It really depends whether you’re interested in tracing the real savings or the money savings. In the case of money savings and, if you regard hoarding as savings, of course it’s impossible for savings to equal investment when people are putting a bunch of savings under their mattresses. If you are interested in tracing the real savings instead, and you regard hoarding as savings, it’s possible for savings to equal investment but very very very unlikely (it would require ALL of the additional purchasing power that comes about as a result of the hoarder taking money out of the economy, and the subsequent fall in prices, to be transfered to investors… in reality a certain portion of that purchasing power is almost certain to be transfered to consumers as well as investors).
If, on the other hand, like Giles appears to be doing you choose instead to define savings as investment then the answer is quite straight forward.
Again, this depends on whether you are interested in tracking real savings or monetary savings. However in both cases I think it’s fair to say that banks will be able to increase the loan volumes under a fractional reserve system and loans will be made to ever more marginal borrowers… so a greater amount of investment will be undertaken at the beginning of the business cycle. However a greater amount of consumption will also be undertaken (in view of the fact that interest rates will be low and so there will be a lack of incentive to save). You essentially have a level of consumption + investment which exceeds the total production of the economy and so you will, temporarily, have a level of investment which exceeds the amount of savings.
This is a peculiar situation and the additional savings must either come from abroad (by borrowing) or by way of cannibilizing capital… both of which have occured more recently in the US with private and public debt rising whilst Mortgage Equity Withdrawls were used to facilitate the cannibilization of capital. Obviously, such a situation cannot persist indefinitely, however, and later on in the business cycle you’re going to get a bust during which investment and consumption combined must necessarily fall short of the total production and thus in which investment will be vastly inferior to savings… this is the price that must be paid for having tried to step outside the Production Possibilities Frontier earlier on.
Again, think carefully about whether you are interested in tracing real resources (and real savings) or dollar notes. The effects in both cases will not necessarily be the same.
For cash, yeah. While it’s in their wallet you’re not sure whether it will be converted into consumption or investment - this you can only know at the time the money is spent.
As Hazlitt pointed out though, the amount of money that is held in cash at any one time is ordinarily so trivial that it barely warrants atttention. It is only in very extreme circumstances that the proportion of people’s savings that they elect to keep on hand as cash will rise to any significant level. When you try to think about the consequences of them doing this, I would urge you to make a concerted effort to separate out the effects of this action (hoarding as the Keynesians call it) on money and its affects on the use of real resources/savings… since the two effects will be quite different.
I tend to focus on the real savings since, for the most part, I think the money is just a side show. It certainly has it’s place and it is an important place to the extent that it communicates price signals (both horizontally and vertically within the capital structure). But the ultimate goals of actors in the economy (whether they are aware of it or not) concern real goods and services with the money as just a stepping stone for obtaining what they want indirectly. As such, much more important than money savings, to my mind, are real savings.