[OPE-L:3956] Dynamic value: Samuelson

From: Allin Cottrell (cottrell@wfu.edu)
Date: Wed Oct 04 2000 - 20:24:29 EDT

This is a reply to Patrick's 3951, and indirectly to Rakesh's
3953 (in that it provides a simple example of what I regard as a
dynamic analyis).

Here's an 'executive summary' of the Samuelson argument Paul C
referred to (shorn of extraneous ideological nonsense).  
The reference is to

Samuelson, P. and von Weiszacker, C. 1972. 'A new labour theory of
  value for rational planning through the use of the bourgeois profit
  rate', in The collected scientific papers of Paul A.  Samuelson,
  Vol. 3, Cambridge, Mass.: MIT Press,

which I'll refer to as SW.

The essence of theq argument can be expressed in terms of a
setup built upon Marx's ideas in the Critique of the Gotha Programme.
Let workers be paid in labour tokens (one per hour) and let the goods
in the public stores be "priced" in labour tokens.  

We want to achieve macroeconomic balance, in the sense that that the
aggregate value of the goods in the stores equals the aggregate issue
(and expenditure, ignoring saving, taxation, etc.) of labour tokens on
those goods.

We also want to get individual prices "right", in the sense that we'll
get to the best allocation of resources if we respond by producing
more of any goods in excess demand, and less of any goods in excess
supply, at those prices.

How should the rational plan prices be determined?  In a static
economy (no technical change, no growth of the workforce) it's easy:
goods should be priced at the standard Marxian values (or vertically
integrated labour coefficients, VILCs, if you prefer).  But in an
economy undergoing growth of the workforce or technical progress such
pricing will be wrong, and will fail to achieve macro balance.

Here's an illustration.  Suppose an economy produces two goods, grape
juice (G) and wine (W).  Each requires a unit labor input but grape
juice requires it one period in advance of consumption while wine
requires it two periods in advance.  To determine the plan prices,
perform the thought experiment of having the economy specialize
entirely in each of these goods in turn.


L(t) = total labor supply at time t, equal to the number of
  labor tokens issued at that time (and spent, within the same

Q(j,t) = quantity of commodity j available for consumption at
  time t, in physical units.
P(j,t) = market-clearing price of commodity j at time t, defined as
  L(t)/Q(j,t).  This price, expressed in labor-tokens per physical
  unit, balances the quantity of the commodity currently available
  against the total expenditure of tokens in the same period.
Suppose population and labor supply are growing at a compound rate g,
while production technology is static.

As of time t, given the unit labor requirements for each commodity, we

Q(G,t) = L(t-1) 
Q(W,t) = L(t-2)
P(G,t) = L(t)/Q(G,t) = L(t)/L(t-1) = (1+g)
P(W,t) = L(t)/Q(W,t) = L(t)/L(t-2) = (1+g)^2

The rational price ratio is not 1:1 (as it would be according to the
VILCs), but rather P(W,t)/P(G,t) = (1+g)^2/(1+g) = (1+g).

Here the rational prices, or "synchronised needed labor costs" in SW's
terminology, are equal to the labor contents marked up at a compound
rate of (1+g).  

  "Synchronised labor costs, as defined here, are seen to be
  interpretable as the ordinary embodied labor requirements for a
  fictitious system in which every... [input] coefficient of the
  actual system is blown up by the growth factor (1+g).  What is
  the rationale for this expansion?
  "In each time interval the population is larger, and if we make the
  assumptions that:

  "a) there is no saving,
   b) total income is equal to total labor expended,
   c) the length of the working week is unchanged,

  "then it follows that the total expenditure of income in each time
  period will be greater than the labor hours used in production during
  the previous period. This will induce an inflation of prices above
  their values." (SW, p. 313)

The case where labour-saving technical progress is proceeding at a
rate g is formally identical.  Again it calls for "marking up" the
past labour input in forming rational plan prices.  There's one twist:
with labour-saving technical progress you'd get the right prices by
using historic labour embodied rather than the VILCs computed in terms
of the current I-O matrix.

Note that a one-time improvement in technology would not call for a
divergence of rational plan prices from simple "values" -- only
a non-zero ongoing rate of technical progress does that.  This is a
case where dynamic analysis has something to tell us over and above a
static comparison of "before" and "after" a discrete technical

Allin Cottrell.

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