How much inflation will changes to official wage benchmarks cause? For example, right now Livable Wage hovers around \$20 an hour. That's around \$40,000 a year.

Let's say the US somehow will give \$50,000 a year as a "Guaranteed basic income". 

How high will the "Livable Wage" go?
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From Investopedia



  Inflation is the rate at which the general level of prices for goods and services is rising and, consequently, the purchasing power of currency is falling. Central banks attempt to limit inflation, and avoid deflation, in order to keep the economy running smoothly.


The Consumer Price Index (CPI) is your best measure of inflation which is (put simply) the change in cost of a representative basket of goods. Each country measures this in a slightly different way.

If you are looking for a numerical increase in inflation, you'll be disappointed. A Basic Income has quite a few effects making this difficult to model. There are anticipated significant impacts on labour/leisure as well as consumption bundles. Also, inflation itself is difficult to model. To make things worse, many reserve banks target inflation with their monetary policy. So you're unlikely to ever get any empirical evidence as well.

Anyway:

Why would increasing income of lower income earners have an inflationary impact at all?

An increase in welfare should result in higher incomes. Higher income leads to higher consumption (or quantity demanded) which should lead to an increase in prices. But, this is only a one-off increase, not an ongoing source of inflation. I would be hesitant to call this inflation and would prefer to call it a permanent demand shock.

Unfortunately, I am not aware of any estimates of this impact but I would expect it the long term impact quite small. The higher the basic income, the greater the impact.

Also worth noting:

I can't think why this would be any more inflationary than any other form of welfare.