Need to integrate modern value theory from duality etc with well known theories of economic growth and savings and refutation of their neoclassical apologetics.

“Development” rather than “accumulation”, “consumption” or “savings”. Related to “capital theory” and “theories of growth” but also integrates some attempt at model for endogenous technological change.

Needs calculus of variations, hamiltonian, lagrange, pontryagin, kantorovich etc.

Try Hestenes:

David Hestenes-New Foundations for Classical Mechanics (geometric algebra)-Kluwer (2002).pdf

David Hestenes_ Anthony Lasenby (foreword)-Space-Time Algebra-Birkhäuser (2015).pdf

after:

Garret Sobczyk (auth.)-New Foundations in Mathematics_ The Geometric Concept of Number-Birkhäuser Basel (2013).pdf

Perhaps in parallel with Rockafellar VA and Muldowney RV but first do basic GA and category theory including CM and PIA.

May need AC0 for proper understanding of Clifford Algebra/Universal Geometric Calculus.

May need Kantorovich etc for Aliprantis etc to get more sophisticated versions.

Frank Ramsey from 1928 is a brilliant classical leftist starting point subsequently mutilated:

@article{F-1928,

doi = {10.2307/2224098},

title = {A Mathematical Theory of Saving},

author = {F. P. Ramsey},

publisher = {John Wiley and Sons},

journal = {The Economic Journal},

issnp = {0013-0133},

issne = {1468-0297},

year = {1928},

month = {12},

volume = {38},

issue = {152},

page = {543–559},

url = {http://gen.lib.rus.ec/scimag/index.php?s=10.2307/2224098},

}

@article{Attanasio-2015,

doi = {10.1111/ecoj.12229},

title = {Frank Ramsey’s A Mathematical Theory of Saving},

author = {Attanasio, Orazio P.},

publisher = {John Wiley and Sons},

journal = {The Economic Journal},

issnp = {0013-0133},

issne = {1468-0297},

year = {2015},

month = {03},

volume = {125},

issue = {583},

page = {269–294},

url = {http://gen.lib.rus.ec/scimag/index.php?s=10.1111/ecoj.12229},

}

Needs to be expressed in terms of disposable free time as “Bliss”.

Instead has been buried in neoclassical “Golden Rule” by pretending virtual depreciation is return on “capital” (with capitalists who live on air!)

@article{Edmun-1961,

doi = {10.2307/1812790},

title = {The Golden Rule of Accumulation: A Fable for Growthmen},

author = {Edmund Phelps},

publisher = {American Economic Association},

journal = {American Economic Review},

issnp = {0002-8282},

issne = {1944-7981},

year = {1961},

month = {09},

volume = {51},

issue = {4},

page = {638–643},

url = {http://gen.lib.rus.ec/scimag/index.php?s=10.2307/1812790},

}

@article{Edmun-1965,

doi = {10.2307/1823937},

title = {Second Essay on the Golden Rule of Accumulation},

author = {Edmund S. Phelps},

publisher = {American Economic Association},

journal = {American Economic Review},

issnp = {0002-8282},

issne = {1944-7981},

year = {1965},

month = {09},

volume = {55},

issue = {4},

page = {793–814},

url = {http://gen.lib.rus.ec/scimag/index.php?s=10.2307/1823937},

}

@article{E-1966,

doi = {10.2307/2974437},

title = {Models of Technical Progress and the Golden Rule of Research},

author = {E. S. Phelps},

publisher = {John Wiley and Sons},

journal = {Review of Economic Studies},

issnp = {0034-6527},

issne = {1467-937X},

year = {1966},

month = {04},

volume = {33},

issue = {2},

page = {133–145},

url = {http://gen.lib.rus.ec/scimag/index.php?s=10.2307/2974437},

}

@article{M-1966,

doi = {10.1007/bf02200134},

title = {Critical Comments on Phelps’ ”Second Golden Rule Essay”},

author = {M. Inagaki},

publisher = {Springer},

journal = {De Economist},

issnp = {0013-063X},

issne = {1572-9982},

year = {1966},

volume = {114},

issue = {9-10},

page = {534–539},

url = {http://gen.lib.rus.ec/scimag/index.php?s=10.1007/bf02200134},

}

@article{-1970,

doi = {10.2307/2296499},

title = {Extensions of “The Golden Rule of Research” of Phelps},

publisher = {John Wiley and Sons},

journal = {Review of Economic Studies},

issnp = {0034-6527},

issne = {1467-937X},

year = {1970},

month = {01},

day = {01},

volume = {37},

issue = {1},

page = {73–93},

url = {http://gen.lib.rus.ec/scimag/index.php?s=10.2307/2296499},

}

Initially try simple illustration of apologetics with neoclassical production from Intriligator Ch 16 (got hardcopy original 1971 edn 5th printing):

@book{book:73048,

title = {Mathematical optimization and economic theory},

author = {Michael D. Intriligator},

publisher = {Society for Industrial and Applied Mathematics},

isbn = {9780898715118,0898715113},

year = {2002},

series = {Classics in applied mathematics 39},

edition = {1st},

volume = {},

url = {http://gen.lib.rus.ec/book/index.php?md5=EE363DEAA575994AA68FC1FCC5B75855}

}

@book{book:338120,

title = {Mathematical Optimization and Economic Theory },

author = {Michael D. Intriligator},

publisher = {Society for Industrial Mathematics},

isbn = {0898715113,9780898715118},

year = {1987},

series = {Classics in Applied Mathematics},

edition = {2Rev Ed},

volume = {},

url = {http://gen.lib.rus.ec/book/index.php?md5=68C2D926A21BB9730D5241FE6CD14870}

}

When first got original (1976-1980?) already worked out simple example. Value added 1 unit total labor time per period. Half net output for consumption, half for accumulation. Consumption is value added. Value of accumulation just replaces virtual depreciation. No profits, no capitalist consumption.

eg

Can easily make discrete time:

Can disguise this single sector model with two different department 1 varieties of G so that each has visibly different inputs and outputs but same essential technology operated in parallel (or inefficiently with individual stocks in alternate periods). Third variety for department 2 output consumption goods with input from department 2.

Could make discrete linear technologies like Bliss CTDI in “capital theory” linked above.

Try evolving barter then money and capital. Need prices based on market makers forming supply with roughly equal values of stocks and cash adjusting bid and offer prices to balance demand, supply, stocks, cash and rates of return.

Aim to illustrate lack of cycles when only circulating capital.

Then introduce fixed capital with more complicated range of technology.

Also substitute goal of free disposable time with consumption/leisure trade off instead of fixed hours and intensity.

Note: As early as 1982 there has been a wonderful literature based on Goodwin’s predator-prey model of cycles comparing labor market studies with optimal bloodsucking by vampires. First saw it in JOTA 1992:

@article{hartl1992cycles, title={Cycles of fear: periodic bloodsucking rates for vampires}, author={Hartl, Richard F and Mehlmann, Alexander and Novak, Andreas}, journal={Journal of optimization theory and applications}, volume={75}, number={3}, pages={559--568}, year={1992}, publisher={Springer} }

Must follow up on other work done by these authors or citing them:

https://scholar.google.com.au/scholar?cites=11971165930071474061&as_sdt=2005&sciodt=0,5&hl=en

Here is an agent based perspective with some political explanation:

https://ourarchive.otago.ac.nz/handle/10523/3662

Other vampire themed, perhaps less relevant:

@article{strielkowski2013mathematical, title={Mathematical models of interactions between species: peaceful co-existence of vampires and humans based on the models derived from fiction literature and films}, author={Strielkowski, Wadim and Lisin, Evgeny and Welkins, Emily}, journal={Applied Mathematical Sciences}, volume={7}, number={10}, pages={453–470}, year={2013} }

This poster for a book “Til the last drop!” on vampire cycles illustrates the use of flow charts to explain cyclical models described in above paper:

http://files.strielkowski.com/200000130-1af3d1beda/Poster%20Vampires%20exist%20PDF.pdf

Via: https://www.emilywelkins.com

http://www.m-hikari.com/ams/ams-2013/ams-9-12-2013/strielkowskiAMS9-12-2013.pdf

This looks like recent useful bibliography and agent based model techniques. Could be relevant for capitalist as opposed to optimal technology diffusion:

@article{Haurand-2017,

doi = {10.1007/s10100-017-0492-9},

title = {Stakes or garlic? Studying the emergence of dominant designs through an agent-based model of a vampire economy},

author = {Haurand, Michelle D.; Stummer, Christian},

publisher = {Springer-Verlag},

journal = {Central European Journal of Operations Research},

issnp = {1435-246X},

issne = {1613-9178},

year = {2017},

month = {9},

day = {22},

page = {–},

url = {http://gen.lib.rus.ec/scimag/index.php?s=10.1007/s10100-017-0492-9},

}

Perhaps more relevant but less mathematical:

@article{neocleous2003political, title={The Political Economy of the Dead Marx’s Vampires}, author={Neocleous, Mark}, journal={History of Political Thought}, volume={24}, number={4}, pages={668–684}, year={2003}, publisher={Imprint Academic} }

http://ricardo.ecn.wfu.edu/~cottrell/ope/archive/0604/att-0138/01-PoliticalEconOfTheDead.pdf