> The marginal utility changes from working vs not working in a BJ scenario are higher than in a BI scenario, almost by definition. Do you disagree that Utility(No Job, no money) < Utility(No job, money)?

That isn't the interesting question for a basic job. If you replace existing welfare with a basic job then the utility function for working is a binary value which asks if you want to starve to death. You can't actually say no.

But most of the basic jobs are going to be makework jobs with minimal economic value. Things that have economic utility approximately equal to (and possibly less than) sitting on your couch and watching Netflix.

The real question with the basic job is whether people will pick the makework basic job over an actually productive real job. The relevant utility function for a basic job is utility(Basic Job, $10,000) vs. utility(Real Job, $10,000), the equivalent of which for the basic income is utility(No Job, $10,000) vs. utility(Basic Income + Real Job, $20,000). But then the basic job falls on its face because people will too often choose the basic job which is easier to get, has more stability, may be easier to do, etc. The Basic Income doesn't have those problems because in that case the income from the Real Job supplements the Basic Income instead of replacing it, so you get compensated for the amount that getting a real job is worse than not getting one.

A basic income also does a much better thing in the case where people choose not to work for a private business. In the basic job case that person is digging ditches and filling them back in, whereas in the basic income case it can be taking care of their children or writing open source software or doing investigative journalism without a wealthy patron -- choices that are socially beneficial but the basic job doesn't give you.

> More words. Still no arithmetic. Why are BI proponents so averse to actually crunching numbers?

The math and the words both mean the same thing.

You want math, fine. Suppose the economy is full of Adams, Betties and Charlies in equal numbers.

In the hypothetical existing system there is a progressive income tax where you pay nothing up to $50,000 and 20% thereafter.

Adams make $20,000, pay no taxes and receive $6,000 in food/housing government assistance which the government withdraws at a rate of $.80/$1 if the Adam were to make more money.

Betties make $30,000, pay no taxes, are not eligible for any of the food/housing benefits Adams get but receive $4,000 in government college assistance which the government withdraws at a rate of $.50/$1 if the Betty were to make more money.

Charlies make $100,000, pay $10,000 in taxes (20% on everything over $50,000) and receive no government benefits.

Now we throw away the existing welfare and tax system and replace it with a $10,000/year basic income and a flat tax of 20%.

Adams make $20,000 but now receive a $10,000 BI and pay $4,000 (20% of $20K) in taxes. Their net transfers from the government are still $6,000 but now if they make another dollar the government takes 20% instead of 80%.

Betties make $30,000 but now receive a $10,000 BI and pay $6,000 (20% of $30K) in taxes. Their net transfers from the government are still $4,000 but now if they make another dollar the government takes 20% instead of 50%.

Charlies make $100,000 but now receive a $10,000 BI and pay $20,000 (20% of $100K) in taxes. Their net transfers from the government are still -$10,000 and their marginal tax rate is still 20%.