Econ 101, Revisited

I've always been slightly bothered by the old Econ 101 equation:

(1) Y = C + I + G + X - M

and its counterpart:

(2) 0 = (I - S) + (G - T) + (X - M)

The thing that's gnawed at me is how exactly it is that savings (a decision not to spend) gets magically channeled into investment (e.g., an active decision to build a factory). Part of the answer is that if I save and don't spend, someone else must have dis-saved. But what if I chop down a tree for some firewood, sell the firewood, and save the money? I saved, but the person who bought the firewood and put it in his garage didn't dis-save! It's hard to call that investment.

Savings are really a claim on future consumption, and you can have this in three ways:

1. Ownership of the actual means of production. That corresponds to investment.
2. Ownership of the goods you want to consume. That's inventory accumulation.
3. Cash dollars. These are the portion of future production against which there are explicit claims. The government can create these dollars, which are not really liabilities of the government per se but rather of the society as a whole -- it is everyone in the society that must redeem the dollars, not just the government. Cash dollars are like goodwill in accounting -- they are a recognition today of value that will be created in the future.
   

All this points to a slight revision of the above. Equation (1) needs to have inventory accumulation (call it N) added to it. And equation (2) needs to be adjusted for cases when the government prints additional money (call monetary growth J).

So we have

(1*) Y = C + I + G + X - M + N

and

(3) G - T = J - SG

where SG is government savings, or more precisely change in publicly held government debt. The new equation (2), adjusted for money growth and inventories, then becomes:

(2*) 0 = (I + N - S) + (J - SG) + (X - M)

Personally, I find this formulation more satisfying, because there's no "magic" about how savings gets transformed into investment; inventories and money provide some wiggle room.

There's much more to be said here about the implications of expanding the money supply. But that is material for another post.