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Physical Economics

Economics is ultimately about who has the right of control over what material things. For the purposes of physical economics a "material thing" is anything that a body can have control over including work (by the hour).

In physical economics, a currency (i.e. money) is simply one material out of many.

Let Q(t) represent the quantity of material of a type i, in the control of body β at time t.

Let ΔQ(t0,t1) represent the increase in the quantity of material of type i, in the control of body β from time t0 up to time t1. So;

ΔQ(t0,t1) = Q(t1) - Q(t0)


There are only two ways that a body will come to change the amount of material they have control over, through a physical process or through a contractual process;

  • Physical processes change materials according to physical laws, i.e. building a house or a chemical reaction for example.
  • Contractual processes change control relationships according to social laws, i.e. agreements between bodies such as barter, exchange, buying and selling, lending and borrowing etc.

From this the amount gained or lost with time, can be split into the contribution from each physical process and from each contractual process. Every process may have a number of terms representing the losses or gains of particular types of material resulting from that process. These terms can be represented;

Let ΔQiβp(t0,t1) represent the increase in the quantity of material of a type i, in the control of body β from time t0 up to time t1 as a result of the physical process p.

Let ΔQiβc(t0,t1) represent the increase in the quantity of material of a type i, in the control of body β from time t0 up to time t1 as a result of the contract c.

Then, from time t0 up to time t1, the increase in the quantity of material of a type i, in the control of body β is the sum of; the increase in the quantity as a result of all the physical terms, plus the increase in the quantity as a result  of all contractual terms. This can be written as;

 ΔQ(t0,t1) = ΔQiβp(t0,t1) + ΔQiαc(t0,t1)
                       ∀p                       c

Any economic body can account for its increase or decrease in material wealth over a time period if the numbers are available to fill this equation. Let this equation be called the Equation of Account. See Accounting for more about the connection between this and accounting.

Processes and Time

Both physical and contractual processes can have their terms spread through time. For example;
  • where for use of a field I promise you a share in the crop at harvest time, or where for the loan of money you agree to pay interest.
  • to physical processes i.e. where it is only by the performance of certain sub-processes at certain times that a baker gets a decent loaf of bread.
The processes may be continuous such as typical interest payments or discrete such as coupons on a bond. Some may involve both.

Contracts involving terms to be met in the future may contain options within the terms. i.e. I may have the option to take a share of a crop or a cash sum.

Temporal contracts during their execution spread rights and obligations over time which means;
  • a party to a contract may have received their rights yet still have future obligations to the other party, or
  • a party to a contract may have performed their obligations yet still have future rights from the other party.
When one has outstanding obligations one is in debt or has a liability, and when one has future rights one is in credit and has an asset. This is the most general definition of debt and credit, assets and liabilities.

A financial debt or liability is simply a contract that has terms expressing an obligation to give an amount or amounts in the future. While a financial credit or asset is simply a contract that has terms expressing a right to receive an amount or amounts in the future.

Contract Processes

Material passed in contract processes may be represented as trade tables whose terms represent the quantity of material of type i passed from α to β in the time interval t0 to t1.


These terms can form a 3 dimensional table.
  • Outputs from body α determining the row, and
  • Inputs to body β determining the column, and
  • material type i determining the depth in the table.
This table provides a convenient way of representing trade i.e. contractual processes.

Any cell in the table ΔQiαβ(t0,t1) can be looked at and by changing t1 future positions based on active contracts could be assessed.

Clearly individual contract types can be examined in their own right.

Clearly the terms ΔQiαβ(t0,t1) can be broken down further by particular contract c.

ΔQiαβ(t0,t1) = ΔQiαβc(t0,t1)
                        ∀ c

The problem with trade tables is their failure to represent physical processes, which are an important aspect of the complete economic picture.

Financial Trade Tables

Trade tables can be reduced further by looking at one type of material only, money in a single currency. Then α and β are used to represent types of industry and the table shows that, for example, the shoe industry spent £143m with the rubber industry or that the public spent £1743m with the shoe industry. These tables are normally called "input-output tables" but this is an over generalisation because they only represent the input and output of currency. A currency is just one kind of material as far as physical economics is concerned, each currency is a different type of material.

When considering a particular currency the terms look like this;


Financial Health

Because prices vary, and financial trade tables show the flows of money and nothing else they are not always a good indicator of true economic health i.e. the well-being of the society, but there can be no doubt that they do show financial health i.e. whether money is circulating forming trade rings, or whether borrowing and lending are distorting the financial markets.

Central banks can lend money for interest at any time. This is how we end up indebted to the central banks! When economic velocity slows because money isn't circulating the temptation is to lower interest rates and lend more to borrowers maintaining trade chains that have not or cannot form trade rings.

Signs of economic ill health include interest payments that are not payable through the production the loans facilitate or excessive outstanding obligations but few rights.

The main point is to see where chains have not been made into rings. Where debt at one end and credit at the other are desperately seeking a join. One must ask about the market;
  • What do those in debt want to sell (offers)
  • What do those in credit want to buy (bids)
to see how the trade chains might fulfil.

Input-Output Table Sources

Physical Processes

Processes obey the laws of nature and one might be forgiven for ignoring them and concentrating on trade and in particular money, as the basis of economics, but do so at your peril. Physical processes can;
  • transport materials or,
  • transform certain types of materials into other types of materials.
Transport processes are the processes of movement of materials from one place to another. In the process energy may be used such as when goods are shipped around the world, or energy may be liberated such as when a river flows down a mountain.

Transformation processes break into two subgroups production processes turn less valued materials into more valued materials and consumption processes turn more valued materials into less valued materials. Notably the former normally consumes energy where as the latter releases it.

Physical processes may require a number of  material types and may result in a number of other material types being produced some of which may be desired products and others waste products of the process.

Economic Momentum

The concept of economic momentum is most simply understood by saying that one a body is engaged in certain kinds of process than there is a cost (not necessarily financial) in changing the rate of performance of that process i.e. a cost in increasing or decreasing production of a factory, and also in nature a biological cost in increasing or decreasing the size of a coral reef! Building a reef takes calcium and sunlight and other materials, and smashing one up takes energy!

Economic momentum may also be called process momentum. Now to explore the basic mathematics of the concept of economic momentum.

In a given time t (seconds) the production/consumption of material type i of a process p is s (units) determined by si = vi t. Then v is called the process velocity vi in units per second. Plus is production, minus is consumption.

In a given time t (seconds) the process velocity vi (units per second) may be determined by vi = ai t. Then ai is called the process acceleration in units per second per second.

Changing the velocity of process, takes a quantity of material. If the cost of changing the velocity of process by Δvi in time Δt is a quantity rj of each type of material j than the economic mass matrix mij is defined by;

    rj= mijΔvi = Δ(mijvi)
            ∀ i                  ∀ i

and the economic momentum vector pj is defined by;

       = Δ (mijvi) = Δ (mijvi) = Δpj
                 ∀ i                  ∀ i  

Of course unlike mass in physics the economic mass will not be a nice constant thing and so over reliance on this mathematics would be silly.

Only Money

In the case of a borrowed sum of money then r is the principle sum and v is the interest payment. To reduce the interest payment to 0 the principle sum must be repaid so;

r = m v  so  m = r/v

The economic mass is the principle divided by the interest rate. Say r = £1000 and v = £50 per year then the economic mass m = 20 years which happens to be the time for the interest payment to equal the principle sum. (Assuming the principle isn't paid off.)

Business Cycles

Given that processes have economic momentum and that trade chains consist of strings of bodies (firms, businesses etc.) therefore trade chains themselves have economic momentum.

Trade chains that have failed to form trade rings build up debt at one end and credit at the other end of the chain which;
  1. will naturally reduce demand at the debt end, and so supply at the credit end, meaning a deflationary recession,
  2. hopefully followed by increased supply at the debt end, and so demand at the credit end,  eventually meaning a deflationary growth.

A balance will be reached thus completing the trade ring but given human tendency to follow others there is a tendency for over reaction and hence oscillation (trade cycles) may result.

Further to this economic momentum may cause unprecedented borrowing and other measures to maintain the old supply chain. i.e.
  • an unhealthy pressure at the debt end to borrow and unhealthy pressure at the credit end to lend, postponing the necessary change and leading the market "up the gum tree!"
The long term result of this a a bigger drop in demand when it comes.

"There is no means of avoiding the final collapse of a boom brought about by credit expansion. The alternative is only whether the crisis should come sooner as a result of a voluntary abandonment of further credit expansion, or later as a final total catastrophe of the currency involved." Ludwig von Mises

The extent of the crisis depends on whether the products were needs or wants. We can do without wants.

(C)2010 Tom de Havas. The information under this section is my own work it may be reproduced without modification but must include this notice.

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