From Cambridge to Eternity: “Factor-hours to Production”

 

A Few Mathematical Terms

             Variable: a quantity of interest, rather varying across space than changing over time

             Constant: a quantity not imagined to be affected by variables

             Functional equation: the effect variable on the left, the cause variables on the right

                                             After all, the left owes its existence to the right. 

 

The Production Function in Macroeconomics: Y= f((L, K, N)

             In the first place “exogenous” to mathematics, there is dimension aberration in the equation: Y for GDP is per annum (T-1) on the left, while L for human stock, K for Kapital stock and N for natural stock on the right are as at a moment (T0). In the financial accounting, the cause side will be called “credit” (sources) and the effect “debit” (uses).  

             To be correct, nominally or really out of Cambridge, the non-null dimension of time shall be represented on the cause side of the equation. If arithmetic is any guide, T-1= T-1∙T0, period. In other words, there must reside “time variables” as legitimate citizens on the right-hand side.

 

A Hypothesis on the Production Function of Reality

Premises: The performance is accounted for not only as per GAAP but also in the paradigm of “the market.” First, the currency unit of the commonwealth is the metric of value (U). Second, the value of consumption utility (M∙U) is accounted for as “revealed in the market” of the community.    

The Performance Accounting per annum at the Firm as “Supplier”:

On the debit: The sum total over the year of a certain final good, service or asset, which is marginally to be created at the firm and valued at a market price valued  in the legal unit (of tender). That is, “The monetary revenue all through the year of selling the good, service or asset.” 

On the credit:

         - Human: The monetary revenue per annum attributable to the man-hours on the job       

          - Kapital: Ditto to the machine-hours                                                                                     

          - Natural land (for farming and extraction): Ditto to the acre-hours

The individual Production Function per annum:

Premise: “Efficiency” of the running factor is to be measured at the price in the rental market of factor-hour. For the sake of convenience, we hold the rental rate un-varying across factor units and over the year.

On the credit: (With “per hour” meaning “per factor-hour”)

            - “Labor income”= (The wage rate per hour) x (the running hours per annum)                    

            - “Capital income”= (The rental rate per hour) x (the running hours per annum)                 

            - Land income = (The rental rate per hour) x (the running hours per annum)

On the debit: "The monetary revenue all through the year of selling the good, service or asset."


The production function: The debit= the credit  as above

 

The Performance Accounting in the Commonwealth:

The economy-wide performance will be the aggregate of the individual performance. On the flipside, there is no place for L, K or N in the sun as at any day whatever of the year!

            

(To tomorrow)

Comments

Post a Comment

Popular posts from this blog

Procrustean Art of Backtracking: “Dimensions in Economics”

  The most basic dimension on earth (L 3 ) is the period of time (T) because the time duration in Here is limited for each and every creature, as opposed to in Eternity across the River (L -1 ) where the time stops lapsing (T 0 ).              The second most critical dimension in Economics is the currency unit defined by the Sovereignty as metric across the commonwealth for the value of utilities (U) of all types and kinds. The sources of utilities are not limited to the apple, the orange, the housing, taking a nap, playing with grandchildren and “leisure,” but way beyond our imagination.              Please do not account for anything in terms of mass (“M”) only, be it called “real quantity.” After all, “real” in macroeconomics may  in reality  mean “surreal,” if not “nominal.” As Adam Smith pinpoints, “It’s the consumption utility!”  ...
Read more

Velocity Wanted: A Trade-off in Eternity

    “It was many and many a year ago, In a kingdom by the sea , Those two maidens there lived whom you may know By the name of Annabel and Lee ” (sorry for the so many unauthorized variations).              Both are presupposed to live for 125 years in the kingdom; the royal economy is eternally stuck to “the natural level of output,” or g= 0 in arithmetic of Annabel and Lee. In 25 years after legitimate conception and subsequent birth, the two maidens begin to take different routes of life: the Cambridge way , viz., π= g+ m= m , vs the Princeton way , namely, π= g+ 2m= 2m . Note:   The Cambridge Quantity equation by J.R. Hicks (1937): M d = k ∙ P ∙ Y                                   The money demand by William Baumol from Princeton (1952): M d = ( b ∙ P ∙ Y / 2 i ) 1/...
Read more

Saving "the Market” out of Cambridge: “Roles of Government”

  Multiple Choices as to multiple Claims of us:             Cl. 1. There are lives in Mars.             Cl. 2. An organism can exist on the Moon.             Cl. 3. A society may be built in Death Valley.                 Cl. 4. A free market is untenable without the rule of law. We are:             Ch.1, kidding.             Ch. 2, silly.             Ch. 3, insane.             Ch. 4, sober.   No matter what we or your answers may be, there without the rule of law won’t be such a thing as liberty or freedom in the...
Read more