Though not adressed to me, I hope you don't mind I'm reading his mail.
I would say that GP might be considered a transitive element, or possibly an input. Outputs would be gold, science, hammers, espionage, and culture since all of those can be used to effect the game.
Obviously outputs and inputs can be transformed, at varying rates and with varying methods.
I think of

as an output because they aren't necessarily present or available from Turn 0 (though they do eventually come around).
They don't show up until
after surplus

(esp. via Specialists) or

(esp. via Wonders) has been converted into

.
Like Wonders, I think any output used or reused back into the economy is certainly a transitive element but probably one more akin to a 'process' than an input, since they directly generate output by way of their own, inate process.
So, I think where Great People and Wonders are concerned, it's a multi-stage process with the
first input being

or

and the
last output being some amount and variety of the aforementioned outputs.
A Religious Economy. Hmmmm, geeze. Let me think about this. Maybe I need to modify my theory.
Not necessarily, because the "Religious Economy" isn't a complete economy or explanation of an economy, because it only explains where the civ is getting the bulk of its

. The "Religious Economy" still needs to define how and where from its

comes.
This means the "Religious Economy" is actually a strategic subset of a more general economic type like the SE, CE or TE.
EDIT: After reading a little more definition of the "Religious Economy" in the
Types of economies thread, I'd define a 'strict' Religious Economy as a type of Production

hammers

Economy, since hammers are being used to build units capable of spreading religion (for gold at the Shrine) and religious Wonders and buildings capable on generating

,

,

and

. If Priest Specialists are also emhasized (both for gold & hammers as well as Great Prophet

), then you could further clarify by saying it's a Priest-oriented Religious Production Economy (since the Priest Specialists'

are being 'recycled' into the economy to more quickly build even more religious wonders and buildings).
In summary, the Religious Economy is a type of Production Economy, because hammers are being invested into units, Wonders and city improvements which provide the bulk of the economy's muscle.
Do I need more inputs/outputs/transitives? Do I need a transitive, maybe

should just be viewed as an input and an output like

? Can you categorize the econs people have been talking about using this?
In a round-about sense, everything in the game can be viewed as a transitive element. After all, if I convert

into a stack of Axemen used to conquer a city, doesn't that make the Axemen a transitive input?
(In that respect and by that definition, we definitely shouldn't try to define every transitive element ... they should instead be defined as necessary per each economic
strategy.)
I wouldn't say I'm entirely versed in every economic model, but I'd say every one I've so far encountered can be defined in this manner.
My particular favourite is the "Trade Economy". In the raw sense, it's a "Food Economy" since it converts surplus food into rapid and large city growth to garner lucrative Trade Routes, but since Trade Routes generate Commerce, it is also (and more appropriately) a "Commerce Economy".
... by similar definition a Cottage Economy is also a Commerce Economy ...
The basic management of a TE (esp. using the sliders) is much like that of a CE, though Technology, Wonder and Diplomatic priorities differ somewhat. Likewise, most of the strategic applications and economic subsets of the CE are shared by the TE.
-- my 2
(I'm gonna go get my dinner now.)