Nonlinear Production Function Research Articles

МОДЕЛЮВАННЯ МАРКЕТИНГОВИХ ТА ІННОВАЦІЙНИХ ПРОЦЕСІВ УПРАВЛІННЯ ПЕРСОНАЛОМ БАНКІВСЬКОЇ СИСТЕМИ У ПОВОЄННОМУ ВІДНОВЛЕННІ ЕКОНОМІКИ УКРАЇНИ

The article examines the modeling of marketing and innovation processes of personnel management of the banking system in the post-war recovery of the economy of Ukraine. It was determined that after the war, the banking system of Ukraine will face a number of challenges: loss of personnel due to migration and hostilities; the need to adapt to new economic and marketing conditions; the need to introduce new technologies to improve work efficiency. Therefore, in such a period, moderate managerial intervention in the banking sector is necessary to regulate personnel and marketing processes. On the basis of the input data of the subjects of the banking system for the last ten years, modeling and further forecasting of the activation of innovative and marketing processes of personnel management of the subjects of the banking system was carried out. At the same time, economic and mathematical methods and models were used, in particular their subclass: linear and non-linear production functions. A study of the dependence of the number of bank clients on the bank's innovation and marketing activity coefficient and the qualification (intellectual level) indicator of bank employees is proposed. The actual, theoretical and forecast value of the number of clients of Ukrainian banks is graphically visualized, taking into account the researched factors and the use of non-linear functions for the period of the study. The growth of the forecast indicator of the number of clients of Ukrainian banks has been demonstrated, and it has been noted that influencing factors such as the coefficient of innovative activity of the bank and the indicator of qualification (intellectual level) of bank employees significantly affect the results of research, analysis, modeling of marketing policy and its forecasting.

Labor market volatility in a fully specified RBC search model: An analytical investigation

I show that including a nonlinear production function with physical capital in the Diamond–Mortensen–Pissarides model lowers the elasticity of labor market tightness with respect to labor productivity by about 11.5% under the Hagedorn–Manovskii’s calibration. My finding is robust against different calibration techniques, as well as against different variants of real business cycle models with search-and-matching frictions. While the recent macroeconomics-labor literature focuses on the fundamental surplus to solve the Shimer puzzle, my analysis highlights the existence of an additional channel through which the nonlinearities implied by a production function with physical capital affect labor market volatility.

Implications of Farmer’s Adaptation Strategies to Climate Change in Agricultural Sector of Gujarat: Experience from Farm Level Data

This study examined the farmer’s perception on climate change and adaptation strategies to mitigate the adverse effect of climate change in the agricultural sector of Gujarat. It used farm level information of 400 farmers who were purposely selected from 8 districts. Thereupon, linear, non-linear and log-linear production function models were used to examine the impact of climate change, farmer’s adaptation strategies and technological change on agricultural production in Gujarat. The descriptive and empirical results specify that adaptation strategies (i.e., change in showing time of crops, mixed cropping pattern, irrigation facilities, application of green and organic fertilizer, hybrid varieties of seeds, dampening of seed before planting, climate tolerate crops, organic farming and technology) have a positive impact on agricultural production. Thus, farmer’s adaptation strategies are useful to mitigate the negative impact of climate change in the agricultural sector. Maximum temperature and minimum temperature, precipitation and rainfall have a negative impact on agricultural production. However, the impact of these factors seemed positive in the agricultural sector when farmers apply aforementioned adaptation strategies in cultivation. Family size, education level of farmers, annual income of farmers, arable land, irrigated area, cost of technology, appropriate technology and financial support from government have a positive contribution to increase agricultural production in Gujarat.

Spiking Neural Membrane Computing Models

As third-generation neural network models, spiking neural P systems (SNP) have distributed parallel computing capabilities with good performance. In recent years, artificial neural networks have received widespread attention due to their powerful information processing capabilities, which is an effective combination of a class of biological neural networks and mathematical models. However, SNP systems have some shortcomings in numerical calculations. In order to improve the incompletion of current SNP systems in dealing with certain real data technology in this paper, we use neural network structure and data processing methods for reference. Combining them with membrane computing, spiking neural membrane computing models (SNMC models) are proposed. In SNMC models, the state of each neuron is a real number, and the neuron contains the input unit and the threshold unit. Additionally, there is a new style of rules for neurons with time delay. The way of consuming spikes is controlled by a nonlinear production function, and the produced spike is determined based on a comparison between the value calculated by the production function and the critical value. In addition, the Turing universality of the SNMC model as a number generator and acceptor is proved.

Simulation of development of individual heavy industry sectors

Nowadays, in the context of the coronavirus crisis, the issue of ensuring the sustainable development of heavy industries is acute. However, theoretical and analytical researches alone are not sufficient for this, and economic science needs to develop fundamentally new approaches to the study of the development of industrial sectors. This article is devoted to the creation and testing of a simulation model for the development of individual sectors of the economy. The object of research is the metallurgical industry, as well as related ore mining, mechanical engineering and production of finished metal products. The theoretical basis of the research is a systematic approach that combines the theory of industry markets, economic growth, industrial economics, system dynamics and mathematical economics. The main research methods used are system analysis, statistical analysis to identify trends in changes in the main economic indicators, econometric modeling to build production functions, as well as mathematical modeling of macroeconomic systems. As a result, a simulation model developed in system dynamics notation is proposed, which makes it possible to evaluate the development of individual industries taking into account various changes. This model is built on the basis of the three-sector model of the national economy, where separate adjacent industries connected by dynamic feedback loops are identified as structural elements. The paper details the structure of the simulation model based on first-order dynamic equations, balance equations and nonlinear production functions. The simulation model allowed us to predict a number of scenarios for the development of metallurgical industries, taking into account changes in the labor force and investment in fixed assets. The results of the work can be used for forming proposals on industrial policy, monitoring the condition and efficiency of individual industries.

Optimal Economic Growth Models with Nonlinear Utility Functions

We study a class of finite horizon optimal economic growth problems with nonlinear utility functions and linear production functions. By using a maximum principle in the optimal control theory and employing the special structure of the problems, we are able to explicitly describe the unique solution via input parameters. Economic interpretations of the obtained results and an open problem about the case where the total factor productivity falls into a bounded open interval defined by the growth rate of labor force, the real interest rate, and the exponent of the utility function are also expressed.

МАКРОЭКОНОМИЧЕСКОЕ МОДЕЛИРОВАНИЕ ВЗАИМОСВЯЗИ ЦЕНОВЫХ И ОТРАСЛЕВЫХ ПРОПОРЦИЙ

The article aims to examine one of the most interesting, in the authors’ opinion, applications of the two-sector model of social technology to identify the relationship between the trajectories of the relative price and the relative share of the product in the total output based on the concept of Pareto optimal, or “efficient”, trajectories of economic growth (i.e. trajectories, each point of which belongs to the surface of production opportunities). Within the framework of this concept, the ratio of prices of individual products corresponds to the marginal rates of these products’ substitution. The rates depend on the product (sectoral) structure of GDP, on the one hand, and on the available labor resources and production assets, on the other. The relationship between the investment component of the output and the growth of funds gives rise to a family of efficient trajectories, in the sense indicated above. Each of the trajectories is characterized by the joint dynamics of industry and price proportions; therefore, the main problem of the study is to examine the general properties of such trajectories. The main feature of the model under consideration is the nonlinear production functions of industries. Even the simplest Cobb–Douglas specification generates the dynamics of the main variables of the model described by a nonlinear differential equation of the second order, which cannot be integrated in general form. Therefore, the analysis of the properties of effective trajectories (at least when specific parameters of trajectories are of interest, and not just general criteria for existence and stability) required the development of a program of numerical experiments on a computer, designed for a fairly extensive test of hypotheses and the convenience of presenting and analyzing the results. To begin with, a variant of the twosector model was chosen, in the future it is planned to expand it to a significantly larger number of sectors. The properties of effective trajectories with constant parameters were analyzed: the marginal rate of product substitution (constant price ratio), constant marginal rate of resource substitution (constant ratio of factor payment rates), constant ratio of net output of industries, constant share of investments in GDP, etc. General conclusions are obtained about the conditions for the convergence of such “iso-trajectories” to trajectories with a constant GDP growth rate and about the characteristics of stationary trajectories. Of greatest interest, in the author’s opinion, is the conclusion that the existence and stability of stationary trajectories is determined by the intersectoral ratio of the elasticities of the output with respect to the funds of the sectors under consideration: for an industry producing investment products, this parameter should be of lesser importance. The derived equation, which can be interpreted as an expression of a trend that determines the form of the relationship between the proportions of industry outputs and prices in the economy, opens the way to a meaningful macroeconomic analysis of the relationships between these proportions, depending on the configuration of the parameters of social technology Ai, αi, aij, B and scenarios of their changes over time.

Input-Output Production Structure and Non-Linear Production Possibility Frontier

Input-output (Leontief) production function is widely used in economic analysis. And diminishing marginal rate of return is a very well accepted economic fact. Leontief production function normally results in a linear production possibility frontier (PPF) due to its linear feature, whereas diminishing marginal rate of return implies a non-linear PPF. In this paper, the authors aim to fix this problem by considering multiple primary inputs in a simplified two-sector economy. The authors find that it is possible to curve a non-linear PPF by using Leontief production function when the authors add heterogeneous primary inputs. The authors also discuss the PPF using non-linear production function. Furthermore, the authors propose that three commonly used economic presumptions cannot hold in the same framework. These presumptions are “single primary input”, “fixed-proportion inputs” and “law of diminishing marginal returns”.

Hydrothermal scheduling in the continuous-time framework

Continuous-time optimization models have successfully been used to capture the impact of ramping limitations in power systems. In this paper, the continuous-time framework is adapted to model flexible hydropower resources interacting with slow-ramping thermal generators to minimize the hydrothermal system cost of operation. To accurately represent the non-linear hydropower production function with forbidden production zones, binary variables must be used when linearizing the discharge variables and the continuity constraints on individual hydropower units must be relaxed. To demonstrate the performance of the proposed continuous-time hydrothermal model, a small-scale case study of a hydropower area connected to a thermal area through a controllable high-voltage direct current (HVDC) cable is presented. Results show how the flexibility of the hydropower can reduce the need for ramping by thermal units triggered by intermittent renewable power generation. A reduction of 34% of the structural imbalances in the system is achieved by using the continuous-time model.

Asymptotic dynamics of a system of conservation laws from chemotaxis

This paper is devoted to the analytical study of the long-time asymptotic behavior of solutions to the Cauchy problem of a system of conservation laws in one space dimension, which is derived from a repulsive chemotaxis model with singular sensitivity and nonlinear chemical production rate. Assuming the \begin{document}$ H^2 $\end{document} -norm of the initial perturbation around a constant ground state is finite and using energy methods, we show that there exists a unique global-in-time solution to the Cauchy problem, and the constant ground state is globally asymptotically stable. In addition, the explicit decay rates of the solutions to the chemically diffusive and non-diffusive models are identified under different exponent ranges of the nonlinear chemical production function.

Unit-commitment via logarithmic aggregated convex combination in multi-unit hydro plants

We present a new strategy to solve the hydro unit commitment (HUC) in plants with many generating units (GUs), where the nonlinear Hydro Production Function (HPF) is linearized via Logarithmic Aggregated Convex Combination (LACC). Although the LACC is an efficient technique, the solution procedure via Mixed-Integer Linear Programming (MILP) solver in plants with several GUs is still a challenging task. Thus, this paper proposes a solution strategy that is divided into two steps. In the first step, the identical GUs are aggregated into an equivalent one, and the resulting MILP is resolved for obtaining the starting values of the gross head (GH). In the second step, the GH is used to determine the optimal dispatch considering the individualized HPF for each UG. The performance of the proposed strategy is analyzed in a Brazilian hydro plant composed of 50 GUs of two different types.

Dynamic incorporation of nonlinearity into MILP formulation for short-term hydro scheduling

Optimization tools are widely used for solving the short-term hydro scheduling (STHS) problem in a cascaded hydro system. In a mixed integer linear programming (MILP)-based formulation, the nonlinear and non-convex hydropower production function (HPF) is represented by piecewise linear approximation. However, instead of using a set of predefined curves with static breakpoints or a preprocessing phase to define the complete relationship between the power output, the net head, and the water discharge, this paper proposes a novel method in which the breakpoints in the linearization are determined dynamically, taking into account the time-varying head effect, intake loss, penstock loss, tailrace loss, and head-dependent turbine efficiency. Only one binary variable is needed to indicate the on/off status and power generation of a unit per period. Furthermore, there are few studies available on how to represent the HPF precisely for the hydraulic system where penstocks are shared by multiple generating units. In this paper, we investigate three heuristics to explicitly incorporate the nonlinear and state-dependent power loss in shared penstocks into the STHS problem. The method and heuristics have been implemented in an operational STHS tool used by many hydropower producers in Nordic countries. We use a simple hydro system to illustrate the method and heuristics and a real hydro system in Northern Norway to study calculation efficiency and solution quality. The numerical results indicate that the proposed method can precisely represent the head-dependent and nonlinear operating characteristics of the generating units. The accurate modeling of a system with multi-level shared penstock configurations is crucial for obtaining the optimal unit commitment. The heuristics can effectively handle the power loss in shared penstock in various operating conditions.

A Nonlinear Supply-Driven Input-Output Model

One of the major limitations of the supply-driven input-output (I-O) Ghosh model concerns its linear production function. Using the I-O table, this paper replaces the linear production function with the Cobb-Douglas (CD) production function within the supply-driven model. The two models are compared both theoretically and empirically. Nonlinear production function, relative substitutability of primary factors, and variability of the proportion of intermediate inputs over product levels are the characteristics of the proposed model. The consideration of sectors' Solow residual as Total Factor Productivity (TFP) of sectors is yet another characteristics of the proposed model. The model is also plausible in value added and supply shock computations.

Re-Evaluating the Knowledge Production Function for the Regions of the Russian Federation

The present study picks up on the aspect of knowledge generation—a key part of every national innovation system—in the context of the Russian Federation. Following Fritsch and Slavtchev (2006), a knowledge production function can be used to account for the efficiency of an innovation system. In detail, this study implements a panel quantile regression estimation approach and thus presents a novel approach in studying national innovation system and, more specifically, their efficiency. In particular, a non-linear knowledge production function is estimated to quantify for a possible non-linear impact of knowledge inputs on domestically—sing patents from the Russian Patent Office—and internationally—using patents from the European Patent Office—oriented knowledge output. Using regional data, it is shown that a non-linear impact of the inputs especially on Russian domestic patents can be found. The results offer new insights into the structure of the Russian innovation system as a threshold is identified where the innovation system switches from increasing returns of researcher input to decreasing returns. This implies that only smaller research systems work efficiently, and starting from a size of approximately 900 researchers, their efficiency steadily decreases.

Modelling the cost-effectiveness of introducing the RTS,S malaria vaccine relative to scaling up other malaria interventions in sub-Saharan Africa

ObjectivesTo evaluate the relative cost-effectiveness of introducing the RTS,S malaria vaccine in sub-Saharan Africa compared with further scale-up of existing interventions.DesignA mathematical modelling and cost-effectiveness study.SettingSub-Saharan Africa.ParticipantsPeople of all ages.InterventionsThe...

Boundedness in a chemotaxis system with nonlinear signal production

This work deals with the zero-Neumann boundary problem to a fully parabolic chemotaxis system with a nonlinear signal production function f(s) fulfilling 0 ≤ f(s) ≤ Ksα for all s ≥ 0, where K and α are positive parameters. It is shown that whenever 0 < α < \(\frac{2}{n}\) (where n denotes the spatial dimension) and under suitable assumptions on the initial data, this problem admits a unique global classical solution that is uniformly-in-time bounded in any spatial dimension. The proof is based on some a priori estimate techniques.

Approximate method for stochastic chemical kinetics with two-time scales by chemical Langevin equations.

The frequently used reduction technique is based on the chemical master equation for stochastic chemical kinetics with two-time scales, which yields the modified stochastic simulation algorithm (SSA). For the chemical reaction processes involving a large number of molecular species and reactions, the collection of slow reactions may still include a large number of molecular species and reactions. Consequently, the SSA is still computationally expensive. Because the chemical Langevin equations (CLEs) can effectively work for a large number of molecular species and reactions, this paper develops a reduction method based on the CLE by the stochastic averaging principle developed in the work of Khasminskii and Yin [SIAM J. Appl. Math. 56, 1766-1793 (1996); ibid. 56, 1794-1819 (1996)] to average out the fast-reacting variables. This reduction method leads to a limit averaging system, which is an approximation of the slow reactions. Because in the stochastic chemical kinetics, the CLE is seen as the approximation of the SSA, the limit averaging system can be treated as the approximation of the slow reactions. As an application, we examine the reduction of computation complexity for the gene regulatory networks with two-time scales driven by intrinsic noise. For linear and nonlinear protein production functions, the simulations show that the sample average (expectation) of the limit averaging system is close to that of the slow-reaction process based on the SSA. It demonstrates that the limit averaging system is an efficient approximation of the slow-reaction process in the sense of the weak convergence.

A one-sector model of economic growth with a nonlinear production function and related environmental quality

In this paper we suggest a stylized one-sector optimization model of national economic growth with a nonlinear production function and environmental quality control. A steady-state point of the Hamilton system is found analytically, while the optimal trajectory is constructed numerically. And finally, we adjust the model to the Russian economy.

Using Semidefinite Relaxation to Solve the Day-Ahead Hydro Unit Commitment Problem

In this paper, we present a mixed-integer formulation with nonlinear production functions of the day-ahead hydro unit commitment problem for hydro-dominant power systems. The objective is to minimize unit startup and shutdown costs and maximize water use efficiency in the daily operation of multiple hydro plants. Determination of hourly generation dispatches and unit configurations is subject to reservoir dynamics, power balance, as well as target constraints coupling short-term generation with long-term reservoir operation goals. In addition, ac power flow constraints are considered. An equivalent quadratically-constrained quadratic formulation is approximated by successive convex semidefinite programming relaxations in a branch-and-bound algorithm for optimal solutions. Numerical case studies for several system configurations are presented to illustrate the effectiveness of the relaxation algorithm.

Mixed strategy under generalized public goods games

The relationship between group's contribution and public goods produced often exhibits nonlinearity, which constitutes the generalized public goods game. Far less attention has been paid to how the mixed strategy evolves in such generalized games. Here, we study the effects of nonlinear production functions on the evolution of the mixed strategy in finite populations for the first time. When the group size and the population size are comparable, cooperation is doomed irrespective of the production function. Otherwise, nonlinear production functions may induce a convergent evolutionary stable strategy (CESS) or a repeller, but cannot yield the evolutionary branching. Moreover, we particularly consider three representative families of production functions, intriguingly which all display the hysteresis effect. For two families of production functions including concave and convex curves, a unique CESS or a unique repeller may occur even if the group size is two. Whereas for the third class encompassing symmetrically sigmoidal and inverse sigmoidal curves, the coexistence of a CESS and a repeller only occurs if group size is above two, and two saddle-node bifurcations appear. Our work includes some evidently different results by comparing with the evolution of continuous investment or binary strategy.