Related papers: A note on the Cobb-Douglas function
The main aim of this paper is to prove the existence of a new production function with variable elasticity of factor substitution. This production function is a more general form which includes the Cobb-Douglas production function and the…
Each production establishment is assumed to have, at any given time, a unique combination of capital and labor (a Leontief function), but the aggregate output at that same time must still be modeled with a Cobb-Douglas function (or a CES,…
Bowley's law, also referred to as the law of the constant wage share, was a noteworthy empirical finding in economics, suggesting that a nation's wage share tended to remain stable over time, as observed through most of the 20th century.…
This paper presents the identification of heterogeneous elasticities in the Cobb-Douglas production function. The identification is constructive with closed-form formulas for the elasticity with respect to each input for each firm. We…
In their seminal 1928 work, Charles Cobb and Paul Douglas empirically validated the Cobb-Douglas production function through statistical analysis of U.S. economic data from 1899 to 1923. While this established the function's theoretical…
Charles Cobb and Paul Douglas in 1928 used data from the US manufacturing sector for 1899-1922 to introduce what is known today as the Cobb-Douglas production function that has been widely used in economic theory for decades. We employ the…
We prove that when individual firms employ constant-returns-to-scale production functions, the aggregate production function defined by the maximum achievable total output given total inputs is always linear on some part of the domain. Our…
Heterogeneity of economic agents is emphasized in a new trend of macroeconomics. Accordingly the new emerging discipline requires one to replace the production function, one of key ideas in the conventional economics, by an alternative…
We extend the work on optimal investment and consumption of a population considered in [2] to a general stochastic setting over a finite time horizon. We incorporate the Cobb-Douglas production function in the capital dynamics while the…
The aggregate Cobb-Douglas production function stands as a central element in the renowned Solow-Swan model in economics, providing a crucial theoretical framework for comprehending the determinants of economic growth. This model not only…
We introduce a general Hamiltonian framework that appears to be a natural setting for the derivation of various production functions in economic growth theory, starting with the celebrated Cobb-Douglas function. Employing our method, we…
This paper studies inter-firm heterogeneity in production. Unlike much of the existing research, which primarily addresses heterogeneous production through unobserved fixed effects, our approach also focuses on differences in factors'…
Productions functions map the inputs of a firm or a productive system onto its outputs. This article expounds generalizations of the production function that include state variables, organizational structures and increasing returns to…
Standard dynamical systems approaches to economic modeling, such as those deriving the Cobb-Douglas and CES production functions from exponential growth trajectories, typically rely on integer-order differential equations. While effective,…
Considering the production processes, it was noted that the use of various equipment leads to an increase in output -- the phenomenon that is usually described as the substitution of labor with capital. The proposed theory of substitution…
Automation raises productivity and reduces paid human labor, but it also reallocates income and ownership claims. This paper studies that tradeoff in a static benchmark and in a stationary heterogeneous-agent general equilibrium. Firms…
For a class of stochastic dynamical models of exchange economies that we call ``fully connected Cobb-Douglas'', the paper proves convergence of the probability distribution to an equilibrium, in total variation metric as time goes to…
The Solow-Swan model is shortly reviewed from a mathematical point of view. By considering non-constant returns to scale, we obtain a general solution strategy. We then compute the exact solution for the Cobb-Douglas production function,…
In this note we classify quasi-sum production functions with constant elasticity of production with respect to any factor of production and with proportional marginal rate of substitution.
This paper takes a look at the Talmudic rule aka the 1/N rule aka the uniform investment strategy from the viewpoint of elementary microeconomics. Specifically, we derive the cardinal utility function for a Talmud-obeying agent which…