Our strategy is first to consider the dynamic problem of how fast, and with what communications overhead, an economy can converge on equilibrium. We will demonstrate that this can be done faster and at less communications cost by the planned system. We consider initially the dynamics of convergence on a fixed target, since the control system with the faster impulse response will also be faster at tracking a moving target.

Consider an economy **U**<#370#> is the commodity flow
matrix and <#371#>**p**<#371#> a price vector.
We will assume, as is the case in commercial arithmetic,
that all quantities are expressed to some finite precision
rather than being real numbers. How much information is required to
specify this equilibrium point?

Assuming that we have some efficient binary encoding method and
that

Let **A**<#375#> and an intensity vector

where **
A**<#380#> and some

As the economy nears equilibrium the conditional
information required to specify it will shrink, since ^{6}
Intuitively we only have to supply the
difference vector between the two, and this will require less and less
information to encode, the smaller the distance between

We now construct a model of the amount of information that
has to be transmitted between the producers of a market
economy in order to move it towards equilibrium. We make the
simplifying assumptions that all production process take one timestep to
operate, and that the whole process evolves synchronously. We
assume the process starts just after production has finished, with the
economy in some random non-equilibrium state. We further assume
that each firm starts out with a given selling price for its product.
Each firm

<#429#>

- It writes to all its suppliers asking them their current prices.
- It replies to all price requests that it gets, quoting its current
price
#tex2html_wrap_inline520#. - It opens and reads all price quotes from its suppliers.
- It estimates its current per-unit cost of production.
- It calculates the anticipated profitability of production.
- If this is above
#tex2html_wrap_inline522# it increases its target production rate #tex2html_wrap_inline524# by some fraction. If profitability is below #tex2html_wrap_inline526# a proportionate reduction is made. - It now calculates how much of each input
#tex2html_wrap_inline528# is required to sustain that production. - It sends off to each of its suppliers
#tex2html_wrap_inline530#, an order for amount #tex2html_wrap_inline532# of their product. - It opens all orders that it has received and
- totals them up.
- If the total is greater than the available product it scales down each order proportionately to ensure that what it can supply is fairly distributed among its customers.
- It dispatches the (partially) filled orders to its customers.
- If it has no remaining stocks it increases its selling price by some increasing function of the level of excess orders, while if it has stocks left over it reduces its price by some increasing function of the remaining stock.

- It receives all deliveries of inputs and determines at what scale it can actually proceed with production.
- It commences production for the next period.

Experience with computer models of this type of system
indicates that if the readiness of producers to change prices is too
great, the system could be grossly unstable. We will assume that the
price changes are sufficiently small to ensure that only
damped oscillations occur. The condition for movement towards
equilibrium is then that over a sufficiently large ensemble of points

where

We are now in a position to express the communications costs of
reducing the conditional entropy of the economy to some level

Letters through the mail contain much redundant pro
forma information: we will assume that this is eliminated and the
messages reduced to their bare essentials. The whole of the pro
forma will be treated as a single symbol in a limited alphabet of
message types. A request for a quote would thus be the pair

If we assume that each of

Let us now contrast this with what would be required in a planned economy. Here the procedure involves two distinct procedures, that followed by the (state-owned) firm and that followed by the planning bureau. The firms do the following:

<#432#>

- In the first time period:
- They send to the planners a message listing their address, their technical input coefficients and their current output stocks.
- They receive instructions from the planners about how much of each of their output is to be sent to each of their users.
- They send the goods with appropriate dispatch notes to their users.
- They receive goods inward, read the dispatch notes and calculate their new production level.
- They commence production.

- They then repeatedly perform the same sequence replacing
step 1a with:
- They send to the planners a message giving their current output stocks.

The planning bureau performs the complementary procedure:

<#433#>

- In the first period:
- They read the details of stocks and technical coefficients from all of their producers.
- They compute the equilibrium point
#tex2html_wrap_inline596# from technical coeffients and the final demand. - They compute a turnpike path (Dorfman, Samuelson and Solow, 1958) from the current output structure to the equilibrium output structure.
- They send out for firms to make deliveries consistent with moving along that path.

- In the second and subsequent periods:
- They read messages giving the extent to which output targets have been met.
- They compute a turnpike path from the current output structure to the equilibrium output structure.
- They send out for firms to make deliveries consistent with moving along that path.

We assume that with computer technology the steps b and c can be undertaken in a time that is small relative to the production period (Cockshott 1990, Cockshott and Cottrell 1993).

Comparing the repsective information flows, it is clear that the
number of orders and dispatch notes sent per iteration
is invariant between the two modes of
organisation of production. The only difference is that in the planned
case the orders come from the center whereas in the market they
come from the customers. These messages will again account for a
communications load of

The difference comes on subsequent iterations, where, assuming no
technical change, there is no need to update the planners' record of
the technology matrix. On

The consequence is that, contrary to Hayek's claims, the amount of information that would have to be transmitted in a planned system is substantially lower than for a market system. The centralised gathering of information is less onerous than the commercial correspondence required by the market. In addition, the convergence time of the market system is slower. The implication of faster convergence for adaptation to changing rather than stable conditions of production and consumption are obvious.

In addition, it should be noted that in our model for the market, we have ignored
any information that has to be sent around the system in order to make
payments. In practice, with the sending of invoices, cheques, receipts,
clearing of cheques etc., the information flow in the market system is
likely to be twice as high as our estimates.
The higher communications overheads of market economies are
reflected in the numbers of office workers they employ,
which in turn leaves its mark on the architecture of cities---