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Still, I would not call allocative efficiency a form of "equality". I do believe a free and educated society will produce more equality based on human nature. However, even if it were to produce huge disparities, we would still have to accept that. Thus, equality was not the true aim, but rather justice.
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<p>Ah, but if the allocation were just, what we should see is a sort of normal distribution, because statistically speaking, the least productive and the most productive individuals inherently occur in equal probabilities in society, and most of the income should reside in the middle, not in the rich, deserving as each individual might be, they are simply not as numerous.</p>
<p>The point is to allocate proportionately to contribution (accounting for the fact that eventually it's cheaper to pay someone else for that same ounce of contribution than to keep extracting it from the most capable individual). Ideally, poverty should be residual, like the natural rate of unemployment -- there is a natural inequality in how talent (and therefore contributive ability) is distributed, along the normal distribution curve, that will always be there. There will be occasional inequality on top of this because one entrepreneur will have discovered something before an equally deserving entrepreneur discovers something else, facilitating a sort of advancing race. </p>
<p>But this is not what we see -- in this case we see a distribution heavily skewed towards the rich. Technically, the most capable deserve more, but the most capable also are less numerous compared to the general population. Mathematically speaking (after creating our dear density function which has the exponential function e in it because of the whole idea of dividing the quantification of ability up into infinite parts and allocating each infinitesimal piece based on probability -- yay for probability and calculus!) we should get a normal distribution of income. </p>
<p>But this isn't case because it so happens that those with higher incomes have a greater ability to self-actualise, so the abilities of society increase at a non-constant rate as a sort of differential equation. Technically, the abilities of each poor individual should increase as society's technology and knowledge progresses -- but it's not actualised because he has received no capital that would allow him to realise it.</p>
<p>This forms the theoretical basis for the equivalent of redistribution of income, because those individuals are performing below efficiency. (Of course this redistribution must not occur top-down, but grassroots-up, because the State is mightily inaccurate at knowing how much to reallocate). Eventually there comes a point where even the growth of the top echelons lag because of the ceiling posed by having failed to allocate to the lower class. </p>
<p>The other important element of an economy besides self-interest is the learning economy principle, which I am saddened to find has not been implemented in the AP exams. No one has perfect information (or else we might as well implement a planned economy) and the reason why firms might not even see there is economic profit in subsidising the poor (or by investing in African education, for example) is because they haven't the foresight or the "lesson". </p>
<p>I really dislike how the AP micro exam teaches market failure correction so conveniently -- what it's missing is the learning principle. Externality occurs in production and consumption of X. If X is demand-elastic, impose tax Y to compensate, for the costs will go to the suppliers! But gee, if you knew how much Y to impose, mightn't you as well plan the entire economy???</p>