2019
I made some major changes to this article yesterday and today, including adding more examples of marginal rates from phase-outs, adding more detail on long term capital gains and qualified dividends, adding a section on payroll taxes, adding a small section on marginal utility, and adding a clearer explanation of after-tax rates of return. I also tried to make it read and flow better, and made some organization changes along those lines.

I think some more changes could be justified:
 * Deletion of the "special cases" section on 0 marginal rates and flat tax. I don't think these add enough to the article to justify their inclusion.
 * Examples should be updated to at least 2018 due to the major changes in tax law.
 * Deletion of the Appendix; while I love theory, I'm not sure this adds enough to most readers to justify inclusion.

But rather than make these changes I think I should see how the community responds to the ones I've made already. This is my first edit to the BH Wiki :-).

Along these lines, I didn't add references and links in most cases, because this is somewhat tedious and I want to make sure the community doesn't want to reverse my edits first. Feel free to add these on your own, but I'll check back over the next few weeks and add some, if my edits are still here.


 * Above was added by Fyre4ce, 26 April 2019‎, 15:54. Welcome to the BH wiki! Suggestion - We follow Wikipedia practices. It is customary to add your signature in talk pages (3rd toolbar icon from the left).
 * Please discuss these edits in the wiki editor's forum thread titled "Wiki page needed: Traditional vs Roth", as the earlier edits represented a consensus of opinion. Also, references and links should be provided - regardless of the effort involved. --LadyGeek 00:55, 27 April 2019 (UTC)
 * Major edits should be first discussed in the wiki editor's forum. Per Wikipedia policy, I have created a draft user page for your proposed updates. See: User:Fyre4ce/Marginal tax rate (No content has been modified) Please discuss in the wiki editor's forum thread titled "Wiki page needed: Traditional vs Roth". --LadyGeek 01:36, 27 April 2019 (UTC)

Earlier Comments
A summary from various sources, references listed. I'd like a 2nd opinion to check for errors or omissions (or "OK"). LadyGeek 19:18, 6 February 2009 (UTC)


 * Looks fine to me. I like the google:define touch also. It might be a good idea to add one these to all glossary entries. Blbarnitz 21:47, 6 February 2009 (UTC)


 * What are you referring to when you say, "a flat tax has a marginal rate of zero"? A flat rate tax has a constant marginal rate, not zero; a tax with a marginal rate of zero is a fixed-amount tax, such as a tax of $100 on every house rather than a percentage of the value of the house.Grabiner 04:37, 7 February 2009 (UTC)


 * David, I went ahead and substituted your wording. I think we've nailed it. Blbarnitz 09:02, 7 February 2009 (UTC)


 * David, Barry - That's why I asked for a review. My bad. I took the last sentence of the Wikipedia section for Marginal and removed the word "poll" from "poll tax". Original wording was "A flat rate poll tax has a marginal rate of zero,...". I didn't realize this was an error. The house tax example above clearly explains what I did wrong and is now on the main page. LadyGeek 19:34, 7 February 2009 (UTC)

Marginal Tax Rate Calculations
Could you please show how you got the marginal tax rates of of 27.75% and 46.25% (with explanation)? I couldn't reproduce these results, so I'm missing something. Also, it might help to say "each additional $1" instead of "each $1" to be clear that this is marginal.
 * If you are in the range in which Social Security becomes taxable, each $1 of income causes an extra 50 or 85 cents of Social Security to be taxable at the same tax rate, until 85% of the whole benefit is taxable. If you are in the 15% bracket and each $1 causes 85 cents to be taxable, your marginal tax rate is 27.75% ; if you are in the 25% bracket at each $1 causes 85 cents to be taxable, your marginal tax rate is 46.25%

LadyGeek 16:43, 11 October 2009 (UTC)
 * If you earn an extra $100 and each $1 causes 85 cents to be taxable, your taxable income increases by $185, and in a 15% tax bracket, you pay $27.75 tax on that $185. Thus the marginal tax rate is 27.75%.  A clarification will be added.Grabiner 00:33, 12 October 2009 (UTC)
 * The example is now computed in detail at Taxation of Social Security benefits.Grabiner 01:13, 13 October 2009 (UTC)
 * Now I understand, thanks. LadyGeek 22:13, 13 October 2009 (UTC)

Why is the statement below important for a marginal tax rate? Is it because corporate and municipal bonds are not taxable and therefore the after-tax rate is the same as before-tax rates?
 * "If your marginal federal tax rate is 25%, then a corporate bond fund with a 4% yield and a municipal bond fund with a 3% yield have the same after-tax value to you."

LadyGeek 22:13, 13 October 2009 (UTC)

Reader feedback: Please give a real example, ...
24.254.55.6 posted this comment on 1 March 2014 (view all feedback).

"Please give a real example, such as: The social security statement says when I retire next year (early retirement) I will start collecting social security of $1,923. My other income (State retirement income) will $2,200 per month. What will my social security tax be? Thanks"

Any thoughts?

Blbarnitz 03:13, 2 March 2014 (CST)

The reader may be wishing to have an example which matches his/her situation. Using Social Security presents a more difficult problem and is better addressed in Taxation of Social Security benefits.

The examples currently shown intentionally do not go into any detail because tax law complexities arise. At a detailed level, we may provide advice based on incomplete information and risk giving an incorrect (or misinterpreted) answer. For the purposes of a simple illustration, I believe the existing examples are sufficient. --LadyGeek 14:50, 2 March 2014 (CST)

Reader feedback: This page needs better elabo...
204.99.118.14 posted this comment on 10 October 2017 (view all feedback).

"This page needs better elaboration in the Traditional vs. Roth section. The examples are not clear."

Any thoughts?

Peculiar Investor 10:27, 13 October 2017 (EDT)

It's too bad the commenter didn't give more specifics about what isn't clear.

Perhaps some of the differential calculus is also more confusing than helpful. For most personal finance purposes, stopping at the "delta" equation is better than moving to the partial or full derivative forms. That's what the second sentence of this wiki uses.

--FiveK 00:20, 19 October 2017 (EDT)


 * There may also be an assumption that the reader is familiar with the concepts behind the IRAs. I agree to leave the page content as-is. --LadyGeek 06:43, 19 October 2017 (EDT)

Variable Marginal Rates with Section 199A Deduction
Define variables:

$$ \begin{align} T(N, Q) & = \text{tax liability as a function of income} \\ N & = \text{non-Qualified Business Income} \\ Q & = \text{Qualified Business Income} \\ TB & = \text{tax bracket (eg. 24 percent)} \\ D & = \text{below-the-line deduction (eg. standard deduction)} \\ UL & = \text{upper limit of deduction phase-out (eg. 426,600 for MFJ 2020)} \\ R & = \text{phase-out range (eg. 100,000 for MFJ 2020)} \\ \end{align} $$

This analysis will assume a single tax bracket, although because the equation will be differentiated, the results will apply to any tax bracket.

The total tax liability can be written as follows. If total taxable income is below the beginning of the deduction phase-out ($163,300 for single or $326,600 for MFJ, for 2020), total tax is:

$$T(N, Q) = (N+Q-D) \cdot TB - 20% \cdot Q \cdot TB$$

In the phase-out range ($163,200-$213,300 for single or $326,600-$426,600 for MFJ), total tax is:

$$T(N, Q) = (N+Q-D) \cdot TB - 20% \cdot Q \cdot \left ( \frac{UL - (Q + N - D)}{R} \right ) \cdot TB$$

Above the phase-out range ($213,300 for single or $426,600 for MFJ), total tax is:

$$T(N, Q) = (N+Q-D) \cdot TB $$

Above the phase-out, the Section 199A deduction has no effect. Below the phase-out, the marginal tax rates with respect to QBI and non-QBI are found by taking the partial derivative of T with respect to N and Q:

$$\frac{\partial T(N, Q)}{\partial N} = TB$$

$$\frac{\partial T(N, Q)}{\partial Q} = (1 - 20%) \cdot TB = 80% \cdot TB$$

In the phase-out range, the marginal tax rates with respect to QBI and non-QBI are found by taking the partial derivative of T with respect to N and Q:

$$\frac{\partial T(N, Q)}{\partial N} = TB - 20% \cdot Q \cdot \left ( \frac{-1}{R} \right ) \cdot TB$$

$$\frac{\partial T(N, Q)}{\partial N} = TB \cdot \left ( 1 + \frac{20% \cdot Q}{R} \right )$$

$$\frac{\partial T(N, Q)}{\partial Q} = TB - \frac{\partial}{\partial Q} \left ( \frac{20% \cdot TB}{R} \cdot (UL \cdot Q - Q^2 - N \cdot Q + D \cdot Q)\right )$$

$$\frac{\partial T(N, Q)}{\partial Q} = TB - \frac{20% \cdot TB}{R} \cdot (UL - 2Q - N + D)$$

$$\frac{\partial T(N, Q)}{\partial Q} = TB \cdot \left ( 1 + \frac{20%}{R} \cdot (2Q + N - UL - D) \right )$$

The second partial derivatives are:

$$\frac{\partial^2 T(N, Q)}{\partial N^2} = 0$$

$$\frac{\partial^2 T(N, Q)}{\partial Q^2} = \frac{2 \cdot TB \cdot 20%}{R}$$

$$\frac{\partial^2 T(N, Q)}{\partial Q \partial N} = \frac{TB \cdot 20%}{R}$$

Example
A MFJ couple has $120,000 of non-QBI income and also earns QBI. They take the standard deduction of $24,800. Below $326,600 of taxable income, they are in the 24% bracket. Their marginal tax rates for non-QBI and QBI income are:

$$\frac{\partial T(N, Q)}{\partial N} = 24%$$

$$\frac{\partial T(N, Q)}{\partial Q} = 80% \cdot 24% = 19.2%$$

The phase-out begins when their taxable income, after the standard deduction, equals $326,600. This corresponds to a QBI income of $231,400 ($326,600 + $24,800 - $120,000). Note that although their taxable income is at the 24%/32% threshold, the Section 199A deduction pulls them well down into the 24% bracket. At this income, their marginal tax rates are:

$$\frac{\partial T(N, Q)}{\partial N} = 24% \cdot \left ( 1 + \frac{20% \cdot $231,400}{$100,000} \right ) = 35.1072%$$

$$\frac{\partial T(N, Q)}{\partial Q} = 24% \cdot \left ( 1 + \frac{20%}{$100,000} \cdot (2 \cdot $231,400 + $120,000 - $426,600 - $24,800) \right ) = 24% \cdot \left ( 1 + \frac{20%}{$100,000} \cdot $131,400 \right ) = 30.3072%$$

At some point in the phase-out range, the couple will cross into the 32% bracket, and then into the 35% bracket. At the top of the phase-out, when QBI income is $331,400 ($426,600 + $24,800 - $120,000), marginal tax rates will be:

$$\frac{\partial T(N, Q)}{\partial N} = 35% \cdot \left ( 1 + \frac{20% \cdot $331,400}{$100,000} \right ) = 58.198%$$

$$\frac{\partial T(N, Q)}{\partial Q} = 35% \cdot \left ( 1 + \frac{20%}{$100,000} \cdot (2 \cdot $339,000 + $100,000 - $415,000 - $24,000) \right ) = 35% \cdot \left ( 1 + \frac{20%}{$100,000} \cdot $331,400 \right ) = 58.198%$$

Above $331,400 QBI, the Section 199A deduction is completely eliminated and the marginal rates become:

$$\frac{\partial T(N, Q)}{\partial N} = \frac{\partial T(N, Q)}{\partial Q} = 35%$$

Maximum possible rates
By inspection of the above formulas, the maximum possible rates occur at the very top of the phase-out range, when:

$$N + Q - D = UL$$

The maximum also occurs when Q is largest, so:

$$N = 0$$

and

$$Q = UL + D$$

Substituting these values into the above equations for the marginal rates give:

$$\frac{\partial T(N, Q)}{\partial N} = TB \cdot \left ( 1 + \frac{20% \cdot (UL + D)}{R} \right )$$

and

$$\frac{\partial T(N, Q)}{\partial Q} = TB \cdot \left ( 1 + \frac{20%}{R} \cdot (2 \cdot (UL+D) + 0 - UL - D) \right ) = TB \cdot \left ( 1 + \frac{20%}{R} \cdot (UL + D) \right ) $$

Note that the two formulas are the same.

For single filers for 2020, UL = $213,300 and R = $50,000, and we will assume the standard deduction D = $12,400. $213,300 taxable income is barely into the 35% bracket, which begins at $207,350 taxable income, so TB = 35%.

$$\left (\frac{\partial T(N, Q)}{\partial N} \right )_{max} = \left (\frac{\partial T(N, Q)}{\partial Q} \right )_{max} = 35% \cdot \left ( 1 + \frac{20% \cdot ($213,300 + $12,400)}{$50,000} \right ) = 66.598%$$

The QBI required to achieve this rate is:

$$Q = $213,700 + $12,400 = $225,700$$

For married joint filers for 2020, UL = $426,600 and R = $100,000, and we will assume the standard deduction D = $24,800. $426,600 taxable income is barely into the 35% bracket, which begins at $414,700 taxable income, so TB = 35%.

$$\left (\frac{\partial T(N, Q)}{\partial N} \right )_{max} = \left (\frac{\partial T(N, Q)}{\partial Q} \right )_{max} = 35% \cdot \left ( 1 + \frac{20% \cdot ($426,600 + $28,400)}{$100,000} \right ) = 66.598%$$

The QBI required to achieve this rate is:

$$Q = $426,600 + $24,800 = $451,400$$

Note that the single and married joint maximum rates are the same. If itemized deductions are larger than the standard deduction, the maximum rate will be slightly higher.

--Fyre4ce 17:37, 17 February 2020 (UTC)