As discussed in connection with Value's Measure, every SFEcon model transacts a zeroth commodity through a zeroth sector. Good J=0 constitutes an artificial financial unit that we have labeled ‘the global currency unit’ GCU, or G. The GCU is a constant value unit insofar as its quantity is always fixed at whatever level it is given at the inception of emulation; and its turnover fraction V0 is always set at 1/year in recognition of its meaning to the financial computations it supports.

At stasis, sector IK’s flow of value EI0K G/yr will equal the combined value of its asset flows EIJK units/year ...

where an asset J’s absolute unit value is given by YJ G/unit. The sum of all EI0K over I and K must always equal value’s constant output rate Y00 G/yr

Keeping EI0K current is accomplished by operation of Model 0’s regular circuit of physical flows. This operation presumes knowledge of: 1) P0K, the price of one GCU in terms of the currency of an economy K; and 2) asset values YJ. In this article we will continue our presumption that P0K is known (it will be determined anon) and proceed here to a express a commodity J's absolute marginal value through the familiar notion of a demand schedule.

We begin with an awareness of IK’s turnover of value EI0K as known in the manner any asset’s turnover rate EIJK, viz.: VJ times IK’s stock of J. EI0K’s significance lies in its value equivalence G/year to a sector IK’s budget constraint sIK $/year of monies to be expended for asset replenishment:

An estimate of what IK needs to expend in order to approach optimality is critical to the analysis because s is the basis of one of our approaches q to an economic sector's financial discriminant z:

       Eqa. 7-5

If this equation is to be useful in calculating a global, constant-value commodity prices YJ G/unit, then we must require that q $/year be expressed as its equivalent in G/year. We hereby introduce Q=q/P0K as this equivalent. As we are now at a point in the computational cycle prior to our discovery of P0K, Q must be computed by substituting -EI0K for s in Equation 7-5: 


Our next reference is to the generic hyperbolic demand schedule:

which we note 1) requires a reference to the financial identities of the sectors I, viz.: zI, and 2) being limited to a single economy, neglects the subscript K.

Expression of a commodity J's demand schedule for the global sum of all economies K requires attachment of the subscript K=0 to the parameters and independent variables in the above, together with the obvious substitution of QIK G/year for all IK’s financial identities zIK:

Subscript 0 implies that DJ0 is the sum of DJK over all K=1…M and that UIJ0 is the sum of UIJK over all K=1…M. (The second of these sums further implies that the global production function for a sector I can be created by merely adding the production parameters for each J of sector I across all economies K=1…M. Our justification for this procedure is the obvious continuation of an earlier discussion on the peculiar nature of hyperbolic indifference surfaces.)

Construction of J’s global demand schedule is completed by summing the financial discriminants zIK of the sectors I over all economies K. This process is deterred by a consideration that the zIK’s occur in the differing (and varying) financial units of the respective economies K, e.g.: $/year, €/year, £/year, ¥/year, etc. Of course the intention all along has been to substitute QIK G/year for all IK’s financial identities zIK — which necessitates the ultimately desired end that PJ0 must be interpreted as YJ G/unit. It only remains to note that our procedure for creating a global demand function out of national demand functions continues the application of our ratio/sum technique.