That is, if we implement a guaranteed minimum income, would inflation not eventually rise to a point where it is essentially useless? I would expect prices to be adjusted knowing people have a certain amount of money available. Any explanation would be helpful!
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$\begingroup$ "Eventually" can mean decades, and in the mean time new legislation can increase the GMI. However I'm not too sure if that's what you're asking. The answer below explains why the "wipe out" effect is not immediate. $\endgroup$– FizzMar 22, 2019 at 16:45
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I will not discuss fairness (for example employers gains versus employees gains and bargaining power) principles as you did not ask about those.
Is "crowding out" the right phrase here?
Even if inflation lessens the effect of a minimal income there may still be an effect. Imagine that there are two people, $A$ with an income of 0 $B$ with an income of 60, so total income is 60. The government issues a minimal income of 30 so $A$'s income is changed to 30, total income is changed to 90. If this has no real effect on the economy then all prices rise accordingly, that is they rise by 50% because that is by how much nominal incomes haved changed. However if you adjust for this 150% price level, $A$ still can buy goods in value of $\frac{30}{1.5} = 20$ while $B$ can buy goods in value of $\frac{60}{1.5} = 40$. So there could at least be a redistribution effect as previously $A$ could not buy anything and $B$ could buy more things.
One concern is that inflation may not be even. Only the income of poor people will be raised hence demands for goods poor people buy will rise but demand for goods consumed by rich folks will not change. As a result the poor may experience larger inflation than the well to do, making the redistribution of incomes one between only poor people. The lines between poor and well to do here are murky. If (due to inflation) a pop-tart costs \$10 then people will buy quality food unless it is even more expensive. If a pop-tart's price rises to \$1,000 people will buy caviar unless its price is also raised.
A hope of governments implementing such policies is that (aside from fairness and solidarity principles) a minimal wage will also help minimum wage earners be more financially secure. Some studies have shown that in extreme poverty you make worse decisions and are less productive simply as a result of stress. If this is indeed a main effect then a minimum wage (or a higher minimum wage) can increase overall productivity. Thus inflation will not be the only effect of the policy but also an increased number of goods will be produced.