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In this paper, I present a visual representation of the relationship between mean hourly total compensation divided by per-capita GDP, hours worked per capita, and the labor share, and show the represented labor equilibrium equation is the…
Labor productivity was studied at the microscopic level in terms of distributions based on individual firm financial data from Japan and the US. A power-law distribution in terms of firms and sector productivity was found in both countries'…
We analyze inequality aspects of the agent-based model of capitalist economy named it Social Architecture of Capitalism that has been introduced by Ian Wright. The model contemplates two main types of agents, workers and capitalists, which…
This work proves that ranks and shares are statistically dependent on one another, based on simple combinatorics. It presents a formula for rank-share distribution and illustrates that Zipfs law, is descended from expected values of various…
Studies of collective human behavior in the social sciences, often grounded in details of actions by individuals, have much to offer `social' models from the physical sciences concerning elegant statistical regularities. Drawing on…
We identify a causal effect of top inventor inflows on the patent productivity of local inventors by combining the idea-generating process described by Marshall (1890) with the Bartik (1991) instruments involving the state taxes and…
Dividend discount models have been developed in a deterministic setting. Some authors (Hurley and Johnson, 1994 and 1998; Yao, 1997) have introduced randomness in terms of stochastic growth rates, delivering closed-form expressions for the…
The question about fair income inequality has been an important open question in economics and in political philosophy for over two centuries with only qualitative answers such as the ones suggested by Rawls, Nozick, and Dworkin. We…
This paper discusses the empirical validity of Goodwin's (1967) macroeconomic model of growth with cycles by assuming that the individual income distribution of the Brazilian society is described by the Gompertz-Pareto distribution (GPD).…
In this paper, a sum rule means a relationship between a functional defined on a subset of all probability measures on $\mathbb{R}$ involving the reverse Kullback-Leibler divergence with respect to a particular distribution and recursion…
The Large Deviation Principle (LDP) and the Central Limit Theorem (CLT) are central pillars of probability theory. While their formulations are established under the i.i.d. assumption, the probabilistic foundation for power-law…
A robust thermodynamic relation between inflation corrected monetary valuation and energy emerges from existing work. This is based on the energy used, the aggregate efficiency of all production processes ($\Lambda(t)$) in terms of Joules…
We extend the stochastic production planning framework to manufacturing systems, where the set of admissible production configurations is described by a general smooth convex domain $\omega $. In our setting, production operations continue…
Translation from the Latin of Euler's "Observatio de summis divisorum" (1752). E243 in the Enestroem index. The pentagonal number theorem is that $\prod_{n=1}^\infty (1-x^n)=\sum_{n=-\infty}^\infty (-1)^n x^{n(3n-1)/2}$. This paper assumes…
The excessive compensation packages of CEOs of U.S. corporations in recent years have brought to the foreground the issue of fairness in economics. The conventional wisdom is that the free market for labor, which determines the pay…
This paper presents an empirical application of the Gause-Witt model of population ecology and ecosystems to the income distribution competitive dynamics of social classes in economic systems. The Gause-Witt mathematical system of coupled…
We establish a general equilibrium theory for systems of large language model (LLM) agents operating under centralized orchestration. The framework is a production economy in the sense of Arrow-Debreu (1954), extended to…
Economic engineering is a new field wherein economic systems are modelled in the same manner as traditional mechanical and electrical engineering systems. In this paper, we use Newton's theory of motion as the basis for the theory of…
We propose in this work a kinetic wealth-exchange model of economic growth by introducing saving as a non consumed fraction of production. In this new model, which starts also from microeconomic arguments, it is found that economic…
The Lucas-Moll system is a mean-field game type model describing the growth of an economy by means of diffusion of knowledge. The individual agents in the economy advance their knowledge by learning from each other and via internal…