# the argument from dynamics

#./dynamic.tex# Does Hayek's concentration on the dynamic aspect of prices, price as a means of dynamically transmitting information, make any sense?

In one way it does. Consider the price of a cup of coffee. Notionally this can be written in a couple of digits---80 pence, say---which would imply that on information theoretic grounds it transmits about 7 bits of information. But look more closely, and this is almost certainly an overestimate. Not only is the price likely to be rounded up to the nearest 5 pence, implying an information content of about 5 bits, but yesterday's price was probably the same. If the price changes only once a year, then for 364 days the only information that it conveys is that the price has not changed. The information content of this, #math30##tex2html_wrap_inline735#, is about #tex2html_wrap_inline737# of a bit. Then when the price does change its information content is #math31##tex2html_wrap_inline739# where #tex2html_wrap_inline741# is the number of bits to encode the price increase. For a reasonable value of the increase, say 10 pence, the whole amounts to some 12 bits. So on the day the price changes, it conveys some 3000 times as much information as it did every other day of the year.

So it is almost certainly true that most of the information in a price series is encoded in the price changes. From the standpoint of someone observing and reacting to prices, the changes are all important. But this is a viewpoint internal to the dynamics of the market system. One has to ask if the information thus conveyed has a more general import. The price changes experienced by a firm in a market economy can arise from many different causes, but we have to consider which of these represent information that is independent of the social form of production.

We can divide the changes into those that are direct results of events external to the price system, and those which are internal to the system. The discovery of new oil reserves or an increase in the birth rate would directly impinge upon the price of oil or of baby clothes. These represent changes in the needs or production capabilities of society, and any system of economic regulation should have means of responding to them. On the other side, we must count a fall in the price of acrylic feedstocks and a fall in the price of acrylic sweaters, among the second- and third-order internally generated changes consequent upon a fall in oil prices. In the same category would go the rise in house prices that follows an expansion of credit, any fluctuation in share prices, or the general fall in prices that marks the onset of a recession. These are all changes generated by the internal dynamics of a market system, and as such irrelevant to the consideration of non-market economies.

Hayek is of course right that the planning problem is greatly simplified if there are no changes, but it does not follow from this that all the changes of a market economy are potential problems for a planned one. We have demonstrated elsewhere that the problem of computing the appropriate intensities of operation of all production processes, given a fully disagregated input--output matrix and a target final output vector, is well within the capacity of computer technology. The compute time required is sufficiently short for a planning authority, should it so wish, to be able to perform the operation on a daily basis. In performing this calculation the planners arrive at the various scales of production that the market economy would operate at were it able to attain general equilibrium. Faced with an exogenous change, the planners can compute the new equilibrium position and issue directives to production units to move directly to it. This direct move will involve the physical movement of goods, laying of foundations, fitting out of buildings etc, and will therefore take some considerable time.

We now have two times, the time of <#732#>calculation<#732#> and the time of <#733#>physical adjustment<#733#>. If we assume that the calculation is performed with an iterative algorithm, we find that in practice it will converge acceptably within a dozen iterations. Since each of these iterations would take a few minutes on a supercomputer the overall time would probably be under an hour. In a market economy, even making the most favourable assumptions about its ability to adjust stably to equilibrium, the individual iterations will take a time proportional to the physical adjustment time. The overall relaxation period would be around a dozen times as long as that in the planned system.

But of course these assumptions are unrealistically favourable to the market system. Long before equilibrium was reached, new external shocks would have occurred. Even the assumption that the system seeks equilibrium is questionable. There is every reason to believe that far from having stable dynamics, it is liable to oscillatory or chaotic behaviours.

Hayek is to be commended on his ability to make the best of a bad case, to make virtues out of necessities. The unavoidable instabilities of the market are disguised as blessings. The very crudity of prices as an information mechanism are seen as providentially protecting people from information overload. #./dynamic.tex#