Economy as Dynamic System

In Evolution of dynamic systems economics is mentioned as an example and here this is elaborated on qualitatively.

Dynamic System

Free market is based on elementary principles shared by every dynamic system. The elementary interaction of the evolution of dynamic systems is selection, which consists of

• variable (a set of selectable/distinguishable elements) = space
• value (selection from the variable) = time

In economic parlance, but without reducing abstractness, this is

• supply (of resources, like alternative products) and
• demand (selection from competing alternative products)

Like other dynamic systems, economy diversifies on top of long-lasting structures. The interaction to buy a complex product like a smartphone, is the top of a hierarchy of interactions.

The individual is the smallest entity considered in economy, although interactions in the brain, coming from biological evolution and education, are the foundation of human interaction.

Every encapsulation (subsystem, company, economic node) has interior selections, which correspond to its inner energy. The further down the hierarchy, the smaller the time steps.

Every level undergoes a creative phase (adding information)

• where investments create new resources (new products)
• to produce profit (net input)
• to create further resources

In a selective phase the subsystem optimizes (removing information)

• by filtering out products (variables) not getting momentum
• by reducing cost by changing the company's context (outsourcing, cooperation, change of product components, ...)
• to improve higher level contexts, especially those of people

This is annealing that produces macroeconomic evolution.

The internal of non-closed subsystem, where input and output of energy balance, can keep the same internal cycle, as if closed. With an internal storage a subsystem can acquire a more independent trajectory. Input and output are interactions on the level of peer subsystems, like a physical system of interacting particles.

microeconomy vs macroeconomy

Understanding every node of economy from the two perspectives,

• from inside (one node): microeconomy
• from outside (all nodes): macroeconomy

allows to find alternative interactions to counter unwanted developments according to needs, personality and ethical values.

Valuing Resources

Resource, product, service or good are all comprised in the hypernym variable when regarding economy as a dynamic system.

The physical energy of economy ultimately comes from the sun, that feeds us via the food chain, but due to economic diversification the connection is not direct any more.

A resource is (the source of) something that satisfies a human need (Maslow pyramid). The higher needs are there to protect the lower needs. How well the sum of all needs is satisfied determines the living standard. Availability of resources is wealth.

One resource is one degree of freedom: All products satisfying the same need form the supply of a resource to the market (= those interested).

A resource is an extensive variable. An extensive variable is a variable, where

• each value is a set with a
• measure defined

The measure usually is money using a currency as unit. Although, a high percentage of economy is measured

• not at all
• not in detail
• with a local measure

In bartering the measure is a possibly ad hoc unit of another resource. Through trading different measures will acquire an exchange rate. Here money stands for any measure, local or global.

Valuing (pricing) a product

• can be done directly through bargaining, or else
• is a collective (market) process by supply and demand

Pricing on the supply side is based on

• production cost
• strategic anticipation of customer valuing, to maximize profit

Valuing on the demand side (= market) is a mix of

• taste
• utility or marginal utility
• competition and
• available money

Initial pricing of a new product will get adjusted by the market over time, as a compromise between people's individual valuing. Very different valuing groups will split the market, e.g. in poor and rich market.

For small markets (e.g. team, family) the valuing compromise is too burdensome, and prone to conflict.

Valuing changes over economic evolution as new (types of) resources emerge.

Comparison to Physics

There is a layer of complicated emotional and/or rational decision making between the physical world and economy before any economic selection happens.

In physics the

• number of selections per cycle is action (information) and
• the selections per time is energy

The selections are observed at a space point x, consisting of more components. So the energy V is associated to the location: V(x). The change of a component is a momentum. Simultaneous elementary momenta, summarized via p, determine a ΔV(x) = V(x + Δx) − V(x). Via bookkeeping energy thus associates a kinetic energy change ΔK to p: ΔK(p) − ΔV(x) = 0.

The following mathematical analogy to physics is to be understood qualitatively.

Economy's key difference to physics is

• energy is not directly given by selections per time
• but there is a valuing of the selections, different for every resource i and at every location x: V_i(x)

time:	Transactions

Selections are transactions and happen in space and time. They define economic space and time. Via comparison to physical space and time we get

• momentum when looking at one resource (space, momentum)
• energy when combining selections per physical time step (time, energy)

space:	resources

Resources form a many-dimensional space. A physical location x corresponds to:

• assets
• means of production (methods, tools, ...) not traded
• links to other companies
• ...

Resources are linked to physical time and space, e.g. natural resources are localized, crops grow better where and when there is sun and water.

momentum:	Transactions of one resource.

Transactions of a unit dx_i of a resource x_i per time dt for a price m_i along an established link between two agents:

p_i = m_iv_i(t)   v_i = (dx_i(t))/(dt)

p_i do not mix in an euclidian way, but mostly linearly: p = ∑p_i.

If product i is composed of x^j units of product j with unit price P_ij, then one p_i transaction is "simultaneous" with the according p_j transactions.

p_i = ⎲⎳_jP_ijx^j

All p = p_i together are operations, describing which products are transacted.

mass:	price

The price m_i corresponds to mass in physics, but different for every product i.

p_i = (d)/(dt)⌠⌡dI(x_i) = m_i(d)/(dt)⌠⌡dx_i = m_iv_i(t)

It considers

• lower level selections with pricing strategies
• a mutual cost of selection (transaction cost)

One transaction cost comes from establishing links between agents for the resource. From the sellers side it is advertisement, from the buyers side filtering out the right product, despite ads. The economic links can be accounted to a company's goodwill.

search vs ads

A strategy of advertisement is to select everybody. But with so many products it becomes a nuisance. Even targeted ads never turn up at the right time. But they still anchor and frame. Findability is preferable, best through dedicated unbiased product comparison sites, as paid inclusion in search engines are flawed by a bias.

velocity:	demand

Like physical mass, prices m_i can depend on velocity v_i: inverse demand function, price elasticity .

A negative v_i codes expenses (cost)

A positive v_i codes revenue (sales, wages or salary,...)

v_i is expressed in a product specific unit. It could be expressed relative to a maximum production capacity c_i.

phase space: economic context

Time t links momentum p_i with space x_i. The economic context at time t is given by both p_i and x_i. With constant (input and output of) energy, (x_i, p_i) will cycle more or less the same way.

action:	economic value

The accumulated economic value I(x) = ∫dI(x) is the result of a valuation process.

For a product this is the price.

For a company valuation happens annually via financial statements. I(x) at a point in time t is given by the balance sheet

• once split by category (assets)
• once by ownership (liabilities and owner's equity)

The balance sheet includes the results of operations:

• by category: cash, accounts receivable and accounts payable for unfinished transactions
• by ownership: retained earnings under owner's equity to sum up finished transactions of the separate income statement

Changes of balance sheet with regard to the last fiscal year are in the cash flow statement.

Accounting throughout the year considers finer details of value flow (energy), associated with many sub-accounts (subsystems).

energy:	economic growth

Operations p(t) represents the kinetic energy K(p(t)) = p(t) of a company. They are input and output and summarized in the income statement. Summing over a fiscal year gives profit P = ∫p(t)dt. It is loss, if negative.

V(x(t)) = dI(x(t)) ⁄ dt can be seen as potential energy (Current assets, non-current assets in the balance sheet).

H(x, p) = V(x(t)) + K(p(t)) is the total change of value of a company (GDP macroeconomically for a country).

H = 0: Without input V =  − K, i.e. operations change the company value or vice versa. V = dI(x) ⁄ dt = ∂I(x) ⁄ ∂x_idx_i ⁄ dt =  − Σm_iv_i = Σp_i =  − p(t) =  − K.

H > 0 is the default, because people produce a net input through p(t).

Economic growth rate g gives the relative change of growth. g is normally positive, but not constant. With a modified g as CAGR it is still exponential growth on the average.

(dH)/(dt) = gH ⇒    H(t) = H₀e^gt   I(t) = (H₀)/(g)e^gt

The human-valued driving force of a company (and thus of economy as a whole) is to improve the value of context x ultimately for the purpose of improving the context of people according their values:  − dV(x) ⁄ dx = F

By analysing the context, simulating variations and valuing them to be better, a change towards the new context, according to simulated plan, will be better. So the value of a company will increase in normal conditions:

g > 0

Company products offered to the market compete with products from other companies. Price, perceived quality, advertisment manipulations are competition factors. If the market value does not cover the investment the company either adapts or dies in an orderly way. Still, on average, i.e. from a macroeconomic perspective g > 0, and this is what an average company in the market can expect, too.

This table summarizes the correspondence between physics and economy.

Physics	Economy
mass (inner selections)	price
time (selection)	any selling/buying event: transaction
space	very high dimensional economic context every product type a variable every product a value
momentum	profit
action (information)	economic value, not equal to profit
energy (information per time)	economic growth

Structural Evolution

Structural evolution produces higher level resources through improvements on top of longer living lower level resources. Every invention x_i (usage of new resource) can be considered an evolution time step in the metaspace of product types. Every invention is a paradigm shift that changes x = x_i and p = p_i.

dx is the addition of a resource x_i and dp are the transactions for i: p_i.

dx and dp are independent:

• dx is structural: adding variable
• dp is dynamic: selecting values of the new variable

The valuing I is local. If a product i has more potential at the side (x + x_i = x + Δx) of customer c, than given by the market price, transactions i start to make up ṗ_i: (I_c(x) − I_c(x + Δx)) ⁄ Δx = F_i = ṗ_i = m_iẍ_i.

The value element dpdx is activation value. The total value is:

I(x, p) = ∬dpdx

This entails an average growth H = I ⁄ T = mv² ⁄ 2 in time T, assuming an average constant m, which is true for prices and wages only considering inflation.

Hamilton-Jacobi equations:

• (∂I)/(∂t) =  − H

  Structural change is growth through investment  − H.

• (∂I)/(∂x) = p

  A move to a new context involves selections.

Newton second law, using Hamilton equations:

• F = ∂H(p, x) ⁄ ∂x = ṗ

  A change in growth through structural change implies a change in profit.

• ∂H(p, x) ⁄ ∂p =  − ẋ

  Growth change through profit change implies structural change, like simplifications.

Symmetry:

• space symmetry: there are x changes that keep p constant
• time symmetry: there are simultaneous x and p changes that keep H constant A company who's value is kept constant via balancing input and output.

During operations the company cycles through the phase points (x, p). With input and output balancing, this can be compared to circular motion. Growth H = ∬dIdω is an accumulation of structure I times angular velocity ω = 2πf = 2π ⁄ T. As the cycle time can vary between companies or projects, instead of time one uses action angle w, a kind of phase. With constant cycle frequency ω we have w(t) = ωt.