Calculus based (Bio-)Physical Economics

Transcription

1 BPE 2016 Washington, D.C. Introduction to Calculus based (Bio-)Physical Economics Synthesis of Social and Natural Sciences? Jürgen Mimkes, Physics Department Paderborn University, Germany Calculus Macroeconomics Production Growth

2 Calculus

3 Oxford Econophysics & Physical Economics Richmond Mimkes Hutzler

4 Introduction 2. ICE 2013 Kavala, Greece Question: Every investor would like to calculate the course of profits or share prices in advance (ex ante) like the flight of a ball or an arrow! Why is this not possible? Answer: All economic terms may be divided into two categories: they may be calculated before or afterwards: ex ante (at all times certain) or ex post (in the beginning uncertain)

5 Problem: Neoclassical Macroeconomics Solow model of economic growth: Y = F (K, L) But: Income (Y) is an ex post term (uncertain). A function (F) is an ex ante term (certain) Uncertain cannot be equal to certain! Y F (K, L)

6 Solution: Calculus of two variables, because economics depends on two production factors: capital and labor. 1. Riemann integral of exact differential d F d F = F (B) F (A) depends on limits A and B path independent (certain) 2. Stokes integral of not exact differential δ Y p δ Y = Y p (K, L) 3. Integrating factor (λ) path (p) dependent integral there is no stem function Y! (uncertain) δ Y = λ d F (K, L) replaces Y F (K, L)

7 Closed integrals Closed Riemann integrals of exact differentials are always zero! (Path independent integral, certain) A B df 0 ring

8 Closed integrals Closed Stokes integrals of not exact differentials are never zero! (Path dependent integral, uncertain) A B M = M 0

9 Examples for closed Stokes integrals A household (H) works in industry (In) earning 100 per day and spends 90 for food and goods. The surplus is 10 per day. A Monetary balance M B Δ M H M = Y H C H = Δ M H

10 Examples for closed Stokes integrals The closed Stokes integral is a basis of Bio-Physical-Economics C + O 2 Blood circuit Heat pump Production circuit C O 2 Biology Physics Economics

11 Macroeconomics

12 Double-entry accounting: Excel balance A household (H) works in industry (In) earning 100 per day and spends 90 for food and goods. The surplus is 10 per day. (monetary units: ) (energy units, kcal, MJ) monetary account + productive account = 0 Double-entry accounting the basis of economics

13 Double-entry accounting: Stokes integral A household (H) works in industry (In) earning 100 per day and spends 90 for food and goods. The surplus is 10 per day. (monetary units: ) (energy units, kcal, MJ) M + L = 0 The monetary account measures the productive account (in ) This is the fundamental integral of economics

14 The fundamental laws of Economics monetary units M = L Fundamental law

15 The fundamental laws of Economics monetary units M = L Fundamental law 1. law: M = d K L Diff. double entry balance Profit = Capital Labour

16 The fundamental laws of Economics monetary units M = L Fundamental law 1. law: M = d K L Profit = Capital Labour 2. law: δ M = λ d F Diff. double entry balance Existence proof of the production function F

17 The fundamental laws of Economics monetary units M = L 1. law: M = d K L 2. law: δ M = λ d F

18 The fundamental laws of Economics monetary units M = L energy units Q = W 1. law: M = d K L Q = d E W 2. law: δ M = λ d F Oilprice: δ Q = T d S 118 MJ= 33 kwh

19 The fundamental laws of Economics Econo - Physics M surplus Q heat (uncertain) d K capital d E energy (certain) L labour W work (uncertain) d F prod. function d S entropy (certain) l living standard T temperature Unit:,$,, Unit: J, kwh, kcal dimension: money dimension: energy

20 The temperature (l) of an economic/social system: GDP per capita and energy consumption per capita

21 Production

22 Double-entry accounting: Stokes integral A household (H) works in industry (In) earning 100 per day and spends 90 for food and goods. The surplus is 10 per day. (monetary units: ) (energy units, kcal, MJ) M + L = 0 The monetary account measures the productive account (in ) This is the fundamental integral of economics

23 l M = L l 2 l 1 The mechanism of production (Capitalism) F

24 Closed Stokes integrals lead to a two-level Carnot process: Production process: two separate levels l 1 and l 2 : Companies: Trade: Banks: Societies: Economies: capital and labor buyer and seller investors and savers rich and poor 1. world and 2. world Carnot process: two separate temperatures T 1 and T 2 : Motors Refrigerators Heat pumps Generators hot and cold hot and cold hot and cold hot and cold Econophysics: Production is a Carnot process Motor, generator productive circuit, company Heat pump, fridge monetary circuit, bank

25 Growth

26 Economic growth is a two level process Growth by international trade (p < 0,5) US - China

27 Economic growth by trade in the world Growth in the world: Labour: 3 % Capital 6 % Data by Thomas Piketty

28 Linking Social Sciences to Natural Science and Engineering Economics 1. Production and trade (Carnot process) 2. Economic growth and degrowth (heat of motors) 3. Income: How much should a manager earn? (barometer) 4. Financial markets, financial crisis (statistics, roulette) Societies 1. Homogeneous societies: hierarchy (collective), democracy (individual) and global state (solid, liquid, gas) 2. Heterogeneous societies: Cooperation, integration, segregation and aggression: Example: US integration, The war in Bosnia (binary alloys) 3. Public decisions: The analysis of US elections (crystal growth) 4. Mobility in Germany (diffusion) Politics 1. Afghanistan, China (solids) 2. Standard of living and politics: the Arab revolution (phase diagram) 3. From Marshall plan to present EU problems: (conduction of heat) 4. Migration and refugies in a globalized world (atomic diffusion)

29 Thank you for your attention

30 Economic growth d Y 1 (t) = p (Y 2 - Y 1 ) d t d Y 2 (t) = (1- p) (Y 2 - Y 1 ) d t p : distribution of surplus to the lower side 4 Two interdependent economic systems Two interdependent countries Capital growth Y p = 0,10 p = 0,10 p = 0,25 p = 0,25 p = 0,50 p = 0,50 Growth of economic levels Y 2,5 1,5 0,5-0, time t time t p = 0,75 p = 0,75 0 < p 0,5 p = 0,75

31 Economic growth is a two level process States between Capitalism and Communism Efficiency: = (l 2 - l 1 ) / l 2 p = 0,00: Colonialism: Max! (Very high prices, very low wages) strong market (Colonial Africa) p = 0,10: Capitalistic: Max! (High prices, low wages) strong market (USA, China, Germany) p = 0,25: Socialism: Min! (Lower prices, higher wages) weak market (France) p = 0,50: Fair deal: const. (Prices and wages nearly equal) p = 0,75: Stagnation: nearly equal) Decreasing! (Low prices, too high wages) weakening market (Greece) p = 1,00: Communism: zero! (One class system) the market will break down (USSR, DDR) Communism is like opening the door of a fridge mixing hot and cold. The refrigerator will stop.

32 Economic growth and fertility in the 90 biggest countries World GNP and fertility hierarchies GNP per person in US $ democracies transition democracies transition line hierarchies fertility f, children per women GdP per capita and fertility for 90 countries

33 The fundamental laws of BioEconoPhysics Q = W δ W = d E T d S Bio - Econo - Physics Q life M surplus Q heat d E food d K capital d E energy W work P production W work d S genetics d F prod. Function d S entropy L food level λ living standard T temperature Stokes integral: Mechanism of production Animals: Blood circuit Production circuit Carnot motor Plants: Chlorohyll circuit

34 Outlook Social sciences Natural sciences Accounting Calculus ex ante, ex post differentials (exact, not exact) accounts (balanced, unbalanced) integrals (Riemann, Stokes) Macro-economics Thermodynamics capital, labour energy, work Business Mechanical engineering capitalism: companies, banks Carnot: motors, heat pumps Micro-economics Statistical mechanics Lagrange free energy Finance Statistics capital, finance energy, entropy Social Sciences Chemistry Homo- and heterogen agents atoms, molecules networks crystal structures Politics Materials hierarchy, democracy, global solid, liquid, gas

35 Outlook δ L = d E δ W = Λ d S δ M = d K δ W = λ d F δ Q = d E δ W = T d S Life sciences Chemistry atoms, ions reactions, exo-, endotherm Biology food, work Biological engineering Blood circuit, Chlorophyll cycle Bio-Statistics genetics Physio-Chemistry cells cell structures Life Materials life in solids, water, air Social sciences Natural sciences Accounting Calculus ex ante, ex post differentials (exact, not exact) accounts (balanced, unbalanced) integrals (Riemann, Stokes) Macro-economics Thermodynamics capital, labour energy, work Business Mechanical engineering capitalism: companies, banks Carnot: motors, heat pumps Finance Statistics Finance of capital energy and entropy Social Sciences Chemistry Homo- and heterogen agents atoms, molecules networks crystal structures Politics Materials hierarchy, democracy, global solid, liquid, gas

36 Linking Social Sciences to Natural Science and Engineering Accounting balances Macro-economics income, labour Business companies, banks Calculus differential equations Thermodynamics heat, work Mechanical engineering motors, heat pumps Micro-economics Statistical mechanics capital, finance energy, entropy Social Sciences collective, individual, global crisis, revolution Chemistry solid, liquid, gas phase transitions: melting, freezing cooperation, integregation compounds, solutions segregation, aggression insoluble, chemical reaction Politics hierachy, democracy, global Physics ice, water, vapor

37 Unemployment: The same Carnot mechanism for people and machines People are replaced by machines Y W = Q C P dk - ldf W de -TdS German people working in agriculture 1900 : 50 % 2007 : 2 %

38 Unemployment: The same Carnot mechanism for people and machines People are replaced by machines (de, dk): Carnot cycle T 2 T 1 mean energy T Y W = Q C T 2 T 1 P dk - ldf Entropy S W de -TdS White collar work (ordering, planing) is replaced by computers (ordinateurs)

39 Problem of unemployment and energy resources: The most important resource is our human intelligence. Julian S. Simon ( )

40 Government: Mechanics for repairs and accidents Market rules and enforcement Anti trust laws Bank laws Regulation of markets by taxes: Low taxes for low risk productive markets High taxes for high risk financial markets High taxes for exceeding manager incomes Support Welfare, unemployment support Start up of small business Mechanics for repairs in accidents

41 The law of survival in economic systems: In economic units or systems the law of survival is still valid for the system, but not anymore for every single element! This is a positive result for the individual weak, for babies in a family, for sick people in a company or jobless in a society. This is a negative result for each economic system. Families have to work harder for their babies, companies have to make up for the missing work, the society has to build resources for the jobless. An economic system may manage to survive, if all individuals cooperate, but a system may fail, if the individual do not cooperate: e.g. divorced families with children, cities with not cooperating unemployed, the EU with not cooperating members.

42 Cooperative Systems: Economics retailer Biology dairy farm company cow labor gras Ecosystem robust systems

43 Not cooperating (aggressive) Systems: Finance hedge fonds Biology lion - Europe buffalo tax payer gras Ecosystem sensitive systems

44 Economic systems

45 Critical review of classical models François Quesnay ( ), French economist and medical doctor. His book Tableau économique (Economic Table, 1758) will the basis of this discussion. Adam Smith ( ), Scottish philosopher of political economy. His classic work: The Wealth of Nations (1776) is still valid today. Karl Marx [ ( ), German economist, sociologist and journalist. Marx's books The Communist Manifesto (1848) and Das Kapital ( ) are still used.

46 Calculus of two variables in meteorology Stokes integrals (spirals) in meteorology spiral In high and low pressure systems winds go up and down in spirals

47 Concepts of Thermodynamics in Economic Agent Networks Probability with constraints and risk (r) of detection P = (1-r) / [(1-r) + exp (- Y/l) ] Calculation and data on theft and risk in D 2002 Rate of murder D 2002, A = 1.9, E/T = -3 Rel. number of thefts, risk Bayern Baden W. Rheinld Pflz Risk data Theft data and calculations S. Anhalt Nieders. Saarland Hessen NRW Hamburg rel. numbers 1,5 murder data and calculations 1,25 1 0,75 Risk data 0, year murders per 100 risk calculation Probability of theft at risk of detection, BKA 2002 Probability of murder at risk of detection, BKA 2002

48 The new production function entropy When John von Neumann at Bell Labs asked Claude Shannon in 1949 how he was getting on with his information theory, Shannon replied*: [ The theory was in excellent shape, except that he needed a good name for "missing information". "Why don t you call it entropy", von Neumann suggested. "In the first place, it already exists in Boltzmann's statistical mechanics, and in the second place, no one understands entropy very well, so in any discussion you will be in a good position. *Avery, John (2003). Information Theory and Evolution. World Scientific. ISBN

49 Thank you for your attention

50 Economic level Y(t) Economic growth Growth: p = 0,25 and 0,10 Interdependent economic systems a = 0,10 ln Y a = 0, time t Capital - labor

51 BPE 2016 Washington, D.C.

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53 Entropy: the natural production function Shannon: d S = - d N (p i ) ln (p i ) 0 If we open a perfume bottle, the perfume will leave the bottle and it will never return into the bottle. Entropy is a measure of disorder, of distribution.