Risk tolerance and income

Food for thought: As a person's income rises, their risk tolerance increases. If the money is saved or invested, then as the risk tolerance increases, the average return on investment also increases. As the average return on investment increases, the net present value of that income also goes up. If you take the resulting net present value and tax it at a flat rate, you get something that looks an awful lot like a progressive tax system.

Likewise, if you assume that income below a certain threshold is unlikely to be saved, you end up with the standard deduction. And if you continue to calculate the NPV for an income below that threshold, you end up with a partial version of Milton Freidman's proposal for a negative income tax.

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