Let me start off by saying I actually have to thank someone I formerly worked with, Kelly Hernandez. We got into a discussion about UBI, the poor, etc. and from our conversation I discovered this amazing idea. You can read more about it in this article:

https://cdchester.co.uk/2018/06/05/thoughts-on-the-negative-income-tax/

## The Negative Income Tax

### Milton's Formula

\begin{align*}

Variables: &

\: Final \: Income \: \Longrightarrow \phi_{\: F} \\&

\: Inital \: Income \: \Longrightarrow \phi_{\: i} \\&

\: Exemption \: Level \: \Longrightarrow \phi_{\: \Xi} \\&

\: Tax \: Rate \: \Longrightarrow \phi_{\: R} \: ; \: 30 \leq \: \phi_{\: R} \: \leq 50

\end{align*}

\begin{aligned}\therefore \phi_{\: F} =

\phi_{\: i} - 0.01(\phi_{\: R})(\phi_{\: i} - \phi_{\: \Xi})

\end{aligned}

\begin{aligned}

If \: \phi_{\: R} = 30 \Longrightarrow

\therefore \phi_{\: F} = \dfrac{7 \phi_{\: i}+3 \phi_{\: \Xi}}{10} \\ \\If \: \phi_{\: R} = 50 \Longrightarrow

\therefore \phi_{\: F} = \dfrac{\phi_{\: i}+\phi_{\: \Xi}}{2}

\end{aligned}

\begin{aligned}

\therefore \dfrac{\phi_{\: i}+\phi_{\: \Xi}}{2} < \dfrac{7 \phi_{\: i}+3 \phi_{\: \Xi}}{10} \: ; \:

\phi_{\: i} > \phi_{\: \Xi} \\ \\\therefore \dfrac{7 \phi_{\: i}+3 \phi_{\: \Xi}}{10} < \dfrac{\phi_{\: i}+ \phi_{\: \Xi}}{2} \: ; \:

\phi_{\: i} < \phi_{\: \Xi}

\end{aligned}

### Prominent Features

- Guaranteed minimum income (modified UBI)
- Optimal tax collection mechanism
- Libertarian Redistributionism
- Replace other welfare options (simplifies options)
- Progressive incentive

## Theoretical Applications and Ammendments

Milton stated that there are many amendments that can be discussed but the principles of the system are established. Some things he discussed in his books, columns, and interviews included: by household size, COL adjustment, setting the EL and TR, non-annual implications.

#### Household Size

This is my speculation as to what to do about household size. My way works similiar to the way the** Federal Poverty Line** (FPL) works.

**Start with the basic individual and add a yearly adjusted amount** (2017 amount stands at $4,180) for every extra person in the household. For instance, 2018's amount would now be adjusted to $4278.64 and 2019 to $4,358.33.

Calculations can be easily done using the CPI Inflation Calculator (use March as the standard month).

As an example say you are in a household of 5 in 2107 making $50,000 in a scenario of a $40,000 EL and 50% TR. Then:

\begin{aligned}

\therefore \left[ 50,000 + 4(4,180) \right] = 66,720 \\ \\\therefore \phi_{\: F} = \dfrac{66,720 + 40,000}{2} = 53,360\end{aligned}

Therefore, you would not be taxed rather supplemented by $3,360. This updates the Initial Income portion of Milton's Formula into:

\begin{aligned}

\alpha_n = \rm{Alloted \: Amount \: in \: n^{th} \: year \: / \: Extra \: Person} \end{aligned} \begin{aligned}

\Delta_\rho = \rm{no. \: of \: Extra \: Persons} \end{aligned} \begin{aligned}

\therefore \phi_{\alpha} = \phi_i + \alpha_n \Delta_\rho

\end{aligned}

#### Non - Annual Orientation

So this might seem hard to solve but transforming the NIT from its traditional annual format to a specific time frame is actually quite easy. **All you have to do is orient the EL to the time frame.** For instance say you are paid twice a months (paid 24 times / year) then you divide the EL by 24.

As an example, say you make $300 / week at a $50,000 EL with a 50% TR. Then the oriented EL is ~ $961.54 and the Final Income for that week will be ~ $630.76 (supplement of ~ $330.76).

\begin{aligned}\therefore \phi_{\: T} = \dfrac{\phi_{\Xi}}{\Delta_{\tau}}

\end{aligned}

\begin{aligned}

\therefore \Delta_{\tau} \: ; \:

\rm {where \: this \: is \: the \: Time \: Proportionality \\ Constant \: relative \: to \: a \: year}\end{aligned}

In the example the proportionality constant was 52 (~ 52 weeks / year). If you were paid bi - monthly the constant would be 24. Monthly is 12 ... and so on to whatever orientation you encounter.

#### COL Adjustments

Using whatever standard you wish to use all you need to do is **relate the COL from one place to another**. I'd suggest finding and using the lowest COL in whatever area span (likely national) as 1 and relating the other COLs in terms of multiple. If Alabama has a COL Index of 87 and Florida as 100.5 then orienting Alabama to 1 then Florida is ~1.155.

\begin{aligned}

\therefore \phi_{ \: \mu} = \phi_{\: T} \Delta_{C} =

\left( \dfrac{\Delta_{C}}{\Delta_{ \tau}} \right) \phi_{\Xi}

\end{aligned} \begin{aligned}

\therefore \Delta_{C} \: ; \:

\rm {where \: this \: is \: the \: COL\: Proportionality \\ Constant \: relative \: to \: said \: places}

\end{aligned}

## Theoretical Formulas Preferences

- Start the
**EL at the National Median Income (NMI)**and relate the COL to the respective state; if possible all the way down to the city- makes it so that ~ 50% of people don't have to pay taxes
- most of
**Middle Class pays minimal taxes**(0 - 15% roughly)

**TR at 50%**to maximize help to disadvantaged- maintain that
**double the FPL is less than half the chosen EL** **Head of Household obtains AA**for extra persons in household

## Inclusive NIT Formula at Given Preferences

EXAMPLE:

Initial Income - $1,000

Time PC - 52

COL PC - 1.1

EL - $60,000

Extra Persons - 2

AA - $4,000

Final Income - $1211.54

## Real World Simulation (2017 Data Used)

Using 2017 data found here:

https://www.census.gov/library/publications/2018/demo/p60-263.html

I created these two PDFs analyzing how my NIT formula would orient the US populace.

The US made ~ $3.316T with Income taxes contributing $1.587T.

In my NIT version of **EL at $60K** and **TR at 50%** **~ 50.61% (give or take 1.6%) did not pay any taxes** and the **upper middle class had an ~ 12 - 15% tax rate**. In reality most of the upper middle class pays a 25 - 35% tax rate. Overall, **everyone had at least $30K** to use throughout the year at minimum (half of 60) which is **slightly above the poverty line for a 5 person household** and ~ 2.5 times for an individual.

My NIT produced a **worst case scenario of $2.08T and best case of $2.78T**; a significant increase made primarily by a shift in who is the tax payer. **After supplementing those below the EL produced ~ $1.07T - $1.92T** left over (which close to the revenue collected in reality).

**I should note that this is not adjusted for COL or no. of persons per household.** It simply uses the $5K intervals of households as its basis. Regardless, I doubt a crazy amount would change and it would likely end in a higher supplementation amount (making it better / easier for the populace).

## References

**Insight on COL and Class**https://www.investopedia.com/financial-edge/0912/which-income-class-are-you.aspx

**US Total Tax Revenue by Year (1960 - 2018)**https://www.thebalance.com/current-u-s-federal-government-tax-revenue-3305762

**US Tax Revenue Data Breakdown of 2017**https://www.thebalance.com/how-trump-amended-obama-budget-4128986

**Income and Poverty in the United States: 2017**https://www.census.gov/library/publications/2018/demo/p60-263.html

**2017 FPL Guidelines**https://www.peoplekeep.com/blog/2017-federal-poverty-level-guidelines

**Tax Brackets and Rates, 2019**https://taxfoundation.org/2019-tax-brackets/

**Thoughts on the Negative Income Tax**https://cdchester.co.uk/2018/06/05/thoughts-on-the-negative-income-tax/

**Check out the bottom of the last link for links to videos of Milton, academic studies on NIT, and other articles on NIT (pro v con).**