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