Hoarding: Causes and Consequences

I was having a look at "What Has Government Done to Our Money" by Rothbard, and got thinking about the problem of hoarding, or increasing one's cash balances. This may be relevant in the current economic climate if people are losing faith in the banking system and yet trying to rebuild their wealth after the excesses of a boom. This primary analysis of hoarding, however, takes place in the context of an idealised free society. These thoughts are rough and I would very much like to tighten them up. Would greatly appreciate corrections and suggestions.
To begin, recall that the supply of money means the total money stock (e.g. 3000 tonnes of gold) while the demand for money means all of the goods and services produced in exchange for money plus cash balances and money not spent.
Someone who hoards increases their cash balances, yet one may assume that their productivity remains the same. If you think about it in terms of the flow of goods and services, then what is happening is that the hoarder is continuing to supply goods and services to other people, while the share of other people's goods and services which the hoarder consumes drops in accordance with how much money they choose to retain.
The supply of labour is unchanged. The hoarder's cash balance gradually rises, while the rest of the population shares the economy's output amongst themselves. Money's purchasing power rises with the deflationary impact of the hoarder's actions. The losers are those who would otherwise have satisfied the hoarder's immediate demand for goods and services. The hoarder has chosen to transfer this demand to suppliers at some future period of time. And note that the flow of money to the hoarder, if it were to continue indefinitely with a constant supply of money, must eventually slow to a trickle. This is because of the deflationary impact of hoarding. Since prices express relative preferences for goods and services, ie. since prices are types of ratios, they must contract in proportion to the supply of money. Therefore prices paid, including those to the hoarder for his own output, must decline.
It might be instructive to compare the consequences of hoarding with the consequences of deliberately destroying all cash balances available to you. This is purely deflationary (since the money can then never be spent, not even at some point far in the future) and the result is that the person who does this is quite simply donating their share of economic output to the rest of society, to each other actor in proportion to the amount of still existent cash held by that actor.
So far there is no problem. Now imagine that there is a generalised apprehensive mood among economic agents. For some reason (suppose fear of a catastrophe), all of them want to grow their cash balances. Hoarding is intimately related to uncertainty: as Rothbard observes, if the future could be predicted with certainty, then there would be no need for cash balances at all. If any money was received it would be immediately loaned out with a guaranteed maturity at the future point when it was needed.
What happens in this scenario? The supply of money is unchanged, yet the demand for money has changed because of an increase in cash balances. The supply of goods and services produced in exchange for money is unchanged. Therefore the purchasing power of money goes up, and anybody who continues to offer the same prices as before everybody began to hoard will find that they can afford to purchase a much larger share of output. Their cash balances will dwindle because of the superior saving-to-spending ratio of the rest of the population.
Yet, if there were no exceptions and if everybody did hoard at the same rate, what effect would that have? Clearly there would be a short-term deflation, as there was with the individual hoarder. Surprisingly to me, however, in terms of the distribution of goods and services, there is no reason to expect an immediate change. Since everybody has cut back at the same rate, they will find when they go to market that they can afford to purchase the same goods and services as they could before.
What practical purpose could this possibly achieve then? Rothbard writes:
"Now, suppose, for whatever reason--perhaps growing apprehension--people's demand for cash balances increases. Surely, it is a positive social benefit to satisfy this demand. But how can it be satisfied when the total sum of cash must remain the same? Simply as follows: with people valuing cash balances more highly, the demand for money increases, and prices fall. As a result, the same total sum of cash balances now confers a higher "real" balance, i.e., it is higher in proportion to the prices of goods?to the work that money has to perform. In short, the effective cash balances of the public have increased. Conversely, a fall in the demand for cash will cause increased spending and higher prices. The public's desire for lower effective cash balances will be satisfied by the necessity for given total cash to perform more work.
Therefore, while a change in the price of money stemming from changes in supply merely alters the effectiveness of the money-unit and confers no social benefit, a fall or rise caused by a change in the demand for cash balances does yield a social benefit--for it satisfies a public desire for either a higher or lower proportion of cash balances to the work done by cash."
I would like to explore what kind of social benefit this could be. For suppose that the reason there is a greater demand for cash balances is a greater apprehension about some future event. Now if that future event - an earthquake, for example - were to strike and to hurt each person simultaneously and proportionately such that they all wished to dispose of their cash balances at that point, there appear to be some strange consequences. The inflation that would be thus caused by the arrival of everybody's cash to the marketplace would prevent any person from having a financial advantage over any other which they would not have had if nobody had chosen to hoard. Prices would rise universally!
This suggests that hoarding is only useful in this scenario if ones hoards at some kind of higher rate to other people. Hoarding less than others will cause money to flow to them, while hoarding at the average rate will yield no advantage after the catastrophe. The efficacy of hoarding is relative to the hoarding behaviour of others.
Of course, if the potential catastrophes are specific to each individual and not simultaneous, then hoarding will serve to manage the risk by allowing each person to purchase a larger share of the total economic output with their cash balances at the time when the need arises, though each such spending of savings will reverse the previous deflationary effect of that hoarder.
What about the rate of hoarding itself? Since each hoarding rate can have an equivalent effect on the distribution of goods and services, is it in some sense arbitrary? I would say that it is not, for the reason that hoarding should settle at the point which equilibrates demand for current goods with the uncertain demand for future goods. It is resolved by supposing that each person attempts to hoard at the rate of 100%. This abrupt and total deflation would permit any person to purchase any good and service, or indeed the entire output of the economy, using the smallest existing units of money. Of course by so doing they lower the rate of hoarding from 100%. This helps us to understand that as long as there is still at least some kind of underlying demand for current goods, the rate of hoarding can never reach 100%. On the other hand, if there is really no demand for current goods then exchanges will cease to take place and the rate of hoarding can reach 100%.
From the point of view of society at large, the hoarding rate serves to inform us of the scale of uncertainty and to distribute goods and services according to the relative strength of the preferences of various agents to prepare for an uncertain future.