No expenditures means no MPC which means we're not even talking about "the same logic as the Keynesian cross" anyway, but if you take his implied MPC you get the same result: income equals income (or if you make the mistake he did, income equals 0.99999999 times income).
But my point basically boiled down to "you don't knock the Keynesian cross by saying income equals income".
Commenter Malcolm gets to the point much quicker:
"I just posted this at Landsburg. This is all "a lot about nothing":Yep.
Sigh. This is worthless
If Y = E + L and E= .999999Y then L = .000001Y then
Y-E =L means
Y(1-.999999) =L which means that
Y = L/(.000001) which means that
Y = .000001Y/.000001
and all this means is that Y=Y. Hmmm."
Some (edarniw, for example) think that my harping on the expenditure/income distinction and the MPC/income share distinction is beside the point and just adding extraneous complaints to Landsburg's post. It's not extraneous. Malcolm works out in the context of the problem why it's not extraneous and ALSO why I say that Landsburg has an implicit MPC of 1, not 0.99999999, even thought he solved the problem as if his MPC was 0.99999999.
Think of it this way: L pays E for a good or service. Some fraction of E's subsequent spending will go to L for a good or service that L produces. So L's consumption matters too, and if we're conflating income share and MPC the way Landsburg has chosen to that means MPC = 0.00000001 + 0.99999999 = 1.
Which gives you "income equals income".
Which is not any kind of argument against the Keynesian cross. It's an argument that leaves off half the Keynesian cross and any mention of investment which is the crux of the whole theory.