[OPE-L:6903] [OPE-L:393] Macroeconomics equilibrium structure

Gerald Levy (glevy@pratt.edu)
Sat, 12 Dec 1998 01:42:18 -0500 (EST)

Emilio Josť Chaves <chavesej@hotmail.com> asked me to forward this message
to OPE-L for consideration. The following is a revised, and less lengthy
and technical, version of a paper Emilio gave at the Marx II conference
in Paris last Fall. / In solidarity, Jerry


Macroeconomics equilibrium structure

by Emilio J. Chaves, october 1998
1. Abstract
An alternative macroeconomics equilibrium is proposed. It includes a
brief development of theory, a numerical example from UN-1953, and short
comments. It is intended to promote debate inside OPE-L members.
2. Antecedents and Objective
>From a former reading of OPE-L debates, Alan Freeman brings some
numerical examples of 2-sector economies to defend his TSS (Temporal
Single System) vs. the "symultaneous" solution. Freeman's examples were
qualified as outside real economies -with good reasons-. However there
is a valid question behind the point: What are the conditions that
permit to propose an imaginary example so it keeps analogy with real
economics? To answer it is the same as to explain inner macroeconomics
This paper is an attempt in that goal, from an heterodox view, based on
Marx concept of surplus and exploitation, but not in his LTV (labor
theory value). It only employs market prices, it has been applied with
succes to input-output national accounts in spite of the flaws of this
accounting method.
3. National Accounts and Equilibrium
Here, Say's equilibrium is accepted in the following sense: even though
productive and economic life change everyday, there is an internal
balance in the final accounts of a long period that express the 'average
dynamics' during it. It is like a byke cyclist in a one year trip:
sometimes velocity is slow or fast, othertimes is zero, othertimes he
rides backwards, etc, but after aggregating all this, we may determine
the total net vector of his annual movement, and average speed. In other
words, equilibrium in balance does not exclude desequilibrium moments
that accompany change. This is part of real life of firms whose
accounting balances does not imply equal structure in all months, nor in
different sectors, departments or products.

4. Theory Applied - Short demonstration
In any firm with subindex "i" let's call the following variables:
Ni = (Non-labor costs, instead of the normal C for capital costs
transfered to the product, to stress its flow essence).
Li = (Labor costs paid to workers)
Qi = Ni+Li (Total Cost for producer)
Yi = Ni + Li + Si (Total incomes)
Si = Yi-Qi (Total Ganance, or Surplus obtained by proprietors).
Ai = Vi + Gi (Aggregated value, created only by human activity).

When several sectors are aggregated we use the same letters without
subindex "i".

In national accounts, the following additions take place:
Zigma(Ai) = Y (Total of aggregated-values = national income)
Zigma(Yi) = GNP (Total of incomes = gross national product)
L, S, N express the net addition of particular components.

Here comes the hardest premise: At national context, the total cost
equals the national income, because what is produced with the cost of
human activity is what is finally distributed. This deserves further
discussion, but not here -just assume it for the moment-. So:
Q = Y then
N+L = L+S so:
N = S (It says that total non-labor costs equals total surplus!!)

GNP = N + L + S so,
GNP = S + L + S (Given that Y = L+S):
GNP = S + Y (Dividing by Y, and calling a=GNP/Y):
a = S/Y + 1
S = (a-1).Y [1] From it we can derive other relations:
L = (2-a).Y [2]
GNP = a.Y [3]
p=S/L = (a-1)/(2-a) [4] Surplus rate
a = (2p+1)/(p+1) [5] "a" as function of "p"

If we define the rate of profit as
r = S/(S+L) = S/Y [6] we get:
r = a-1 [7] Replace [5] in [7] and you will get [6]

This seven equations resume the alternative theory propposed, based in
aggregations of real prices. It is a marxist hybrid system. Additional
comments are silenced, for now. Now let's see some 'imaginary examples'.

5. Example from UN Input-Output Table (1947):

This is a 3 sectors economy: agriculture, industry, services:

A................. B.... C.... D.....E
.................. AGRIC.INDUS...SERVI...TOTAL
2. INDUSTRY INPUTS TO 10 40 5 55
3. SERVICE INPUTS TO 10 10 10 30
4. N = 1+2+3...... 25 80 15 120
5. L = LABOR...... 40 40 75 155
6. COSTS= 4+5..... 65 120 90 275
7. INTERESTS........... 5 5 10 20
8. CAPITAL RENTS... 15 5 5 25
9. PROFITS........ 15 20 40 75
10.Surplus=7+8+9.. 35 30 55 120
A=Aggregated Value
11. Aggr.Value=10+5.... 75 70 130 275
12. BRUTE PRODUCTION... 100 150 145 395

Table 2: SUMMARY
A................. B C D E
.................. AGRIC.INDUS..SERVI.....TOTAL
4. N =........... 25 80 15 120
5. L = LABOR..... 40 40 75 155
6. COSTOS= 4+5... 65 120 90 275
10. SURPLUS....... 35 30 55 120
11. AGGR.VALUE=10+5.... 75 70 130 275
12. BRUTE PRODUCTION... 100 150 145 395

Let's check:
a. Total cost = Income [E6]=[E11] =275
b. Total N = Total S [E4]=[E10] =120
Now, please take a calculator and check the following:
c. Parameter 'a':
GNP = a.Y [3]
[E11] / [E5] = 395/275 = 1.436363636

b. Surplus rate from a:
p = (a* - 1 )/( 2 - a* )= (1.436363636-1)/(2- 1.436363636) p =
c. Surplus rate from S/L
[E9] / [E6]= 120/155 = .774193548
d. Total surplus from S = (a-1).Y
(1.436363636-1) x 275 = 120
e. Total labor from L = (2-a).Y (2 - 1.436363636) x 275 = 155
f. GNP from GNP = 2S + L
155 + (2 x 120) =395

6.0 Conclussions
6.1 Previous calculations express the equilibrium relationships of a
balanced economy in price markets without LVT, without
productive-unproductive labor considerations, without value-price
conversion problems.
6.2 Examples of global economies, even of two sectors, can not be
created by random procedures because they normally do not conduce to a
valid example. This was not known by Marx: we can not blame on him.
6.3 Situation gets worse if we deny Say's supply-demand equilibrium, or
when we add strange premises for mathematical convenience to solve our
6.4 Allan Freeman examples are valuable because they promote civilized
debate and good thinking. Obviously, they do not match with the theory
here exposed.
6.5 I invite to study this short paper and to make your comments and
critics to it inside OPE-L, so I can read it from outside.
6.6 There are other matching examples with colombian NIPAs, but they
carry on several complexities to be avoided at this point.
6.7 If this theory has "scientific merit" it may bring hard consequences
on Marx's Falling Tendence of Profit Rates, on the relevance of organic
composition as an analytical tool, and other points.
6.8 The author admires Marx the most, but he reserves the right to doubt
about some parts of his collosal job.
Cordial brotherhood for all of you,
Emilio Josť Chaves M.
Pasto, december 11th, 1998

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