1 / 15

Socio Econo Ensamble (SEE) (Version 1.0.0)

Socio Econo Ensamble (SEE) (Version 1.0.0). Dr. Willy H. Gerber. Abstract :. Model to describe the socio economical behavior of a society based on the mathematics developed for statistical mechanics in physics. www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00. Basics.

lynch
Download Presentation

Socio Econo Ensamble (SEE) (Version 1.0.0)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Socio EconoEnsamble (SEE) (Version 1.0.0) Dr. Willy H. Gerber Abstract: Model to describe the socio economical behavior of a society based on the mathematics developed for statistical mechanics in physics. www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  2. Basics N persons εi wealth of a person i E is the total wealth of the system Σ E = εi The question is how is the wealth distributed among the N persons or witch is the probability that a person has a wealth between ε and ε + dε p(ε)dε = ? www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  3. Hypothesis The allocation of resources to the N different people: (ε1, ε2, ε3, ε4, … εN) with is a possible state of the System. Σi E = εi My hypothesis is that each possible state is equal alike. The set of different possible states is called in physics an “Ensemble” If the total wealth is kept constant we speak of a “Canonical Ensemble”. www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  4. Counting states Total wealth Number of states N(E) People Simple case: 1(E) = 1 Wealth split in ΔE wealth steps delivering M possible states: E ΔE M = www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  5. Counting states Number of states for N = 2 distinguible people 2(E) = M Number of states for N = 3 M M (M + 1) 2 Σ 3(E) = 2(E – mΔE) = m = 0 Number of states for N = 4 M (M – 1)M(M + 1) 1·2·3 Σ 4(E) = 3(E – mΔE) = m = 0 www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  6. Counting states General equation for N people (M + 1)! (M – N + 2)! 1 (N - 1)! N(E) = In case M >> N and N >> 1: (M + 1)! (M + 1 – (N - 1))! (M + 1)! (M – N + 2)! = MN-1 ≈ reduce to N-1 ( ) 1 (N - 1)! E ΔE N(E) = www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  7. Probability Probability of a person to have wealth between ε and ε + dε: N-1(E - ε) N(E) p(ε)dε = In case N >> 1 with N E E N β = ε = or ε ε the probability is -βε -ε/ e e 1 Δε p(ε)dε= = β dε www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  8. People in a state The allocation of resources in n states: (ε1, ε2, ε3, ε4, … εn ) with N people distributed in each state: (n1, n2,n3,n4, … nn) Satisfying Σi Σi E = niεi N = ni and Number of people in a state + Lagrange parameter α -β(n1 ε1+n2 ε2+n3 ε3+..) + α e -βnsεs + α e Σ Σ ns ns n1,n2,.. ns ns = = -βnsεs + α e -β(n1 ε1+n2 ε2+n3 ε3+..) + α e Σ Σ ns n1,n2,.. www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  9. Boson Statistics Earning like a Boson ns = (0,1,2,3,4,…) -βnsεs + α e Σ ns 1 ns ns = = -βnsεs + α e -βεs + α e Σ - 1 ns α is in physics the “chemical potential” and has to be chosen to fulfill: Σi N = ni www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  10. Boson Statistics Wages distribution (US) Data: OES statistics for the US market in 2005 www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  11. Fermion Statistics Purchasing like a Fermion: Product with a price εs I’m buying the product ns = 1 I’m not buying the product ns = 0 Number of people purchasing the product “if you have no other choice”: -βnsεs + α e Σ ns 1 ns ns = = -βnsεs + α e -βεs + α e Σ + 1 ns www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  12. Fermion Statistics α to be chosen to fulfill: Σi N = ni This equation is known in marketing as the “Logistic Distribution”. Its an empirical equation that describes the probability that a product is sold. 1 ns = -βεs + α e + 1 -βεs + α = 0 At or At a value equal α/β half of the customers will purchase the product. I will call this factor the “product value”. It’s the price the customer “thinks” will be ok. εs = α/β ns = 0.5 www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  13. Fermion Statistics But in sociology the decision is not only price; there are additional criteria's (c1,c2,c3, …) that people take to account in there decision. This mean that we must extend the ensemble to the decision criteria of the people: ( ε, c ) And I can introduce a new quantity called wellbeing ωs defined by ωs = εs + η·c In marketing studies η is calculated from the survey and represents what relevance the interviewed people assigned to the particular criteria c. www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  14. Fermion Statistics With the extension of the ensemble to the decision criteria I arrive at the classical Logistic Distribution: 1 ns = -βωs + α e + 1 There model not only delivers the known distribution, it also adds to new insides. First, the criteria term η·c becomes a “truth price” in a natural way, and second, the introduction of α allows to model the comparison between different alternatives ns1 , ns2 , ns3the Logistic Distribution are not defining how to estimate. www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

  15. From here Erik/Raquel: • - Partition Function • Hamiltonian • Terrorism Theo: - Gini - BE Condensation - unemployment www.gphysics.net – UACH-Socio-Econo-Ensamble-SEE-Version-1.00

More Related