____________      rdahal's  

PRINCIPLES OF PROSPERITY

1.Introduction of Principles of Prosperity

1. What is earning, worth, time value. and prosperity?

Time value of human community at any unit time is a quantitative availability of consumables or usable to human beings within that unit time period. While the whole consumable resources created by human civilization within a unit time is human time value of the whole community, average share of that time value by each individual is average human time value to person. Time value of individual person, i.e. personal time value may differ from person to person. Thus, personal time value is worth or possible availability of consumables to one individual in one unit time.

While personal time value is an absolute measurement of one's worth, prosperity indicates personal worth, relative to other's worth of that very period or relative to any standard time value of that period.  

Personal time value sometimes is denoted by absolute poverty and prosperity - by relative poverty.

Earning of an individual is remuneration for his physical and mental labour of a unit time. Generally, it is proportional to his contribution within that period. Earning is sometimes is mistaken for worth. Worth of a person is availability of consumables to a person within a unit time irrespective of his contribution to the job or society. Of course, earning contributes to worth but it is not a sole source of consumables' availability. Even an income without any work may be a part of worth of that individual. However, it is true that monetarily income of an individual, in most of the cases, is in par with worth.

2. Calculation of Earning, income, Worth & Prosperity

Yes, monetary income of an individual in most of the cases is in par with worth and in most of the cases, that income is proportional to the earning of an individual. For simplicity, we work with time value as earning.

Human economic structures are multi-layers, having different time value for similar work activity. Such layer or stratum of time value gives vertical worth. In addition, different proficiencies have different time prices in the same stratum providing lateral worth.   

If w is earning of individual of a social layer or stratum denoted by m superscript and of proficiency denoted by n subscript and A is number of earners of that proficiency in that stratum, above defined individual human resource may be symbolized as following.

Individual human resource = ^mw_n   

Also,

Number of people of n^th profession in m^th stratum= ^mA_n

Then,                                                                                                    _n=1

Human resource or time value of m ^th Stratum = ^mW = Σ( ^m w_n * ^mA_n­­^­ )

                                                                                                                  ⁿ

where * (asterisk) stands for multiplication sign.

Similarly,

for any n^th profession in m strata

                                                                                                     _m=1

Human resource time value of n^th profession, W_n= Σ( ^m w_n  * ^mA_n)  

                                                                                                     ^m

Human resource or time value of all professions in all strata in a unit time= Human time value=   

                 _{m=1, n=1}

=W_g =Σ( ^mw_n * ^mA_n) 

          ^{m, n}     

 As ^mA_n indicate number of people in n^th profession in m^th stratum,        

                                                                     _n=1

No of people of n proficiencies in m^th stratum, A_s = Σ ^m A _n     

                                                                     ⁿ

                                                                 _m=1

No of people of n^th profession in m strata, A_p = Σ ^m A _n     

                                                                 ^m

                                                                       _{m=1, n=1}

Number of people of all proficiency in all strata, A_g = Σ ^m A _n

                                                                      ^{m, n}

Then,

Average human time value =

=Human time value/number of people in total = w_g = W_g / A_g

If personal time value of an individual = ^mw_n then

personal prosperity (in m^th stratum with n^th proficiency) relative to human time value= =^mτ_n= ( ^mw_n / w_g)

Average Stratum Time Value =

= Stratum time value/No of people in stratum, ^mw = ^mW / ^sA

where ^sA is number of people in stratum

Stratum Prosperity relative to human time value=  ^mτ= ^mw  / w_g

Individual Prosperity with respect to Average Stratum Time Value=

=Personal time value/ Average stratum time value=

= ^mτ_i = ^m w_n   / ^m w  

Similarly,

Average Proficiency Time Value =

= Proficiency time value/No of people in profession

i.e  w_n = W_n / A_n

where A_n is number of people in profession.

Proficiency Prosperity relative to human time value= τ_n = w_n  / w_g

Individual Prosperity with respect to Average Proficiency Time Value=

=Personal time value/ Average proficiency time value

i.e.  τ_ni = ^m w_n   / w_n  

2.Deductions of Prosperity Corollaries

1. First Corollary of Principles of Prosperity

 If two earners 2 and 1 of strata indices ^m2 and ^m1 and with proficiency indices _n2 and _n1 earn ^m2w_n2 and ^m1w_n1 respectively, then prosperities ^m2τ_n2 and ^m1τ_n1 can be expressed as followings.

^m2τ_n2/^m1τ_n1 =  (^m2w_n2 / w_g ) / ( ^m1w_n1 / w_g) = 

 =(( ^m2w_n2 / ^m2w)( ^m2w /w_g)) / (( ^m1w_n1  / ¹w)(¹w/w_g ))

=( ^m2τ_i .^m2τ )/( ^m1τ_i .^m1τ  )= ( ^m2τ_i / ^m1τ_i )( ^m2τ / ^m1τ )

i. e.

Prosperity of 2 with respect to 1=

=(Prosperity of 2 within its own stratum m₂/Prosperity of 1 within its own stratum m₁)*(Prosperity of Stratum m₂/Prosperity of Stratum m₁)

Similarly,

 If two earners 2 and 1 of strata indices ^m2 and ^m1 and with proficiency indices _n2 and _n1 earn ^m2w_n2 and ^m1w_n1 respectively, then prosperities ^m2τ_n2 and ^m1τ_n1 can be expressed as followings.

 ^m2τ_n2/^m1τ_n1 =  (^m2w_n2 / w_g ) / ( ^m1w_n1 / w_g) = 

 =(( ^m2w_n2 /w_n2)( w_n2 /w_g)) / (( ^m1w_n1  / w_n1)(w_n1/w_g ))

=( τ_n2i . τ_n2 )/( τ_n1i .τ_n1  )= (τ_n2i /τ_m1i )( τ_n2 / τ_n1 )

i. e.

Prosperity of 2 with respect to 1=

= (Prosperity of 2 within its own profession n₂/Prosperity of 1 within its own profession n₂)*(Prosperity of profession n₂/Prosperity of profession n₁)

Thus, comes up First Corollary of Principles of Prosperity.  

"Ratio of prosperity of any two earners is directly proportional to ratios of their proficiency and their stratum prosperity."     

i. e.

"Prosperity of person is directly proportional to prosperity of his profession and that of his stratum." 

B. Second Corollary of Principles of Prosperity  

 Production cost C of any item is a total of human and non-human cost inputs S, M respectively in production process. Production costs of two items of same proficiency in two different strata can be expressed as following. 

C₁ = M₁ + S₁     and    C₂ = M₂ + S₂    

Difference of production cost per item   C₁ - C₂ = ( M₁ - M₂ ) + ( S₁ - S₂ ). 

Non-human input of like items is more or less same everywhere with few exceptions and so it can be taken as

   M₁ = M₂  

 and then   

C₁ - C₂ = S₁ - S₂ 

Producers of equal proficiency produce equal quantity of items N in unit time with a time value W, then per item cost of production S would be  

S = W / N  

i. e. time value per item S₁, S₂ by two producers will be

S₁ = W₁ / N   &   S₂ = W₂ / N 

i.e.   S₁ / S₂ = W₁ / W₂ = τ₁ / τ₂

And thus 

C₁ - C₂ = S₁ - S₂ = S₂ (τ₁ -τ₂ ) / τ₂ 

In a balanced trade between these two producers, the second producer has to pay

                       (τ₁ - τ₂) / τ₂

times more of its time value to the former for the same type of item and the former prospers in expense of later one.

Thus comes up Second Corollary of Principles of Prosperity. 

"Prosperity difference is directly proportional to value of traded time input difference between producers." 

C. Third Corollary of Principles of Prosperity 

 Let β₁ be per annum increment of less prosperous economic society 1 and β₂ be that of more prosperous one 2 and ¹τ₀ and ²τ₀ be the prosperities of those societies respectively in base year and in average prosperity indices of societies, let the subscripts denote number of years and superscripts denote societies then

¹τ₁ = (1+β₁) ¹τ₀

¹τ₂ = (1+β₁) ¹τ₁ = (1+β₁)(1+β₁) ¹τ₀ = (1+β₁)² .¹τ₀

¹τ₃ = (1+β₁) ¹τ₂ = (1+β₁)¹τ₂ = (1+β₁)(1+β₁)¹τ₁ = (1+β₁)(1+β₁)(1+β₁) ¹τ₀ =(1+β₁)³ . ¹τ₀

Thus

¹τ_n = (1+β₁)^{n  1}τ₀    

 Similarly,

 ²τ_n = (1+β₂)ⁿ.  ²τ₀

 If in the n th year the two prosperities are equalized, then

 ²τ_n =(1+β₂)ⁿ. ²τ₀ = ¹τ_n =(1+β₁)ⁿ . ¹τ₀

 Or   (1+β₂)^{n  2}τ₀ = (1+β₁)^{n 1}τ₀

Or    ²τ₀/ ¹τ₀ = (1+β₁)ⁿ/ (1+β₂)ⁿ

Or    ²τ₀/ ¹τ₀ = [(1+β₁)/ (1+β₂)]ⁿ

Or    n = (log ²τ₀ – log ¹τ₀)/ [log(1+β₁) – log(1+β₂)]

The prosperity of less prosperous economy will equal to that of more prosperous economy after n years (which may come never), if the growth is more than that of more prosperous one and if lesser one can maintain trade at its side.

Thus comes up Third Corollary of Principles of Prosperity.

"In a competitive production market least prosperous member can hardly raise its prosperity without external interference"