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June 8, 2014 Proof of Thomas Piketty’s Thesis Enrique Woll Battistini 2014 Piketty’s Thesis simplified: “When the return on Capital is greater than the growth of the economy, economic inequality will increase. In many countries, Piketty argues, capital (which he equates with wealth in the form of real estate, financial assets, etc.) is growing at a faster rate than the economy. The income produced by capital tends to be concentrated in the hands of a small group of people, whereas income from labor is dispersed throughout the entire population. Therefore, when capital earnings increase faster than wages, inequality grows because those who own capital accumulate a higher proportion of income. And given that growth in wages is directly dependent on the growth of the economy as a whole, economic inequality is bound to get worse if the economy expands at a slower clip than capital earnings. http://www.theatlantic.com/international/archive/2014/05/the-problem-with-pikettys-inequality-formula/371653/ ” If the GNP of a given economy at a macro level were defined as the sum of income flows to Capital, C, and income flows to Labor, L, then: GNP = C + L Therefore d(GNP) = d(C + L) dt dt And given that d(C + L) = dC + dL dt dt dt And taking the growth of the GNP to be less than the growth of Capital as an axiomatic and sine qua non truth for Capitalism to exist as it does, and evident to all, and widely empirically verified: d(GNP) < dC dt dt Then dC + dL < dC dt dt dt Therefore dL < 0 dt And Thomas Pikkety’s thesis of growing inequality is proven at the macro level, between classes, the Capitalists and the Laborers. However, this says nothing about individual inequality. And therefore, given that Cp, the Capitalist population, is smaller than the Lp, the Laborers population, inequality between classes, the Capitalists and the Laborers, or inequality at the micro or per capita level would require that: C <> L Cp Lp Now, also taking as an axiomatic and sine qua non truth for Capitalism to exist as it does, and evident to all, and widely empirically verified is the fact that: C > L Cp Lp Which establishes the basic bounds for Thomas Pikkety’s thesis. Finally, this says nothing about the effects of corruption, to which Pikkety rightly attributes a major share of the blame for economic inequality between classes, at the individual level, as above. Clearly, corruption can have a multiplier effect on C, MC, and a multiplier effect on L, ML, which can be factored in as follows: MCC > L MLCp Lp Which establishes the complex bounds for Thomas Pikkety’s thesis ***