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(Mostly) ignore money for this growth issue; it's by and large a red herring that's distracting you. Instead just think of technological progress for instance. Assume everyone is washing their clothes by hand. That takes a fair bit of time. Now someone invents a washing machine. Everyone (who can get a washing machine) will then have more time on their ...

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The short answer is that money is not the same wealth. You yourself probably have less money than the value of all the stuff you own. When the economy grows the total amount of wealth grows. (This is usually also accompanied by growth of money, but that is a separate matter.)

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A random variable $X$ has a Pareto distribution with Pareto exponent $\theta$ if $$\text{P}(X>x)=\begin{cases} \left(\frac{x}{x_m}\right)^\theta \quad \text{ if } x\geq x_{min}\\ \ \ 1 \quad \quad \quad \text{ if } x<x_{min} \end{cases}$$ In this case, the Pareto exponent is $\theta = \alpha - 1$. Remember that \$P(X>x)=\int_x^\infty p(x')\...

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