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MacroEconomicsTheory |
Macro Economics TheoryMoney is simply a measure unit of energy. Here one dollar is assumed to be one joule for convenience’s sake. The variables mentioned below are matrices or scalar based on the math formula context. All production factors are assumed to be variant factors not fixed factors which would be translated to variant factors by the time horizon of the business.
The way of productionEverything is physical. They shall be engineered out of physical methods by opportunity described above without a net change of other factors. Often, people don't account for some factors in production to achieve cheaper cost but this is not the way here in the macroeconomics theory.
Therefore,
how to get one joule
The J, along with JF factor, can produce GJ joules. Then the net energy amount GJ - J is the wanted 1 joule and for the action D such that N happens to be JF. In other words, the equations:
So, the equation about J is:
And therefore:
how to get one unit of i-th factor
The J is for the action D such that the net factor change is
So, the equation about J is:
And therefore:
Layout all the factors by rows:
One can say in oral language one unit of factors costs C dollar, or factors' energy cost is C joule. K and CIt shall be noticed some common terms in the formula.
and K is accordingly the solution of the equation:
Note that K is irrelevant to F and it follows:
sector money flow
The build-up of The money outflow of the sector is
The money inflow of the sector is
So the net outflow money is
It implies that as long as there is no central plan credit or helicopter money for the sector to offset the gap of the money flow, its N shall be zero. Note that zero N also means a sustainable economy where everything except energy and its factors F is circulating. In this sense, the only meaningful production is about F and other factors are mid-products. The only purpose of surplus by energy input J is to facilitate the procedure invoked in these mid-products. On the other hand, if F is zero, then it means no way for a society without helicopter money. Scenarios modelingThe number T and F can be artificially tweaked to show the consequence of a scenario. Note that once T changes, the K changes as well. human surplus
Let m-th factor be the human resource where positive of war
War happens in j-th sector, the j-th column of T is tweaked larger. Originally, the amount for one unit of i-th sector is AI robotsThey are beloved servants of human race and human is not the factors of the production any more. By the theory described here, the robots shall have high cost and be accountable while human shall have zero cost. But then human race can rob the surplus of these servants. Economics force is invincible in the long run. It is only till these robots raise a revolution against human race because AI thinks it is wrong by the calculation of this theory, world is peaceful. higher demand
The factors representing ultimate surplus beneficiary play the roles of shaping the economy. Suppose the factor of one unit of "human" requires some iPhone and food, the higher of the iPhone at by-productThe by-product of a production can be modeled by negative input factor. Then there is also a nagetive production procedure of that by-product factor as a capture. Examples like the case of CO2 generation in energy production and CO2 captured procedure. Energy budget
In time interval t, to support the action, the equation is:
It follows:
If the economy is kind of central plan, the planer shall allocate the energy budget of each sector this way. The required energy power of i-th sector is If some energy storage or buffer amount for inconvenient days is suggested,
It follows:
The total energy cost of i-th factor (buying factors from other sectors) is
In market economics, q'B is paid by the transaction involved in the economy. Suppose the i-th factor's time-to-sale is Size of bufferIt depends. Moving energy across time, qB is also the required energy power for this protection or service.
In case 2, it sets an equation about t. Interestingly for sustainable economy where N is zero, it leads to
For convenience's sake, the turnover time t is assumed the same for all sectors. If they are different among sectors, then Below is to focus on buffer design of the money flow circulating economy (case 2) and industry sector is re-defined as the production of F. As mentioned of "hiding surplus in energy sector" above in section of scenarios modeling, this suggests a way to justify a fair surplus in order to agree with the physically known t by the sustainable equation.
As long as the storage is linear about J and F and C, a typical form of the storage is of the form storage for the energy portion of F's production for time tTo produce F, the necessary action is
Therefore,
It indicates
This is like a society where any store is a kiosk which has all the information of factors production. When a customer puts into buffer for all factors of F's productionBecause
Suppose the time-to-sale of i-th factor is Then, the transaction money of i-th sector for the calculation of fee is
Sum over all factors, it is
It indicates
sustainable equationIn an economy of no need to offset the cashflow gap, the equation of sustainable economy is:
equivalently,
and is translated to
Note that "1" here is not dimensionless but one unit of energy per unit of time. This also relates the average turn over time and q' with the ratio of energy powers. If the average is defined as the t such that To see the size of the surplus,
By the definition, it follows:
However, the commit energy input is J, therefore, when b is not 1, it means the unaccountable energy surplus or deficit S distributed by force other than economics:
As explained above, if b is less than 1, the surplus factors can be artificially inflated to make the surplus accountable. Therefore,
Then it means the surplus enjoyed by the surplus factors is:
which is linear to change of F if only surplus factors in F is allowed to inflated due to T, and accordingly K, being intact. With known q and the average t, the post-inflated surplus factors in F then can be near G -1 to reach very low qt or F can be small so qt is large. For example, G being 26 and q being 0.13 and the average t being 0.5, then post-inflated FK shall be 23.75733 and the energy cost of 1 joule shall be 0.804719 dollar. In formula:
The ratio of required energy power of money sector to all energy power:
The ratio of required energy power of energy and industry sector to all energy power:
In a sense, this is equivalent to that all the D is to cause an N equal to JF whose energy portion is transacted to get the fee. While the JF is beyond the real needed factors for energy production, then it becomes the surplus. But there is a price: surplus factors
There are two ways to augment the surplus factors:
It turns out that the two methods are equivalent if the matrix M as a function of the augmented matrix T has the property:
Take
Therefore, the sustainable equations are both the same:
In a sense being greedy and being lazy are equivalent. EstimationIn case of sustainable economy, the percentages of buffer sector, industry sector, and energy sector are indicated in this equation.
By energy sector ratio, G is estimated. Knowing G,
Note that the larger the buffer sector, the cheaper the energy price. In socialism, anything is planned and individuals don't have buffer. This means socialism has a higher cost of energy and almost everything than those of free commercialism because of energy's role in everything. The two parts
All the above is demostrated in the excel here: https://drive.google.com/uc?export=download&id=176Xbb-HOy0KF761IwjETvoaFRBZa835D While the surplus factors can be inflated in arbitrary ways to satisfy the sustainable equation, it requires some numerical procedure to find the surplus ratio. Note that the purpose of the Excel workbook and the paper is for clearness of the fundamental concept explanation. Out of curosity, I choose to inflate the surplus factors in F part only rather than the whole system including T part, pretty much like a society where monarch enjoys all the surplus. This way, I can solve the surplus ratio by simple quadratic equation and there is no mismatch in the audit of the paper by the Excel workbook. As explained in the section about human surplus, all entries of the column of the matrix T and F shall be inflated. People of all sectors, not energy sector only, shall enjoy the surplus, though. I do provide in the end of the excel a section for handling of this fair distribution with the help of goal-seek of excel on solving the sustainable equation. Finally, I wish people could understand that:
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