Our discussion of commodity markets centered on the level O_{JK }of a
commodity J that has been produced in economy K, but remains un-purchased. This quantity is modeled
as wasting its economic potential at a rate V_{J}•O_{JK}, where V_{J} is
J’s turnover fraction. Model 0's notion of supply S_{JK} is defined by adding
this ‘market pressure’ to the rate Y_{JK} at which J is currently produced in K:

Our discussion of how adjustments to physical asset levels can be controlled identified an individual
sector IK’s demand for commodity J Q_{IJK} as:

Model 0's notion of domestic demand D_{JK} sums demands of the sectors I for J in K:

Simple addition across all M of the economies K provides global (K = 0) totals Y_{J0},
O_{J0}, S_{J0}, and D_{J0} for all the variables subscripted JK in these
equations. Where S_{J0} and D_{J0} are equal for given commodity J, we can be assured
that there exists an export/import profile X_{JK} such that X_{J0} is null, and that
all domestic demands D_{JK} are satisfied by the sum of domestic supply S_{JK} minus
exports X_{JK}:

(Per the SFEcon sign convention, a negative value for X_{JK} indicates a quantity that is
imported.)

Working as we are within the neoclassical paradigm, we can anticipate creating a regime of prices
that tends to equate demand with supply; but this tendency is necessarily imperfect for any dynamic
model — as, indeed, it must be for any objective counterpart of what the model portrays. It is
therefore essential to exhibit at least one mechanism whereby the X_{JK}’s are calculated
such that X_{J0} will a) approximate zero to the extent that the integer zero can be expressed
as a real number by a digital computer, and b) vary from zero in a way that is temporally unbiased to
the positive or negative.

This is most easily done by envisioning a quantity D_{J}’ for the amount of global
demand D_{J0} that will be satisfied at any given point in time, and a quantity
S_{J}’ for the amount of global supply S_{J0} that will be used at any given
point in time. At any moment, one of two things must be happening: S_{J0} will be diminished
to S_{J}’; or D_{J0} will be diminished to D_{J}’. The factors
accomplishing these diminutions are named FS_{J} and FD_{J}; and, at any given moment,
one of these factors must unity, while the other must be less than unity.

The factors FS_{J} and FD_{J} both derive from the ratio F_{J} of global
supply S_{J0} to global demand D_{J0}:

FS_{J} and FD_{J} will then determine exports/imports X_{JK} of commodity
J from/to economy K:

This equation assures the export/import profiles are such that any X_{J0} will always
compute as close to integer zero as is possible for digital representations of real numbers; and
the overall global system never attempts to export more than is imported, or to import more than
is exported, irrespective of imbalances between supply and demand.

FD_{J} also serves to prevent the sectors IK from taking J off the market in excess of
what is being supplied:

Here we arrive at the final definition of the asset replenishment rate R_{IJK} that controls
SFEcon’s circuit of physical flows. Whenever the global supply of J equals or exceeds global
demand and FD_{J} is unity, the rate R_{IJK} at which a sector IK takes a commodity J off
the market equates to the optimal rate Q_{IJK} for IK to use J. When supplies of J are not adequate
to meet demand, FD_{J} less-than-unity serves to ration asset replenishment rates. An overabundance
of supply for J will be absorbed into the market, where (as we shall see) it depresses prices.

Small negative quanta appearing here and there on the market are allowed as indicia to the model that
a given commodity J must be rationed. ‘Conservation of mass’ is required insofar as a market
is only allowed to go negative to the extent possible during one differential element of time, given that
the market variable began that differential element of time as a positive quantity. Conservation of mass
is reinstated by the definition of supply S_{JK} as output Y_{JK} plus market pressure
V_{J}•O_{JK}: where market pressure is a tad negative, supply becomes a tad less
than current output; and demands are never allowed to be satisfied in excess of available supply.