-1=e^ipi

Social Justice is an Orwellian lie. Nearly everyone supports justice, they just have different understandings of what justice is. Terms like social justice have an implication that those that disagree with it are against justice. So rather than try to justify 'social justice' on its own merits, SJWs just play Orwellian word association games to associate justice with their position and injustice with the opposing position.

I'm deeply offended that you used the acronym LGBTIQ instead of LGBTQIA! Clearly this is a micro-aggression against A people since you are dismissing their experiences or dismissing their existence! Edit: Above comment contains sarcasm. It's fun to use the SJW ideology against it's own adherents.

Because the SJW dogma says so. Reason, empirical evidence, consistency or falsifiability don't matter.

Except it goes further than that. Saying that 'the most qualified person should get the job' or 'race shouldn't matter' is a micro aggression. Denial of someone's claim of racism is a form of micro-aggression. Not believing someone's claims of being micro-aggressioned is micro aggression. These SJWs want to criminalize people that disagree with their SJW ideology. And it's reached critical mass in most universities. Even if 90% of the people in power in a university are reasonable, the 10% will discriminate against anyone that doesn't accept or at least pretend to accept their ideology so SJW types will have an advantage in being hired, published, promoted, tenured, etc. Over time this means more SJW types in power, which results in more discrimination and so on.

So the University of California in Berkeley recently implemented a policy of trying to educate people about 'micro-aggressions' in order to prevent people from doing 'micro-aggressions'. The implication is that those who do perform 'micro-aggressions' may suffer disciplinary such be fired, not get promotions, not get tenure, etc. What are micro-aggressions? Well apparently saying things like 'I believe that the most qualified person should get the job' or 'America is a melting pot' is a racist and sexist statement that means that you hate women, sexual minorities and people of other races and your statement is creating a hostile environment and is meant to chip away at the sense of worth of others. The creation of such a hostile work environment is viewed as legally actionable by UC and the US federal government. http://www.washingtonpost.com/news/volokh-conspiracy/wp/2015/06/16/uc-teaching-faculty-members-not-to-criticize-race-based-affirmative-action-call-america-melting-pot-and-more/ http://www.ucop.edu/academic-personnel-programs/_files/seminars/Tool_Recognizing_Microaggressions.pdf http://www.utsandiego.com/news/2015/jun/19/university-california-microaggression-faculty/

Just for the sake of it, I'll redo the analysis using the Australian labour supply wage elasticity of 0.14. This gives B = 7.01, which gives H = 2222 (which becomes 2406 upon removal of representative consumer approximation). This results at an optimal social welfare with t = 66.65%, T = $19522 or a VAT of 25%, t = 53.52% and T = $24595. I'll point out that I didn't change who the social welfare function values the additional dollar of a rich person to the additional dollar of a poor person (still log utility), I just changed how people value their leisure time vs their consumption.

Redoing the 3rd part of my analysis, my utility function is: U = ln(1-s) - ln(1.481+t) + ln((1-t)*wL + (1.5*t - 0.2595)*mean(wL)) + ln(H-L)/B The social welfare function becomes: mean(U) = ln(1-s) - ln(1.481+t) + mean(ln((1-t)*wL + (1.5*t - 0.2595)*mean(wL))) + mean(ln(H-L))/B From individual utility maximization I obtained BwH = (B+1)wL + (1.5*t - 0.2595)*mean(wL)/(1-t). => BH*mean(w) = (B+1)*mean(wL) + (1.5*t - 0.2595)*mean(wL)/(1-t) => BH*mean(w) = ((B + 0.7504) + (0.5 - B )*t)*mean(wL)/(1-t) => mean(wL) = BH*mean(w)*(1-t)/((B + 0.7504) + (0.5 - B )*t) => BwH = (B+1)wL + (1.5*t - 0.2595)*BH*mean(w)*(1-t)/((B + 0.7504) + (0.5 - B )*t)/(1-t) => L = BH*(1 + mean(w)/w*(1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t))/(B+1) Using B = 10.22 gives: Substituting this back into the 3rd term of the social welfare function gives: mean(ln((1-t)*wL + (1.5*t - 0.2595)*mean(wL))) = ln(BH/(B+1)) + ln(1-t) + ln(mean(w)) + mean(ln(w/mean(w) + (1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t) + (1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t))) ln(BH/(B+1)) is just an arbitrary constant, so can be dropped without loss of generality to get: ln(1-t) + ln(mean(w)) + mean(ln(w/mean(w) + (3*t - 0.519)/((B + 0.7504) + (0.5 - B )*t))) Substituting L into the 4th term of the social welfare function gives: mean(ln(H-L))/B = mean(ln(BH/(B+1)*((B+1)/B - 1 - mean(w)/w*(1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t)))/B = mean(ln(BH/(B+1)*mean(w)/w))/B + mean(ln((1/B*w/mean(w) - (1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t))/B The first term here is a constant, so it can be dropped, leaving: mean(ln((1/B*w/mean(w) - (1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t))/B This means that the social welfare function becomes: ln(1-s) + ln(mean(w)) - ln(1.481+t) + ln(1-t) + mean(ln(w/mean(w) + (3*t - 0.519)/((B + 0.7504) + (0.5 - B )*t))) + mean(ln((1/B*w/mean(w) - (1.5*t - 0.2595)/((B + 0.7504) + (0.5 - B )*t))/B Using B = 10.22 Gives: ln(1-s) + ln(mean(w)) - ln(1.481+t) + ln(1-t) + mean(ln(w/mean(w) + (3*t - 0.519)/(10.9794 - 9.72*t))) + mean(ln((1/10.22*w/mean(w) - (1.5*t - 0.2595)/(10.9794 - 9.72*t))/10.22 To maximize social welfare, the derivative of social welfare with respect to t must be zero: 0 = -1/(1.481+t) - 1/(1-t) + (1.5*(10.9794 - 9.72*t) + 9.72*(1.5*t - 0.2595))/(10.9794 - 9.72*t)^2*(2*mean(1/(w/mean(w) + (3*t - 0.519)/(10.9794 - 9.72*t))) - mean(1/(1/10.22*w/mean(w) - (1.5*t - 0.2595)/(10.9794 - 9.72*t)))/10.22) = -1/(1.481+t) - 1/(1-t) + 13.94676/(10.9794 - 9.72*t)^2*(2*mean(1/(w/mean(w) + (3*t - 0.519)/(10.9794 - 9.72*t))) - mean(1/(1/10.22*w/mean(w) - (1.5*t - 0.2595)/(10.9794 - 9.72*t)))/10.22) This gives a maximum social utility when t = 70.0% and T = $20892. Although with a VAT of 25% one has t = 56.67% and T = $26321. This also results in the bottom 7.5% of current income earners (the ones that earn less than $5000) choosing not to work at all. This results depends on labour-wage elasticity being as low as 0.1, which is arguably on the low end.

If I redo this post with the new social welfare function: With the utility function that agrees with observations of labour supply wage elasticity, I have: Physical Capital's share of income is 1/3 condition: (1.481+t)*r*sum(K) = (1-t)*sum(wL) + sum(T) Revenue Neutrality condition: sum(T) = (1.5*t - 0.2595)*sum(wL) => (1.481+t)*r*sum(K) = (0.7405 + 0.5*t)*sum(wL) => wL = i*(1.481+t)/(2.2215 + 1.5*t) (if rK is proportional to wL) If I combine this with the utility maximization condition (L = (BH - T/w/(1-tm))/(B+1)) I get: BwH = (B+1)wL + (1.5*t - 0.2595)*mean(wL)/(1-tm) => BwH = (B+1)*i*(1.481+t)/(2.2215 + 1.5*t) + (1.5*t - 0.2595)*mean(i)*(1.481+t)/(2.2215 + 1.5*t)/(1-tm) => w = ((B+1)*i + (1.5*t - 0.2595)*mean(i)/(1-tm))*(1.481+t)/(2.2215 + 1.5*t)/B/H Using this I can recalculate the wages by income group under the model as I did before. Once I have w I can get L as L = i*(1.481+t)/(2.2215 + 1.5*t)/w. And again, I can adjust H (to correct for the error due to the earlier assumption of the representative consumer) so that the observed average hours worked per worker agree with empirical evidence. I get H = 2200.

I can take into account this empirical evidence if I change my utility function from ln( c) + ln(l) to ln( c) + 1/B*ln(l), where B is some unknown coefficient. Under the more generalized utility function, setting the derivative with respect to L to zero gives: 0 = 1/(L + T/w/(1-tm)) - 1/B/(H - L) => L = (BH - T/w/(1-tm))/(B+1) The revenue neutrality condition for the representative consumer is still T = (1.5*te - 0.2595)*wL. Thus the labour wage elasticity is 1/(B + 1)*(1.5*te - 0.2595)/(1 - tm). If we use te of 50.31% and tm of 55.87% for the representative Canadian consumer, then this gives a labour wage elasticity of 1.122/(B+1). Setting this equal to 0.1 (to agree with empirical data) gives B = 10.22. If I isolate for H, I get H = ((B+1)L + T/w/(1-tm))/B = ((B+1)L + (1.5*te - 0.2595)*wL/w/(1-tm))/B = L*((B+1) + (1.5*te - 0.2595)/(1-tm))/B. Using L = 1706 for the average Canadian worker gives H = 2060. So this means that I should have used a utility function of U = ln(1-s) - ln(1.481+t) + ln((1-t)*wL + T) + ln(2060-L)/10.22 to better reflect empirical observations of labour supply wage elasticity.

The two links I provided earlier are not good for overall labour supply wage elasticity. Here is a paper that discusses various estimates for Australia, Canada, Britain and NZ: http://www.treasury.gov.au/PublicationsAndMedia/Publications/2007/Treasury-Working-Paper-2007-04. It suggests Australia's labour supply wage elasticity is around 0.14, although Canada's is probably lower (let's say 0.1). So my model could be overestimating labour supply wage elasticity by a factor of 5.

Sorry I made a mistake on the last line. It should be: = -1/(1.481+t) - 1/(1-t) - 9.9834/(1.7504 - 0.5*t)^3*(3*t - 0.519)*mean(1/((w/mean(w))^2 - ((3*t - 0.519)/(1.7504 - 0.5*t))^2)) This gives a flat tax of 9.53% and a transfer of $-5509. Basically it's saying that under the model, the gains made from reducing taxes (due to people working more) far outweight the losses in social welfare due to a less equal distribution of income. One thing to point out is that the model's estimation of labour elasticity could be very wrong.

Almost everyone believes in a god? Does that mean there is a logical basis for the belief in god? There is a difference between a specific tax system and just having a progressive tax system. The set of progressive tax systems is infinitely dimensional, so a belief in a progressive system doesn't tell you what those rates should be.

Seems like it would save money. It would also make it easier for gender non-binary individuals, trans individuals, and a parent with a child of the opposite sex.

And where does the power come from? What is your energy source to produce the hydrogen? Nuclear? I skeptical that hydrogen fuel cars will be superior compared to electric cars with improvements in battery technology.

That's a niche use, yes. I wouldn't call it revolutionary.

Revolutionize the energy industry? Doubt it. But it could have many niche applications. Also, scientific inquiry has value on it's own merit, so even if it doesn't result in something that is very economic, something of value has still been produced. With a country like Canada were wind and solar are not as viable as other places, but where we have larger temperature swings and lots of lakes that can be used as a heat reservoirs, it could be useful.

I'm not sure if I completely understand your question. With respect to the thermoelectric effect, it can be used as a source of renewable energy, although I guess if you could generate materials with better heat conduction properties then maybe this could improve energy transport (idk).

I would prefer to see more research into utilizing the thermoelectric effect. There was a recent paper about phonons having a bad gap structure or something and that this could be used to create more efficient thermoelectric devices (I don't remember where I read about it though). Edit: Maybe this was it: http://www.nature.com/nmat/journal/v14/n7/full/nmat4308.html http://www.rh.gatech.edu/news/417301/can-heat-be-controlled-waves

Why does that sound so unappealing? If you don't think it is 'progressive enough' then may I ask what is your evaluation of what the 'progressiveness' of a society based upon? Why would the relative risk aversion of humans not reflect how much 'progressiveness' a society should have? I'm not sure I agree with this. You are increasing jobs available to low income people and arguably the GAI is high enough to avoid poverty traps. Really? People earning less than ~$33000 would be on the net receiving end of the system. I don't think there was much logic behind how we got to the system we have, it just happened (with the help of lots of logical fallacies by politicians).

Thought I would try to calculate labour elasticity for the model to see if the model is consistent with empirical estimates of Canadian labour elasticity. From the utility maximization of the representative consumer I had: L = 0.5*H - 0.5*T/w/(1-t) Taking the derivative with respect to w gives: dL/dw = 0.5*T/(1-t)/w^2 Thus the labour elasticity is: dln(L)/dln(w) = w/L*dL/dw = 0.5*T/(1-t)/L/w For the representative consumer, T = (1.5*t - 0.2595)*wL. => dln(L)/dln(w) = (0.75*t-0.12975)/(1-t) For an average effective tax rate of 50.3%, this gives a labour elasticity of 0.498. It seems plausible, although it might be a bit on the high end of empirical estimates: Edit: the two links I provided earlier do not have good overall empirical estimates of labour supply. One of the links was about labour demand not labour supply (so I'm a bit embarrassed about that). If my model overestimates the labour elasticity (which means I am overestimating the effect taxes have on output), or if I am underestimating relative risk aversion (i.e. log utility isn't risk averse enough), then my earlier estimates for optimal flat tax & guaranteed income should be larger. Externalities may justify greater income redistribution to poorer people. For example, there is a tendency for poorer people to commit more crime and empirical evidence suggests that lower poverty leads to a lower crime rate. Also, poorer people have worse health outcomes and thus greater income redistribution can lead to lower rate of spread of disease or lower health care expenditures. The magnitudes of these externalities can theoretically be quantified using empirical data. If you put all that together, then I could see a guaranteed income as high as ~10k being justified based on empirical data. Although if consumption & income taxes were the only revenue sources then you would probably need a VAT of 25% and an income tax of 17% to achieve that (assuming you only kept the essential government services of 17.3% of GDP). Also, it would take a while to reach the new Solow equilibrium from a higher savings rate so initially you would only be able to afford ~8k guaranteed income.

Okay, so now let's consider a flat tax so that t = te = tm. The utility function becomes U = ln(1-s) - ln(1.481+t) + ln((1-t)*wL + T) + ln(6051-L). Using the revenue neutrality condition (sum(T) = (1.5*t - 0.2595)*sum(wL)) gives: U = ln(1-s) - ln(1.481+t) + ln((1-t)*wL + (1.5*t - 0.2595)*mean(wL)) + ln(6051-L) The social welfare function becomes: sum(U) = N*ln(1-s) - N*ln(1.481+t) + sum(ln((1-t)*wL + (1.5*t - 0.2595)*mean(wL))) + sum(ln(6051-L)) One can divide by N (number of people) to get an equivalent social welfare function: mean(U) = ln(1-s) - ln(1.481+t) + mean(ln((1-t)*wL + (1.5*t - 0.2595)*mean(wL))) + mean(ln(6051-L)) Now I need to take into account the fact that L depends on the tax rate t. From individual utility maximization I obtained: wH = 2wL + (1.5*t - 0.2595)*mean(wL)/(1-t). Taking the mean over all individuals gives: H*mean(w) = 2*mean(wL) + (1.5*t - 0.2595)*mean(wL)/(1-t) => H*mean(w) = (1.7504 - 0.5*t)*mean(wL)/(1-t) => mean(wL) = H*mean(w)*(1-t)/(1.7504 - 0.5*t) => wH = 2wL + (1.5*t - 0.2595)*H*mean(w)*(1-t)/(1.7504 - 0.5*t)/(1-t) => L = 0.5*H*(1 + mean(w)/w*(1.5*t - 0.2595)/(1.7504 - 0.5*t)) Substituting this back into the 3rd term of the social welfare function gives: mean(ln((1-t)*wL + (1.5*t - 0.2595)*mean(wL))) = mean(ln((1-t)*0.5*H*(w + mean(w)*(1.5*t - 0.2595)/(1.7504 - 0.5*t)) + (1.5*t - 0.2595)*H*mean(w)*(1-t)/(1.7504 - 0.5*t))) = ln(0.5H) + ln(1-t) + mean(ln(w + mean(w)*(1.5*t - 0.2595)/(1.7504 - 0.5*t) + (1.5*t - 0.2595)*mean(w)/(1.7504 - 0.5*t))) = ln(0.5H) + ln(1-t) + mean(ln(w + 2*mean(w)*(1.5*t - 0.2595)/(1.7504 - 0.5*t))) Because ln(0.5H) is just a constant, we can drop it from the social welfare function without loss of generality. So we have ln(mean(w)) + ln(1-t) + mean(ln(w/mean(w) + (3*t - 0.519)/(1.7504 - 0.5*t))) as the 3rd term. Substituting L into the 4th term gives: mean(ln(6051-L)) = mean(ln(6051-0.5*H*(1 + mean(w)/w*(1.5*t - 0.2595)/(1.7504 - 0.5*t)))) = ln(0.5H) + mean(ln(1 - mean(w)/w*(3*t - 0.519)/(1.7504 - 0.5*t))) = ln(0.5H) + mean(ln(1 - mean(w)/w*(3*t - 0.519)/(1.7504 - 0.5*t))) Again, because ln(0.5H) is a constant, we can drop it. Furthermore, mean(w)/w is a constant in this model for a given individual, so without loss of generality the 4th term becomes: mean(ln(w/mean(w) - (3*t - 0.519)/(1.7504 - 0.5*t))) This means that the social welfare function becomes: ln(1-s) + ln(mean(w)) - ln(1.481+t) + ln(1-t) + mean(ln(w/mean(w) + (3*t - 0.519)/(1.7504 - 0.5*t))) + mean(ln(w/mean(w) - (3*t - 0.519)/(1.7504 - 0.5*t))) To maximize social welfare, the derivative of social welfare with respect to t must be zero: 0 = -1/(1.481+t) - 1/(1-t) + mean((3*(1.7504 - 0.5*t) + 0.5*(3*t - 0.519))/(1.7504 - 0.5*t)^2/(w/mean(w) + (3*t - 0.519)/(1.7504 - 0.5*t))) - mean((3*(1.7504 - 0.5*t) + 0.5*(3*t - 0.519))/(1.7504 - 0.5*t)^2/(w/mean(w) - (3*t - 0.519)/(1.7504 - 0.5*t))) = -1/(1.481+t) - 1/(1-t) + mean(4.9917/(1.7504 - 0.5*t)^2/(w/mean(w) + (3*t - 0.519)/(1.7504 - 0.5*t))) - mean(4.9917/(1.7504 - 0.5*t)^2/(w/mean(w) - (3*t - 0.519)/(1.7504 - 0.5*t))) = -1/(1.481+t) - 1/(1-t) + 9.9834/(1.7504 - 0.5*t)^3*(3*t - 0.519)*mean(1/((w/mean(w))^2 - ((3*t - 0.519)/(1.7504 - 0.5*t))^2)) I'm not sure if I can solve this analytically due to things like Abel's impossibility theorem (and I'm tired), so instead I varied t to obtain 0. I obtain a maximum social welfare when t = 24.73%. To find T, I have T = (1.5*t - 0.2595)*mean(wL) = (1.5*t - 0.2595)*H*mean(w)*(1-t)/(1.7504 - 0.5*t). Using H = 6051 and t = 0.2473 gives T = $4588. So this would suggest that a flat tax of 24.73% and a guaranteed income of $4588 would be socially optimal (hopefully I didn't make an error). Note that 17.3% of GDP for essential government services is also funded by this tax system. Now I want to talk briefly about the consumption tax. Recall that from post #274, the simple Solow model gives y = A*(sA/d)^(a/(1-a)). To be consistent with the solow model, let's suppose that mean(w) depends on factors we can't control (call it Q) times s^(a/(1-a)) (i.e. more physical capital gives a higher wage). For a=1/3, a/(1-a) = 0.5. Then the first two terms in the social welfare function become: ln(1-s) + 0.5*ln(s) + ln(Q) To find the optimal s, set the derivative with respect to s to be zero. This gives: 0 = -1/(1-s) + 0.5/s => s = 0.5 - 0.5*s => s = 1/3. Which is the same result as the solow model. As I mentioned earlier, you would probably want to raise consumption taxes to 25% to get the savings rate to 1/3. A 25% VAT consumption tax at a savings rate of 1/3 is equivalent to a (1-s)*(1 - 1/(1 + 0.25)) = 13.33% income tax. So a 25% VAT tax and an 11.4% income tax would be preferable. Increasing the savings rate from 21% to 1/3 would increase GDP by (1/3/0.21)^(1/3/(1-1/3)) - 1 = 25.99%. So the corresponding guaranteed income would be $5780. Of course if you factored in all the efficiency gains from simplifying the tax code, getting rid of employment insurance, minimum wage, etc. then the justified guaranteed income would be even higher.

Firstly, I want to resolve an issue. There is quite a difference between the total income earned by the individuals on that table (~1170 billion) and Canada's 2013 GDP (~1894 billion) there are numerous reasons for this such not everyone filing their taxes, not all income being taxed, error in the method of how I calculated total income, or accounting discrepancies. In my above model, I need GDP to equal the sum of rK + wL for all individuals otherwise there is too much internal inconsistency. So I'll assume that Canada's GDP is roughly 1170 billion. Note that the tax burden being ~32.2% of 1894 billion is still reasonable and is consistent with the government expenditure estimates on the government of Canada website for 2009 (so I'll leave it as is). From here on, I'll use te as the effective tax rate of a specific individual, tm as the marginal tax rate of a specific individual and t as the average effective tax rate of society (weighted by income). I'll also use the functions mean and sum to refer to the mean and sum over all individuals (in an attempt to make notation simpler). T will refer to transfers per capita. Recall that we had rK = ((1-t)*(w*L + r*K) + T)/3/0.827 for the representative consumer. In the more general case, this condition (physical capital's share of income being 1/3 of GDP) becomes r*sum(K) = ((1-t)*(sum(wL) + r*sum(K)) + sum(T))/2.481 => (1.481+t)*r*sum(K) = (1-t)*sum(wL) + sum(T) The revenue neutrality condition becomes: t*(sum(wL) + r*sum(K)) = sum(T) + 0.173*((1-t)*(sum(wL) + r*sum(K)) + sum(T))/0.827 Substituting in r*sum(K) = ((1-t)*sum(wL) + sum(T))/(1.481+t) gives: t*(2.481*sum(wL) + sum(T))/(1.481+t)) = sum(T) + 0.519*((1-t)*sum(wL) + sum(T))/(1.481+t) => sum(T) = (1.5*t - 0.2595)*sum(wL) (this is basically what we had with the representative consumer) Combining the revenue neutrality condition with physical capital being 1/3 of GDP gives: (1.481+t)*r*sum(K) = (1-t)*sum(wL) + (1.5*t - 0.2595)*sum(wL) = (0.7405 + 0.5*t)*sum(wL) If for the sake of simplicity let's choose a model where people's savings are proportional to their labour income, then the above equation becomes rK = (0.7405 + 0.5*t)*wL/(1.481+t). So a person's taxable income is rK + wL = wL*(1 + (0.7405 + 0.5*t)/(1.481+t)) = wL*(2.2215 + 1.5*t)/(1.481+t) => wL = i*(1.481+t)/(2.2215 + 1.5*t), where i is taxable income. For the utility maximization condition of an individual, we get H - L = L + T/w/(1-tm) Substituting in the revenue neutrality condition gives: H = 2L + (1.5*t - 0.2595)*mean(wL)/w/(1-tm) => wH = 2wL + (1.5*t - 0.2595)*mean(wL)/(1-tm) => w = (2*i + (1.5*t - 0.2595)*mean(i)/(1-tm))*(1.481+t)/(2.2215 + 1.5*t)/H Using this, I can calculate the effective hourly wage for each income group (remember that t = 50.31%). Once I have w I can get L as L = i*(1.481+t)/(2.2215 + 1.5*t)/w. I get: Income Range: Approximate Income: % of Population: Marginal Tax Rate: Hourly Wage: Hours Worked: 5000- 2500 7.5% 25.70% $4.37 383 5000-10000 7500 6.7% 25.70% $5.61 892 10000-15000 12500 9.0% 45.75% $8.24 1012 15000-20000 17500 9.6% 45.75% $9.49 1229 20000-25000 22500 8.1% 45.75% $10.74 1396 25000-35000 30000 12.7% 45.75% $12.62 1585 35000-50000 42500 15.9% 49.85% $16.17 1753 50000-75000 62500 15.4% 56.85% $22.07 1888 75000-100000 87500 7.7% 58.86% $28.64 2037 100000-150000 125000 4.9% 62.86% $38.76 2150 150000-200000 175000 1.3% 66.86% $52.17 2236 200000-250000 225000 0.5% 67.86% $64.95 2309 250000+ 381000 0.8% 67.86% $104.00 2442 Now I will point out that this gives an average number of hours worked at 1502, which is slightly lower than the empirical 1706. The reason for this is that my estimate for H in the first part was a rough estimate. Rather than try to analytically rederive H, I'll just vary H until average hours worked is 1706. This gives H = 6051. This modifies the above table to: Income Range: Approximate Income: % of Population: Marginal Tax Rate: Hourly Wage: Hours Worked: 5000- 2500 7.5% 25.70% $3.83 435 5000-10000 7500 6.7% 25.70% $4.94 1013 10000-15000 12500 9.0% 45.75% $7.25 1149 15000-20000 17500 9.6% 45.75% $8.35 1397 20000-25000 22500 8.1% 45.75% $9.45 1587 25000-35000 30000 12.7% 45.75% $11.11 1801 35000-50000 42500 15.9% 49.85% $14.23 1991 50000-75000 62500 15.4% 56.85% $19.43 2145 75000-100000 87500 7.7% 58.86% $25.21 2314 100000-150000 125000 4.9% 62.86% $34.11 2443 150000-200000 175000 1.3% 66.86% $45.92 2541 200000-250000 225000 0.5% 67.86% $57.17 2624 250000+ 381000 0.8% 67.86% $91.54 2775 I'll just reiterate that these are the values that are internally consistent with the model. You guys wanted a rough estimate, so I'm giving a ROUGH estimate. Most likely the assumption that someone's savings are proportional to their wage income is incorrect and this is causing an underestimating of the hours worked and hourly wages of poor people and overestimating these factors for rich people (so to correct for this I would have to greatly complicate the model to look at consumption smoothing behaviour; or alternatively find empirical values for average income by income group and then infer savings by income group to be internally consistent). Another issue is that policies like minimum wage would make this model give inaccurate values for poor people because it doesn't take into account the fact that poor people aren't as able to find as much work as they would like. Anyway, I needed to be able to get values for w by income group and H in order to continue with my rough estimate of optimal flat tax and guaranteed income. To be continued...

No, I did not know that. Cool, can you define burden for me? What % of the $250k person's income results in equal burden as 50% of the 30k person's income?

Since you guys insist, I'll try to give a rough estimate of the magnitude of flat tax and income tax that I think would make sense using a crude and simplistic model. I'll start by trying to estimate the social welfare function. First, let's assume that people have a logarithmic utility function (explained some justification of this earlier) of consumption and leisure (i.e. U = ln( c) + ln(l), where c is consumption and l is leisure). The social welfare function will simply be the sum of the individual utilities. Now I need to estimate the tradeoff between additional taxes and hours worked. For simplicity, let's consider a country with a representative consumer. The consumer will consume (1-s) times their income, where s is the savings rate. The consumer's income is (1-t)*(w*L + r*K) + T, where t is the tax rate, w is the consumer's wage, L is their labour in hours worked, r is the interest rate, K is their Savings and T is transfers. For government expenditure, let's suppose that the expenditure consists of essential services and transfers. Let's look at federal (http://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/govt49b-eng.htm) and provincial (http://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/govt56b-eng.htm) expenditures in 2009. Let's assume that general government services, protection of persons and property, transportation and communication, health, education and environment are essential services and everything else is transfers (you can agree or disagree with this assumption, but I need to make assumptions in order to quantify things). This works out to 53.7% of government expenditure being essential and everything else being transfers. Roughly 32.2% of Canada's GDP is tax revenue (https://en.wikipedia.org/wiki/List_of_countries_by_tax_revenue_as_percentage_of_GDP), so this works out to ~17.3% of GDP being essential government services. If essential government services is 17.3% of GDP, then everything else is the 82.7%. Let's assume that rK is 1/3 of the GDP (i.e. physical capital's share of income is 1/3). Then we get that rK = ((1-t)*(w*L + r*K) + T)/3/0.827 => (1.481+t)*rK = (1-t)*wL + T => rK = ((1-t)*wL + T)/(1.481+t). Substituting this back into consumer income gives (1-t)*(wL + ((1-t)*wL + T)/(1.481+t)) + T = 2.481*((1-t)*wL + T)/(1.481+t). If a person works an additional hour, then get one less hour of leisure, so l = H - L, where H is some constant (note that it isn't really known a priori because for example it is unclear if sleeping counts as leisure). So the person's utility becomes U = ln((1-s)*2.481*((1-t)*wL + T)/(1.481+t)) + ln(H-L) = ln(1-s) + ln(2.481) - ln(1.481+t) + ln((1-t)*wL + T) + ln(H-L). The consumer will try to maximize their utility. Their utility is maximized when the derivative of U with respect to L is zero. This gives 0 = w*(1-t)/((1-t)*wL + T) - 1/(H-L) => H - L = L + T/w/(1-t). If the government is revenue neutral then the tax revenue (t*(wL + rK) = t*(2.481*wL + T)/(1.481+t)) must equal the government expenditures (T + 17.3% of GDP = T + 0.173*((1-t)*(wL + rK) + T)/0.827 = T + 0.519*((1-t)*wL + T)/(1.481+t)). This gives t*(2.481*wL + T)/(1.481+t) = T + 0.519*((1-t)*wL + T)/(1.481+t) => T*(1 + (0.519 - t)/(1.481+t)) = (2.481*t - 0.519*(1-t))*wL/(1.481+t) => T*2/(1.481+t) = (3*t - 0.519)*wL/(1.481+t) => T = (1.5*t - 0.2595)*wL Combining the condition of revenue neutrality with utility maximization gives H - L = L + (1.5*t - 0.2595)*L/(1-t) => H = L*(1.7405-0.5*t)/(1-t) => L = H*(1-t)/(1.7405-0.5*t). This describes the relationship between labour in hours worked and the tax rate. A higher tax rate results in less hours worked. If I take the average annual hours worked per worker for developed OECD countries (http://stats.oecd.org/index.aspx?DataSetCode=ANHRS) and tax revenue as a percentage of GDP (https://en.wikipedia.org/wiki/List_of_countries_by_tax_revenue_as_percentage_of_GDP) then I find that the calculated H values are roughly constant at ~ 4000 hours. In Canada's case I get 3974. However, using a 32.2% tax rate for Canada isn't really accurate for the above calculation since Canada's tax system is 'progressive'. So I should try to take this into account. I can get the distribution of income for Canadians here (http://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/famil105a-eng.htm). I think it only includes working age Canadians, so for the sake of simplicity I'll exclude everyone else. If we treat everyone in each income category as having the middle income of the category (except the last category which I will assume earn $381000 http://www.cbc.ca/news/canada/who-are-canada-s-top-1-1.1703321) then I can calculate the marginal tax rate, the effective tax rate, the percentage of the population and the percentage of total income for each group. For simplicity, I'll pretend everyone lives in Ontario and look at income taxes. I'll also assume that everyone that earns less than $10,000 doesn't pay tax. Income Range: Approximate Income: % of Population: % of Total Income: Marginal Tax Rate: Effective Tax Rate: 5000- 2500 7.5% 0.4% 0% 0% 5000-10000 7500 6.7% 1.1% 0% 0% 10000-15000 12500 9.0% 2.5% 20.05% 20.05% 15000-20000 17500 9.6% 3.8% 20.05% 20.05% 20000-25000 22500 8.1% 4.1% 20.05% 20.05% 25000-35000 30000 12.7% 8.5% 20.05% 20.05% 35000-50000 42500 15.9% 15.1% 24.15% 20.20% 50000-75000 62500 15.4% 21.5% 31.15% 23.46% 75000-100000 87500 7.7% 15.0% 33.16% 25.78% 100000-150000 125000 4.9% 13.7% 37.16% 29.14% 150000-200000 175000 1.3% 5.1% 41.16% 32.19% 200000-250000 225000 0.5% 2.5% 42.16% 34.21% 250000+ 381000 0.8% 6.7% 42.16% 35.49% Now this gives an average (weighted by income) marginal rate of 30.17% and an average effective rate of 24.61%; this works out to ~288 billion dollars. However, Canada's tax revenue is ~32.2% of GDP and GDP was ~1894 billion dollars in 2013 (http://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/econ04-eng.htm), so I'm missing ~322 billion dollars. Obviously Canadian governments have other means of obtaining tax revenue such as consumption taxes, employment insurance and corporate tax. Since these taxes are difficult to determine the distribution and affect everyone (corporate taxes reduce jobs available to poor people) I'll add 27.5% tax to each income category so that the total tax revenue is in agreement with 32.2% of GDP. I am skeptical of how correct this approximation is, but I need to use something to perform a calculation; if anyone wants to provide me with a better distribution of tax burden I will be happy to use that. Anyway, I get: Income Range: Approximate Income: % of Population: % of Total Income: Marginal Tax Rate: Effective Tax Rate: 5000- 2500 7.5% 0.4% 25.70% 25.70% 5000-10000 7500 6.7% 1.1% 25.70% 25.70% 10000-15000 12500 9.0% 2.5% 45.75% 45.75% 15000-20000 17500 9.6% 3.8% 45.75% 45.75% 20000-25000 22500 8.1% 4.1% 45.75% 45.75% 25000-35000 30000 12.7% 8.5% 45.75% 45.75% 35000-50000 42500 15.9% 15.1% 49.85% 45.90% 50000-75000 62500 15.4% 21.5% 56.85% 49.16% 75000-100000 87500 7.7% 15.0% 58.86% 51.48% 100000-150000 125000 4.9% 13.7% 62.86% 54.84% 150000-200000 175000 1.3% 5.1% 66.86% 57.89% 200000-250000 225000 0.5% 2.5% 67.86% 59.91% 250000+ 381000 0.8% 6.7% 67.86% 61.19% This works out to an average effective tax rate of 50.31% and an average marginal tax rate of 55.87%. Again, this is a rough idea of the tax burden due to all taxes, although I suspect I am underestimating 'progressivity'. Anyway, if I go back to my earlier equation that I obtained for imposing the condition that the consumer tries to maximize utility (H - L = L + T/w/(1-t)). I should point out that the t in this equation should correspond roughly to the average marginal tax rate. However, the t in my equation for revenue maximization (T = (1.5*t - 0.2595)*wL) should correspond to the average effective tax rate. So I have H = L*(2 + (1.5*te - 0.2595)/(1-tm)), where te is the effective tax rate and tm is the marginal tax rate. For Canada's average hours worked per year (1706) this gives H = 5326. So I'll use ln(1-s) + ln(2.481) - ln(1.481+t) + ln((1-t)*wL + T) + ln(5326-L) as my utility function. However, the second term is a constant, so I can drop it and simplify my utility function to: U = ln(1-s) - ln(1.481+t) + ln((1-t)*wL + T) + ln(5326-L) To be continued...

Cool, so apparently I want to both harm the poor (Cybercoma) and give them a free ride (Canada_First).