The SFEcon models claim generality in that an economist is free to define as many economic sectors as he needs, and to identify them however he chooses. So long as the economist's choices comprehend all economic activity, he is within SFEcon's modeling parameters. Good 0 is exceptional in that it measures the value of all the inputs J being used by each sector IK. Every model transacts Good 0; and its V0 always has the value of unity per year.
A parameter having a value of unity and a unit of 1/year generally indicates poor practice in dynamic systems analysis — usually a failure to distinguish between a state variable and a rate of change. It is most typically found papering-over some failure in appreciating a tricky aspect of the system under study. The notion of value is indeed a tricky one for economics; but, in our estimation, it is also unavoidable. As was the case in examining more generic applications of the turnover concept, the V0 regulating value’s flow will be revealed in terms of its operative purpose in the SFEcon system.
Column zero of our I/O matrix exists to provide a basis for computing the returns to each sector’s assets, which compose an economy’s overall rate of interest. These returns are necessarily expressed in a unit of time during which the assets are expended; and that period has always been one year. Since the physical periods 1/VJ over which physical assets are expended have no intrinsic connection to the one-year context of financial analysis, the total value of these expenditures must find expression on a per-year basis in order to facilitate computations of returns on investment.
Or, put another way, if the interest rate’s most familiar expression were as a dimensionless fraction per 2.0 years, then V0 would necessarily equal 0.5/year in order to express general asset turnover during the same two-year period.
Some further exploration of this notion underlies our riposte to the Keynesian critique of Pigou’s delay model of consumption, which derives from Keynes’ theoretical antagonist (and personal friend) Arthur Pigou. Kurt Roemer’s examinations on this controversy required an estimate of the delay parameter L that would control Pigou’s model; and his conclusion of L = 0.95/year represented a typical value now for a monetary unit to be delivered in one year:
where -i/year is the interest rate (i is a negative quantity in the SFEcon system).
This familiar annual net present value equation is interesting in that its typical offering has no dimensional integrity: it must resolve to units that are dimensionless; but this equation is clearly not going to function in this way unless its unitary terms have the same dimensionality as the interest rate -i, viz: 1.0/year. Nothing less can satisfy the dimensional integrity of the net present value equation, which requires that L be a dimensionless fraction.
We identify these implicit unitary terms as the velocity of value itself, V0/year. As we make this term explicit in the annual net present value equation, let us also multiply the numerator and denominator of the L ratio by the value of all assets a that flow through the generic industrial sectors, and thereby command a return:
This expression of annual net present value allows us to conjure the meaning that L has for the income/consumption controversy: L is now a ratio of ‘asset values consumed’ to the ‘value of what those assets produce’; or, a ratio of an economy’s ‘cost of sales’ to ‘cost of sales plus profit’. These interpretations lead to an identity of L as an economy's general financial turnover within the yearly period of financial analysis for which V0 and i are defined. It was Roemer's guess for the most likely delay parameter with which to validate Pigou's model of income and consumption.