The main issue I take with your post is this: If the size of the economy increases faster than the increase in the money supply...
With more consumption and less investment, we expect the economy to increase more slowly than in the counterfactual (no BI). So holding money supply constant (which is of course ridiculous), we'd expect more inflation in the BI scenario than the no BI scenario.
The real question here, which is more or less unrelated to inflation: why do we want to shift resources from investment to consumption? Do we have a high discount rate and basically not care about the future?
(If we do have a high discount rate, we should probably shift resources away from long term issues like climate change, education, scientific research.)
Yes, I agree that it seems like there would be more inflation with BI than without it, though, as I said, that will be irrelevant in policy terms as long as the inflation doesn't exceed the BI cash injection. Presumably the level of BI would be tailored to compensate for projected inflation.
> The real question here, which is more or less unrelated to inflation: why do we want to shift resources from investment to consumption? Do we have a high discount rate and basically not care about the future?
I think the answer to this question comes from the fact that BI is a policy designed to alter the distribution of wealth, rather than the overall level of wealth. You might be keeping the same overall discount rate, but adjusting the distribution of rates across society: increasing it for the poorest in society, and decreasing it for the richest, for no net change. There would, therefore, be no change in the handling of long-term issues.
The issue here is not distribution of wealth, it's consumption. The more we consume now, the less we invest in the future. Do you disagree that BI will increase consumption?
Concretely, we could invest in reducing CO2 emissions, building Tesla factories or developing Tinder for Dogs. Alternatively, we could continue emitting CO2, skip the new Tesla factory and instead just ramp up production in the old Toyota factory, and continue producing goods for poor people to consume.
BI pushes us toward the latter alternative. Why should we favor this?
The point of BI is to redistribute consumption to the lower end of the economic distribution, at the expense of the higher end, not to increase overall consumption, though that might happen as a side effect.
The net increase in consumption minus the net productivity gains will be the cost of BI, paid to increase economic equality. However, I have seen quite a few (in fact I would say most) proponents of BI argue that the "cost" will be negative, that the productivity gains will, overall, exceed the increase in consumption.
A basis for this claim is that the marginal return on consumption for poorer people is higher than for richer people, and so they can more efficiently use the redistributed consumption, leading to higher overall productivity. The issue of consumption is, therefore, only half of the argument, and must always be considered in tandem with productivity.
The answer to your final question in this context is that we should favour BI because it is intended to increase net productivity at the same time as increasing consumption on the low end: we will have our cake and eat it.
Putting aside the question of whether a basic income would actually shift resources from investment to consumption, there is a very simple way to offset it. Raise the money using a consumption tax (ideally VAT).
Also, the increase in consumption, from basic income, and hence any direct inflationary effect, is bounded by the level of basic income. For basic income to be worthless the level of inflation on the goods bought by those who are the prime targets of basic income (i.e. the poor) would have to match or exceed the additional cash obtained through the basic income. Inflation in goods and services mostly bought by the rich, due to increased wage pressures, are basically (ho ho) irrelevant.
What is required is an argument as to why the inflation on the price of the relevant goods would be higher than the level of the basic income being used to pay for those goods.