The IS curve is upward sloping and the LM curve is vertical.
I balked at first, particularly over this line: "We all know that firms have a strong incentive to invest in a boom and not invest in a recession. And we know this is what they do. So we know that mpc+mpi>1 is a very plausible assumption, and one that fits the facts. So why don't we want to believe it?
...Because mpc+mpi>1 makes equilibrium in the Keynesian Cross model unstable, and we don't like an unstable equilibrium, so we make the Keynesian Cross equilibrium stable by assuming mpc+mpi<1, and then use it to teach where the IS curve comes from. And mpc+mpi<1 gives us a downward-sloping IS curve."
The bolded line bothered me. I hate just-so stories about why economists think what they think. Things like "economists like the math to be pretty and that explains neoclassicism" or "economists like to please their overlords and that explains Keynesianism". It's lazy, sloppy analysis that is really just thinly veiled criticism.
And I wanted to say to Nick "it's not just that we 'don't like' unstable equilibrium - it's that the sort of equilibrium that this implies doesn't happen in the world we observe, so why should we believe that sort of unstable equilibrium?"
But I've warmed to this particular instability. After all, why - in the more stable Kenyesian IS-LM world - aren't we constantly underemployed? It's been refered to as "full employment by accident" but we seem to do OK a lot of the time. Why?
Innovation and progress.
An IS curve - because of the scientific method, population growth, creative destruction, and the division of labor - is constantly moving to the right.
After that I was more comfortable with Nick's post. An unstable equilibrium with curves that have a tendency to shift right is a less bothersome sort of unstable equilibrium. What economists "like" and "don't like" has less to do with it, I think.