TY  - JOUR
AU  - Yaremenko, Mykola
PY  - 2026
DA  - 2026/05/08
TI  - The Economic Singularity: Core Mathematical Model
JO  - ICCK Journal of Applied Mathematics
T2  - ICCK Journal of Applied Mathematics
JF  - ICCK Journal of Applied Mathematics
VL  - 2
IS  - 3
SP  - 195
EP  - 203
DO  - 10.62762/JAM.2026.366725
UR  - https://www.icck.org/article/abs/JAM.2026.366725
KW  - artificial intelligence
KW  - economic singularity
KW  - financialization
KW  - wealth inequality
KW  - directed technical change
KW  - dynamical systems
KW  - phase transitions
KW  - robot tax
KW  - basic income
AB  - This paper develops a dynamical systems model of an economy with recursively self-improving artificial intelligence and financialization. The model features quadratic self-amplification in both AI capability ($\lambda A^2$) and financial capital ($\gamma_F K_f^2$), coupled through investment flows. It is shown that under mild conditions, the system exhibits a finite-time singularity where AI capability, AI capital, and financial capital diverge. Near the singularity, the wealth ratio between capital owners and workers diverges super-exponentially, with financialization amplifying the exponent by a factor $\gamma_F/\eta$. Introducing taxes on AI returns ($\tau_{ai}$) and financial gains ($\tau_f$) yields three distinct long-run regimes: low-tax (extreme inequality), moderate-tax (stable mixed economy), and high-tax (post-scarcity with universal basic income), separated by critical thresholds derived from workers' budget constraint. Finally, a policy irreversibility result is established: a critical time exists before the singularity after which redistribution becomes politically impossible, as wealth concentration renders feasible tax rates vanishingly small. The results highlight the urgency of early intervention in AI-driven economies.
SN  - 3068-5656
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Yaremenko2026The,
  author = {Mykola Yaremenko},
  title = {The Economic Singularity: Core Mathematical Model},
  journal = {ICCK Journal of Applied Mathematics},
  year = {2026},
  volume = {2},
  number = {3},
  pages = {195-203},
  doi = {10.62762/JAM.2026.366725},
  url = {https://www.icck.org/article/abs/JAM.2026.366725},
  abstract = {This paper develops a dynamical systems model of an economy with recursively self-improving artificial intelligence and financialization. The model features quadratic self-amplification in both AI capability (\$\lambda A^2\$) and financial capital (\$\gamma\_F K\_f^2\$), coupled through investment flows. It is shown that under mild conditions, the system exhibits a finite-time singularity where AI capability, AI capital, and financial capital diverge. Near the singularity, the wealth ratio between capital owners and workers diverges super-exponentially, with financialization amplifying the exponent by a factor \$\gamma\_F/\eta\$. Introducing taxes on AI returns (\$\tau\_{ai}\$) and financial gains (\$\tau\_f\$) yields three distinct long-run regimes: low-tax (extreme inequality), moderate-tax (stable mixed economy), and high-tax (post-scarcity with universal basic income), separated by critical thresholds derived from workers' budget constraint. Finally, a policy irreversibility result is established: a critical time exists before the singularity after which redistribution becomes politically impossible, as wealth concentration renders feasible tax rates vanishingly small. The results highlight the urgency of early intervention in AI-driven economies.},
  keywords = {artificial intelligence, economic singularity, financialization, wealth inequality, directed technical change, dynamical systems, phase transitions, robot tax, basic income},
  issn = {3068-5656},
  publisher = {Institute of Central Computation and Knowledge}
}