# Globalization and income distribution

In the past two decades we have seen both an increase in globalization and income inequality. The question is whether the two are directly or indirectly related.  The GDP of the United States is about 14 trillion dollars, which works out to be about 45 thousand per person.  However, the median household income, which is about 50 thousand dollars per household, has not increased over this time period and has even dropped a little this year. The world GDP is approximately 75 trillion dollars (in terms of purchase power parity), which is an amazingly high 11 thousand per person per year given that over a billion people live on under two dollars a day. Thus one way to explain the decline in median income is that the US worker is now competing in a world where per capita GDP has effectively been reduced by a factor of four.  However, does this also explain the concurrent increase in wealth at the top of the income distribution.

I thought I would address this question with an extremely simple income distribution model called the Pareto distribution.  It simply assumes that incomes are distributed according to a power law with a lower cutoff: $P(I) = \alpha A I^{-1-\alpha}$, for $I>L$, where $A$ is a normalization constant. Let’s say the population size is $N$ and the GDP is $G$. Hence, we have the conditions $\int_L^\infty P(I) dI = N$ and $\int_L^\infty IP(I) dI = G$.  Inserting the Pareto distribution gives the following conditions $N=AL^{-\alpha}$ and $G = \alpha N L/(1-\alpha)$, or $A = NL^\alpha$ and $L=(\alpha-1)/\alpha (G/N)$.   The Pareto distribution is thought to be valid mostly for the tail fo the income distribution so $L$ should only be thought of as an effective minimum income.  We can now calculate the income threshold for the top  1% say.  This is given by the condition $F(H) = N-\int_L^H P(I) dI = 0.01N$, which results in $(L/H)^\alpha=0.01$ or  $H = L/0.01^{1/\alpha}$. For $\alpha = 2$ then the 99 percentile income threshold is about two hundred thousand dollars, which is a little low, implying that $\alpha$ is less than two.  However, the crucial point is that $H$ scales with the average income $G/N$.  The median income would have the same scaling, which clearly goes against recent trends where median incomes have stagnated while top incomes have soared.  What this implies is that the top end obeys a different income distribution from the rest of us.

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