<blockquote>
<p>Would the state be able to guarantee a worthy socio-economic status to everybody with the money earnt this way?</p>
</blockquote>
<p>No, for several reasons.</p>
<p>First the proposal flies in the face of 101 rules of optimal tax policy. One of the most fundamental rule of optimal taxation is that top marginal tax rates of 100% and above are never optimal. This is because marginal tax rates of 100% and above remove any incentive for people to supply more work or be economically active. People would just cut on working hours and negotiate for more non-monetary benefits (e.g. nicer office space etc). This would lead to a collapse of a tax base for such tax.</p>
<p>Moreover, capping also the dividend income,  which is de facto return on capital, would highly discourage new private investments (save for reinvesting retained earnings). This would practically destroy most incentive to start any larger new business venture. Furthermore, empirically large amount of burden from capital taxes is shifted to the labor. Theoretically the whole tax in the long run is shifted (e.g.  <a href="https://www.jstor.org/stable/1911310#metadata_info_tab_contents" rel="nofollow noreferrer">Chamley 1986</a>, and <a href="https://eml.berkeley.edu//%7Esaez/course/Judd_JPubE(1985).pdf" rel="nofollow noreferrer">Judd 1985</a>), although most empirical studies show that only about 50-100% of the burden is shifted to labor (e.g. see  <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2713027#:%7E:text=In%20most%20settings%2C%20higher%20corporate,workers%20and%20monopsonistic%20labor%20markets." rel="nofollow noreferrer">Fuest et al 2018;</a> <a href="https://www.journals.uchicago.edu/doi/abs/10.1086/209877" rel="nofollow noreferrer">Gruber 1997</a>) that is still considerable amount. Hence, it would lead to lower labor wages even for employees not affected by the cap.</p>
<p>Also, unless every country in the world would implement the cap it would lead to massive capital flight out of the country. People would have strong incentives to rather invest their capital in foreign business.</p>
<p>As a result it is absolutely unreasonable to expect that such proposal would raise significant extra revenue for the state. In fact it is not unlikely that the effect on public finance could be even  negative depending on the general equilibrium effects such proposal would cause. Even if the effect would turn out to be positive, there is no way it would rise significant amount of funds. Consequently unless you think that &quot;worthy socio-economic status&quot;, whatever is that supposed to mean, can be achieved with very little or none extra revenue, the revenue generated by this proposal can't do that.</p>
<p>Second, we know how the optimal income tax schedule looks like. Optimal income taxation is already more or less solved problem. Given Rawlsian Max-Min criterion where government <em>only cares about the welfare of the poor</em> and everyone else gets zero welfare weight optimal wage income tax schedule (taken from Saez 2001) looks like this:</p>
<p><a href="https://i.sstatic.net/fbhbv.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/fbhbv.png" alt="enter image description here" /></a></p>
<p>As you can see even when we want to maximize only welfare of the poor and don't care about anyone else the top marginal tax rates are well below 100% for any plausible assumptions on the tax elasticities and utility functions. The optimal capital income taxes are lower due to the previously mentioned issues. In any case this illustrates that the proposal you put forward is not consistent with maximization of welfare of the poor.  That is clearly not good if the objective is to guarantee &quot;worthy socio-economic status&quot; for everybody, unless &quot;worthy socio-economic status&quot; involves lower levels of welfare for poor compared to optimally setting the taxes.</p>

CC BY-SA 4.0
2022-08-12T14:05:18.320Z
Thank you very much for your answer. Now I understand that the "correct" question would have been: what is the optimal tax policy to maximize the welfare of the poor? Which you have addressed clearly in the last paragraph. I also gave a look to Saez article, but I think I miss some of the key macroeconomic concepts to understand easily the formulas. 

Just one doubt: why the marginal tax rate is 100% at the beginning? Shouldn't be 0%? 
 I would expect progressive taxation with small earnings being taxed less. I am not sure I am interpreting plots properly.
Andrea Marino
CC BY-SA 4.0
2022-08-12T14:10:26.380Z
@AndreaMarino that is because economically removing a subsidy is considered a tax. At a bottom the marginal tax rate is 100% as when you care only about welfare of poor you will start removing the subsidies quite fast as people climb economic ladder towards middle class. This is why you see the inverted hump shape. At the bottom of income ladder the high marginal tax rates are generated by lowering subsidies people get (those people don't actually pay any money to the government they just receive less welfare checks) and then eventually people start paying some money to the government and
1muflon1
CC BY-SA 4.0
2022-08-12T14:12:07.277Z
after that people only pay to the government and do not receive any welfare at all. If you want to maximize redistribution toward the poorest (max-min principle) you want very high welfare check for the poorest and then quickly scale it back which creates very high marginal tax rates for the poor - but again those are not money payed to the gov but government scaling back welfare payments as income increases
1muflon1
CC BY-SA 4.0
2022-08-12T14:24:43.783Z
I swear I am trying to understand but I can't XD I would have expected the opposite behavior. For example, 100% taxes for people earning 0% means that all the subsidy is removed, isn't it? Then you start to remove fewer subsidies to richer people... which doesn't make sense (continue)
Andrea Marino
CC BY-SA 4.0
2022-08-12T14:25:10.890Z
Unless... *giving* money to people is considered a tax. Weird, since I am used to think that the higher the taxes, the less I have. Or... maybe redistribution is not considered, so you take all the money from the poor and then you give back to them when you redistribute with subsidies. In other words: how I convert such plots to an effective tax schedule?

PS Thank you very much for the time you are spending for me!
Andrea Marino
CC BY-SA 4.0
2022-08-12T14:32:12.497Z
@AndreaMarino I think this is best illustrated with an example. Suppose your wage is 100euro and at that wage you are entitled to 100e subsidy. You are exempt from paying money to the government at that income. Now suppose your wage income increases to 101e and that leads to you getting only 90e subsidy. That 10e you will no longer get as a subsidy is considered to be tax, so by formula for marginal tax rate we have $\Delta T = 10$ (since we go from 0e to 10e tax), and change in income is 1, so the marginal tax rate is $\frac{\Delta T}{ \Delta W} = 10$ or 1000%.
1muflon1
CC BY-SA 4.0
2022-08-12T14:35:11.403Z
as you can see even at 1000% not all subsidy is removed. This calculation is not that simple, those are marginal tax rate not absolute tax rates. That is 100% tax rate does not mean you loose all money you have, it means if you earn 1 extra euro you loose 1 extra euro. 1000% marginal tax would mean if you earn 1 extra euro you loose 10 euro
1muflon1
CC BY-SA 4.0
2022-08-12T14:43:18.110Z
Aaaaaaah that's clear. I also read again your above comment and now is crystalline. I have a clear picture of how this should be translated into an absolute tax rate schedule. The U-shape makes definitely sense and I find it interesting that asymptotically converges to an optimal flat tax that maximizes the equity-efficiency trade-off you mentioned. This sort of stuff helps me to better understand political issues and reforms, so thanks for the "social" service you have done :)) there should be some economics divulgation channel for these doubts!! But I don't know anyone.
Andrea Marino
CC BY-SA 4.0
2022-08-12T01:52:10.413Z
2022-08-12T02:04:32.567Z
2022-08-12T02:04:32.567Z
1muflon1
<p>I am new here. Please pardon me for my naive question. However, I am a mathematician, so feel free to use any mathematics to model a toy situation.</p>
<p>I would like to understand what would happen if <em>suddenly</em>, a state imposes a limit on the income: you can't earn more than 20k per month, no matter how you do this (working, trading, dividends); the rest goes to the state, that perfectly manages the earnt taxes. Let us limit to a national market, neglecting the exchanges with external markets. Also, all the capital belonging to an enterprise must be re-invested, besides the dividends that shareholders can receive in compliance with such law. There is also a tax (which I think already exists in many countries) on the patrimony of enterprises.</p>
<p>This is an extremization of tax brackets, where at some point taxes are nearly 100%.</p>
<blockquote>
<p>Would the state be able to guarantee a worthy socio-economic status to everybody with the money earnt this way?</p>
</blockquote>
<p>Here is what I thought:</p>
<ol>
<li>Nobody would pay more than 20k per month for a job. This means enterprises would have more money to invest, and the state would receive more taxes. This is a plus point.</li>
<li>The luxury market would lose a lot of money. This means fewer jobs, so possibly more people to support with social actions and fewer taxes from exchanges and patrimony. This is a minus point.</li>
</ol>
<p>What I want to understand: the big tax income the state would receive, would it be enough to compensate for the indirect damages to the market that a limited purchasing power would cause?</p>
<p><strong>Note.</strong> I am not interested in any moral or philosophical consideration about such a measure. I just want to understand how extreme richness and extreme poverty interact on a scale I am not used to.</p>

CC BY-SA 4.0
2022-08-11T23:09:12.237Z
Not sure which loophole you are referring to but yes, there are some delicate ones (what if I pay you in stocks or houses? Isn't that just going back to a sophisticated jar method?). I don't have an answer for any cheating we can think, but let's stay easy for a while. It's not meant to be an actual fiscal law but a mental experiment, which still has a lot of difficulties i guess
Andrea Marino
CC BY-SA 4.0
2022-08-12T09:21:47.650Z
You would need to start closing the borders (the biggest loophole). Otherwise, everybody apart from those that couldn't expect to make more than 20K would leave!
BrsG
<macroeconomics><taxation><social-welfare>
Universal Limited Income
Andrea Marino
# Universal Limited Income

(Asked by: username_0 on 2022-08-11)

I am new here. Please pardon me for my naive question. However, I am a mathematician, so feel free to use any mathematics to model a toy situation.

I would like to understand what would happen if *suddenly*, a state imposes a limit on the income: you can't earn more than 20k per month, no matter how you do this (working, trading, dividends); the rest goes to the state, that perfectly manages the earnt taxes. Let us limit to a national market, neglecting the exchanges with external markets. Also, all the capital belonging to an enterprise must be re-invested, besides the dividends that shareholders can receive in compliance with such law. There is also a tax (which I think already exists in many countries) on the patrimony of enterprises.

This is an extremization of tax brackets, where at some point taxes are nearly 100%.

> Would the state be able to guarantee a worthy socio-economic status to everybody with the money earnt this way?

Here is what I thought:

1. Nobody would pay more than 20k per month for a job. This means enterprises would have more money to invest, and the state would receive more taxes. This is a plus point.
2. The luxury market would lose a lot of money. This means fewer jobs, so possibly more people to support with social actions and fewer taxes from exchanges and patrimony. This is a minus point.

What I want to understand: the big tax income the state would receive, would it be enough to compensate for the indirect damages to the market that a limited purchasing power would cause?

**Note.** I am not interested in any moral or philosophical consideration about such a measure. I just want to understand how extreme richness and extreme poverty interact on a scale I am not used to.

**Tags:** macroeconomics, taxation, social-welfare
> **Comments:**
> **username_0**: Not sure which loophole you are referring to but yes, there are some delicate ones (what if I pay you in stocks or houses? Isn't that just going back to a sophisticated jar method?). I don't have an answer for any cheating we can think, but let's stay easy for a while. It's not meant to be an actual fiscal law but a mental experiment, which still has a lot of difficulties i guess  
> **username_1**: You would need to start closing the borders (the biggest loophole). Otherwise, everybody apart from those that couldn't expect to make more than 20K would leave!  

---

## 1 answers

### Answer by username_2 on 2022-08-12. Score: 3 | Accepted answer

> Would the state be able to guarantee a worthy socio-economic status to everybody with the money earnt this way?

No, for several reasons.

First the proposal flies in the face of 101 rules of optimal tax policy. One of the most fundamental rule of optimal taxation is that top marginal tax rates of 100% and above are never optimal. This is because marginal tax rates of 100% and above remove any incentive for people to supply more work or be economically active. People would just cut on working hours and negotiate for more non-monetary benefits (e.g. nicer office space etc). This would lead to a collapse of a tax base for such tax.

Moreover, capping also the dividend income, which is de facto return on capital, would highly discourage new private investments (save for reinvesting retained earnings). This would practically destroy most incentive to start any larger new business venture. Furthermore, empirically large amount of burden from capital taxes is shifted to the labor. Theoretically the whole tax in the long run is shifted (e.g. [Chamley 1986](https://www.jstor.org/stable/1911310#metadata_info_tab_contents), and [Judd 1985](https://eml.berkeley.edu//%7Esaez/course/Judd_JPubE(1985).pdf)), although most empirical studies show that only about 50-100% of the burden is shifted to labor (e.g. see [Fuest et al 2018;](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2713027#:%7E:text=In%20most%20settings%2C%20higher%20corporate,workers%20and%20monopsonistic%20labor%20markets.) [Gruber 1997](https://www.journals.uchicago.edu/doi/abs/10.1086/209877)) that is still considerable amount. Hence, it would lead to lower labor wages even for employees not affected by the cap.

Also, unless every country in the world would implement the cap it would lead to massive capital flight out of the country. People would have strong incentives to rather invest their capital in foreign business.

As a result it is absolutely unreasonable to expect that such proposal would raise significant extra revenue for the state. In fact it is not unlikely that the effect on public finance could be even negative depending on the general equilibrium effects such proposal would cause. Even if the effect would turn out to be positive, there is no way it would rise significant amount of funds. Consequently unless you think that "worthy socio-economic status", whatever is that supposed to mean, can be achieved with very little or none extra revenue, the revenue generated by this proposal can't do that.

Second, we know how the optimal income tax schedule looks like. Optimal income taxation is already more or less solved problem. Given Rawlsian Max-Min criterion where government *only cares about the welfare of the poor* and everyone else gets zero welfare weight optimal wage income tax schedule (taken from Saez 2001) looks like this:

[![enter image description here](https://i.sstatic.net/fbhbv.png)](https://i.sstatic.net/fbhbv.png)

As you can see even when we want to maximize only welfare of the poor and don't care about anyone else the top marginal tax rates are well below 100% for any plausible assumptions on the tax elasticities and utility functions. The optimal capital income taxes are lower due to the previously mentioned issues. In any case this illustrates that the proposal you put forward is not consistent with maximization of welfare of the poor. That is clearly not good if the objective is to guarantee "worthy socio-economic status" for everybody, unless "worthy socio-economic status" involves lower levels of welfare for poor compared to optimally setting the taxes.

> **Comments:**
> **username_0**: Thank you very much for your answer. Now I understand that the "correct" question would have been: what is the optimal tax policy to maximize the welfare of the poor? Which you have addressed clearly in the last paragraph. I also gave a look to Saez article, but I think I miss some of the key macroeconomic concepts to understand easily the formulas.   Just one doubt: why the marginal tax rate is 100% at the beginning? Shouldn't be 0%?   I would expect progressive taxation with small earnings being taxed less. I am not sure I am interpreting plots properly.  
> **username_2**: @AndreaMarino that is because economically removing a subsidy is considered a tax. At a bottom the marginal tax rate is 100% as when you care only about welfare of poor you will start removing the subsidies quite fast as people climb economic ladder towards middle class. This is why you see the inverted hump shape. At the bottom of income ladder the high marginal tax rates are generated by lowering subsidies people get (those people don't actually pay any money to the government they just receive less welfare checks) and then eventually people start paying some money to the government and  
> **username_2**: after that people only pay to the government and do not receive any welfare at all. If you want to maximize redistribution toward the poorest (max-min principle) you want very high welfare check for the poorest and then quickly scale it back which creates very high marginal tax rates for the poor - but again those are not money payed to the gov but government scaling back welfare payments as income increases  
> **username_0**: I swear I am trying to understand but I can't XD I would have expected the opposite behavior. For example, 100% taxes for people earning 0% means that all the subsidy is removed, isn't it? Then you start to remove fewer subsidies to richer people... which doesn't make sense (continue)  
> **username_0**: Unless... *giving* money to people is considered a tax. Weird, since I am used to think that the higher the taxes, the less I have. Or... maybe redistribution is not considered, so you take all the money from the poor and then you give back to them when you redistribute with subsidies. In other words: how I convert such plots to an effective tax schedule?  PS Thank you very much for the time you are spending for me!  
> **username_2**: @AndreaMarino I think this is best illustrated with an example. Suppose your wage is 100euro and at that wage you are entitled to 100e subsidy. You are exempt from paying money to the government at that income. Now suppose your wage income increases to 101e and that leads to you getting only 90e subsidy. That 10e you will no longer get as a subsidy is considered to be tax, so by formula for marginal tax rate we have $\Delta T = 10$ (since we go from 0e to 10e tax), and change in income is 1, so the marginal tax rate is $\frac{\Delta T}{ \Delta W} = 10$ or 1000%.  
> **username_2**: as you can see even at 1000% not all subsidy is removed. This calculation is not that simple, those are marginal tax rate not absolute tax rates. That is 100% tax rate does not mean you loose all money you have, it means if you earn 1 extra euro you loose 1 extra euro. 1000% marginal tax would mean if you earn 1 extra euro you loose 10 euro  
> **username_0**: Aaaaaaah that's clear. I also read again your above comment and now is crystalline. I have a clear picture of how this should be translated into an absolute tax rate schedule. The U-shape makes definitely sense and I find it interesting that asymptotically converges to an optimal flat tax that maximizes the equity-efficiency trade-off you mentioned. This sort of stuff helps me to better understand political issues and reforms, so thanks for the "social" service you have done :)) there should be some economics divulgation channel for these doubts!! But I don't know anyone.  

---

