The Structure of a Mark II Economy

The Mark
II Economy has five sectors, namely, (i) agriculture, A, which produces
agricultural units (AU), (ii) manufacturing, M, which produces manufacturing
units (MU), (iii) transportation, T, which provides transportation units (TU),
(iv) energy, E, which sells energy units (EU) produced by Nature, and (v)
commercial, C, which produces nothing. All economic transactions take
place by passing through the commercial sector, which, in the no-commerce
cases, functions instead as the automatic collector of sufficient funds that
furloughed workers can continue to be paid according to their needs which may
or may not be reduced to a fixed fraction of the needs of employed
workers. The variable θ_{i}, i = A, R, M, T, multiplies the
consumption of the four commodities for each of the furloughed sectors C_{F},
M_{F}, T_{F}, and E_{F}. Its current values are
1, 1, 1, and 0.5 for transportation as daily commutes consume a large portion
of our personal energy budgets normally. The units are generalized units
that refer to relative magnitude only, therefore fractional units can be
used. An energy unit represents an arbitrary quantity of energy; or, for
that matter, any quantity whatever that plays the role that energy plays in
human economies.

Originally, the entire economy was supposed to have been populated by 200 people with half employed and half unemployed. Each unemployed person was to be supported by an employed person with whom he or she shared a residence. But, instead of people, think of generalized population units that could represent any number of people; therefore, we may employ fractional units.

The population of each sector is further divided into labor, L,
90% and management, M, 10%. According to Table 3.2 in http://tinyurl.com/r4wyr,
after taxes and government subsidies, the top 10% earned 31% of the income;
therefore, I computed that, to match that figure, management should consume
6.052 times as many MUs and RUs as labor but just the same number of AUs and
TUs. This is reflected in the spreadsheets by the components of κ_{i},
i = A, R, M, T, which are (1,1.5051,1.5051,1) in the Base Case and No-Commerce
Case and (1,1,1,1) in the No-Manager Case and No-Commerce-No-Managers
Case. The user can alter these figures easily.

Finally, the workers and managers of each sector are divided into
those retained (M_{W} for working manufacturing people) and those
furloughed (M_{F} for furloughed manufacturing people) according to the
variables z_{i}, i = C, A, M, T, E, which determine the fraction of the
stakeholders of any sector who are on active duty at any one time,
according to the principle that the production per worker for M_{W}, T_{W},
E_{W} remain constant regardless of political economy. (Of
course, instead of furloughing workers, each could work shorter hours to meet
the required production but with less production per worker in the more
efficient political economies. The shortened work week is now reported in
both spreadsheets instead of percent furloughed.)

This model neglects banking and government. Each sector is taken to be a monopoly that pays its workers enough to live and takes enough of its cash flow to do so. Thus, the payroll of each sector is balanced by adjusting simultaneously the fractions retained by the sectors to pay people. The exact algorithm for converging each spreadsheet using macros will be given in an appendix in later versions of this essay.

The workers’ per capita consumption of the four commodities
η_{i }: i = A, R, M, T, is held constant throughout all
experiments on all four political economies for which the spreadsheet is
prepared. The Base Case (BC) corresponds to a market economy that
tolerates a managerial class which consumes over six times the number of
residential units and over six times the number of manufacturing units that
workers consume but the same number of agricultural units and transportation
units. This is an idealization of an American-style market economy.
The No-Managers Case is an idealization of a market economy in which there is
no distinguished managerial class; therefore, all people consume the same
amount as workers whether they work or not. If we wish to stretch a
point, we may consider this to be an idealization of the Chinese system.
The No-Commerce Case can be imagined to correspond to the Soviet system in
which the economy is planned at no cost to the other sectors; however, a
commissar class retains the same privileges as did the managerial class in the
Base Case. The No-Commerce-No-Managers Case (NCNM) corresponds to the
natural economy advocated in *On the Preservation of Species*,
“Energy in a
Natural Economy”, “On the
Conservation-within-Capitalism Scenario”, and “The Demise
of Business as Usual” all of which are hyperlinked to http://www.dematerialism.net/.
The lowest energy budget consistent with the standard consumption for workers
(η_{i }= constant for all i) is that of the natural economy;
therefore, according to Fermat’s Principle whereby the actual trajectory of a
physical system corresponds to the virtual trajectory with the minimum energy,
the natural economy should be the stable outcome of political change.

The eighteen variables (δ_{ij }: i = A, R, M, T, E,
C; j = M, T, E) that determine the number of units of commodity *j* that
must be expended to produce one unit of commodity *i* are held constant;
whereas, the eighteen variables (f_{ij} : i = A, R, M, T, E, C; j = M,
T, E) that determine how the overhead portions of the net cash are divided up
among the manufacturing sector, the transportation sector, and the energy
sector are determined from the δ_{ij}. The sum of the of the
three f_{ij }for j = A, R, and C must equal 1.0 because the sum of the
cash distributions to the manufacturing, transportation, and energy sectors by
the commercial sector – or the economic plan – must equal the total net cash
available after salaries of the commercial workers and other non-producers and
the overhead costs of operating the market have been withdrawn; and, the sum of
the two f_{ij} such that *i* not equal to *j* must equal 1.0
for j = M, T, and E since these sectors are monopolies and do not have to pay
themselves. The equations that relate δ_{ij} and f_{ij }will
be shown in Appendix B in a later version of this paper.

The prices of the commodities, p_{i}, i = A, R, M, T, E,
C, and the fractions retained in each sector to pay workers and managers, x_{j},
j = C, A, M, T, E, appear as ancillary parameters in the equations that relate
the f_{ij }with the δ_{ij}. The homogeneous (in the
p_{i}) constraint equations for the f_{ij} determine the six p_{i},
i = A, R, M, T, C, given p_{E} = 1; the cash balances between salaries
and expenses determine the x_{j}, j = C_{F}, C_{W}, A_{F},
A_{W}, M_{F}, M_{W}, T_{F}, T_{W}, E_{F},
E_{W}; the equality of x_{A}, x_{M}, x_{T}, and
x_{E} – to keep x_{i} between zero and one – determines the
fractions of the population associated with each sector, π_{i,} i*
*= A,M,T,E, subject to the sum of the π_{i }equal to 1.0 with
π_{C} fixed; and, holding production of consumable commodities per
employee of the manufacturing, transportation, and energy sectors constant for
all four cases determines the fractions of employees, z_{i} i = M,T,E,
on active duty. No furloughs are available in the agricultural sector,
and the entire commercial sector is either on active duty or furloughed
depending upon the case studied.

Early on, the great difficulty in converging the spreadsheet was
that the fractions retained by the five sectors converged toward such different
numbers that one or more sectors retained more than 100% of the cash
input. The solution was to construct an iterative procedure to adjust the
values of the components of a vector-valued variable η_{i } i*
*= A,M,T, representing the number of AUs, MUs, and TUs consumed by each
worker until x_{A}, x_{M}, and x_{T} were equal, in
which case none of the fractions exceeded 1.0. The residential component
of η_{i} and the price of one residential unit, p_{R}, can
be set to adjust the fraction of cash flow and fraction of energy flow
associated with the purchase of residential units as there is no residential
sector the salaries of which must be balanced with expenses. This enabled
early versions of the spreadsheet to be brought into balance and accounts for
the peculiar values of η_{i}. The f_{ij }and the p_{i}
were adjusted until the fractions of consumer expenditures and the fractions of
the energy budget going to the various sectors resembled somewhat the US
economy. With a converged solution in hand, it was advisable to fix the
η_{i} and the δ_{ij} and let the prices, p_{i},
and the f_{ij} float as this arrangement corresponds best with physical
reality.

The input of cash into the commercial sector (C ) from the
purchase of each of the commodities (AUs, RUs, MUs, and TUs) after being
diminished by the amount necessary to pay for the overhead of C_{W} and
the expenses of the commercial employees (C_{W}) and all furloughed
stakeholders (C_{F}, M_{F}, T_{F}, and E_{F}),
is divided into three parts for A, R, M, T, E, and C the sums of which must
equal the total net cash paid by C to M_{W}, T_{W}, and E_{W},
which gives six constraint equations in the six prices, p_{i}, i = A,
R, M, T, E, C. This cash constitutes the gross input to M_{W},
T_{W}, and E_{W} to pay for the quantity of MUs, TUs, and EUs
that are required to produce each of the quantity of AUs, RUs, MUs, and
TUs. These are secondary cash flows through the economy. But,
corresponding to the secondary cash flows to M_{W}, T_{W}, and
E_{W} and the cash overhead collected by C_{W} for itself are
tertiary cash flows to M_{W}, T_{W}, and E_{W}
according to the number of MUs, TUs, and EUs necessary to produce the secondary
MUs, TUs, and EUs, and secondary cash flow to C according to the number of MUs,
TUs, and EUs necessary to produce the primary number of CUs. Secondary
cash flows lead to tertiary cash flows and tertiary cash flows lead quaternary
cash flows until all further cash flow is too small to be troubled with.
If this occurs before the bottom of the spreadsheet has been reached, we have
convergence; otherwise, not. The notion of primary flows through the
economy leading to secondary flows and secondary flows leading to tertiary
flows *et cetera* is the fundamental fact of the Mark II Economy.

The prices of the commodities, p_{i}, the fractions of
net cash withheld to pay salaries, x_{i}, the fractions of the
population associated with each sector, π_{i,}, and the fractions
of each sector on active duty, z_{i}, are determined by Newton’s method
as reported in the Convergence Section of the spreadsheets below and to the
right of Cell CP2 columns CP through DA.

Thomas L Wayburn

Houston, Texas

October 2, 2006