Search Results (26)

We study an optimal consumption, leisure, and investment problem over a finite horizon in a continuous-time financial market with partial borrowing constraints. The agent derives utility from consumption and leisure, with preferences represented by a Cobb–Douglas utility function. The agent allocates time between work and leisure, earning wage income based on working hours. A key feature of our model is a partial borrowing constraint that limits the agent’s debt capacity to a fraction of the present value of their maximum future labor income. We employ the dual-martingale approach to derive the optimal consumption, leisure, and investment strategies. The problem reduces to solving a variational inequality with a free boundary, which we analyze using analytical and numerical methods. We provide an integral equation representation of the free boundary and solve it numerically via a recursive integration method. Our results highlight the impact of the borrowing constraint on the agent’s optimal decisions and the interplay between labor supply, consumption, and portfolio choice. Full article

This study presents an innovative application of genetic algorithms (GAs) for optimizing the Cobb–Douglas production function, a cornerstone of economic modeling that examines the relationship between production output and the inputs of labor and capital. This research integrates traditional optimization methods, such as partial derivatives, with evolutionary computation techniques to address complex economic constraints. The methodology demonstrates how GAs outperform classical techniques in solving constrained optimization problems, offering superior robustness, adaptability, and efficiency. Key results highlight the alignment between GA solutions and traditional Lagrangian methods while underscoring the computational advantages of GAs in navigating non-linear and multi-modal landscapes. This work serves as a valuable resource for both educators and practitioners, offering insights into the potential of GAs to enhance optimization processes in engineering, economics, and interdisciplinary applications. Visual aids and pedagogical recommendations further illustrate the algorithm’s utility, making this study a significant contribution to the computational optimization literature. Additionally, the optimization process using genetic algorithms is presented in a step-by-step manner, with accompanying visual graphs that enhance comprehension and demonstrate the method’s effectiveness in solving mathematical problems, as validated by the study’s results. Full article

The inefficient allocation of resources in agricultural production not only affects the quality of agricultural development and the efficiency of resource utilization but also represents a pivotal issue that constrains the sustainable progress of agriculture. Considering the urgent societal need for the optimization and advancement of industries, investigating the issue of resource misallocation within agricultural production and its specific losses on AGTFP is profoundly important in advancing the pursuit of high-quality and sustainable agricultural development. This study employs the Cobb–Douglas function and the theory of price distortion to establish a model for quantifying losses in Agricultural Green Total Factor Productivity (AGTFP). Drawing on provincial panel data from North China spanning the years 2006 to 2022, we analyze the characteristics of resource allocation and the corresponding losses in AGTFP. The findings suggest that AGTFP in North China has been gradually rising, accompanied by notable regional disparities in both the level of AGTFP and its growth rate. Nevertheless, due to the varying effects of distorted agricultural input factors, there exists different resource misallocation across North China. Despite some improvement in resource misallocation, this improvement has not been significant. Consequently, there is a loss of AGTFP in the North China region. If resource misallocation is effectively addressed, AGTFP losses could be reduced by at least 29%. It is anticipated that over the course of the next decade, AGTFP will rise and resource misallocation and AGTFP losses will diminish slightly, and it is crucial to step up efforts to enhance resource allocation. By ensuring adequate agricultural funding, enhancing agricultural efficiency, and optimizing energy inputs, it is possible to mitigate resource misallocation, thereby effectively diminishing AGTFP losses and fostering the sustainable advancement of agriculture. Full article

This paper introduces the integration of the Cobb–Douglas (CD) utility model with quantum computation using the Clairaut-type differential formula. We propose a novel economic–physical model employing envelope theory to establish a link with quantum entanglement, defining emergent probabilities in the optimal utility function for two goods within a given expenditure limit. The study explores the interaction between the CD model and quantum computation, emphasizing system entropy and Clairaut differential equations in understanding utility’s optimal envelopes. Algorithms using the 2D Clairaut equation are introduced for the quantum formulation of the CD function, showcasing representation in quantum circuits for one and two qubits. Our findings, validated through IBM-Q simulations, align with the predictions, demonstrating the robustness of our approach. This methodology articulates the utility–budget relationship through envelope representation, where normalized intercepts signify probabilities. The precision of our results, especially in modeling quantum entanglement, surpasses that of IBM-Q simulations, which require extensive iterations for similar accuracy. Full article

This research presents a comprehensive analysis of sustainable port operations in two countries, utilizing econometric models, including the stochastic frontier and Cobb–Douglas models, to examine critical elements such as the number of empty containers and vessel traffic. These factors, driven by globalization, significantly impact the environmental and social dynamics within port operations. By integrating these models, this study assesses efficiency and sustainability, addressing methodological gaps in existing research, particularly in the quantification and generalization of CO₂ emissions. Findings indicate that, despite differences in port management and operations, CO₂ levels can be estimated using operational variables without the need for complete CO₂ traceability throughout the logistics chain. This study concludes by emphasizing the importance of incorporating international environmental standards into port operations and recommends the use of econometric models as tools for assessing and managing port sustainability effectively. Full article

A model of Edgeworthian economies is studied, in which participants are randomly chosen at each period to exchange two goods to increase their utilities, as described by the Cobb–Douglas utility function. Participants can trade deviating from their bilateral equilibrium, provided that the market and the trade follow appropriate symmetry conditions. The article aims to study the convergence to equilibrium in a situation where individuals or small groups of participants trade in a market, and prices are determined by interactions between the participants rather than by demand and supply alone. A dynamic matching and bargaining game is considered, with statistical duality imposed on the market game, ensuring that each participant has a counterpart with opposite preferences. This guaranties that there is sufficient incentive for trade. It is shown that, in each period, the expected logarithm of the trading price in the Edgeworthian economy equals the expected Walrasian price. This demonstrates that, under symmetry conditions, the trading price in the Edgeworthian economy is related to the Walrasian price, indicating convergence of the trading price in the Edgeworthian economy towards the Walrasian price. The study suggests that, under the right conditions, the decentralized trading model leads to price convergence similar to what would be expected in a more classical Walrasian economy, where prices balance demand and supply. Full article

Inefficiency is a problem in the production process, including in the organic farming sector. Over a long term period, this problem can disrupt the productivity of agricultural crops. This research aims to analyze the production and marketing efficiency of organic cabbage farming in the Kopeng agropolitan area, Indonesia. We utilized a Cobb–Douglas production efficiency analysis with the Stochastic Frontier Analysis (SFA) approach. The variables in this study include organic cabbage production, land area, seedlings, organic fertilizers, organic pesticides, and labor. We conducted in-depth interviews with 60 organic cabbage farmers in Kopeng, Indonesia, from January to August 2023. The research results showed that organic cabbage cultivation was economically inefficient in production, technical, and marketing. The use of organic fertilizers, the ability to diversify products on limited land, and the use of pesticides, have not been utilized optimally yet. The results of the marketing efficiency analysis showed that it was efficient. Organic plants were believed to have their market share and to have a higher selling value than non-organic ones. The implication was that the government needed to provide training in producing organic fertilizers and pesticides to reduce production costs so that organic farming could be technically and financially efficient. This research enriched the discussion regarding the need to analyze production and marketing efficiency to find strategies to increase organic cabbage productivity. Full article

This study derives space travel pricing by Walrasian Equilibrium, which is logical reasoning from the general relativity theory (GRT), the accounting equation, and economic supply and demand functions. The Cobb–Douglas functions embed the endogenous space factor as new capital to form the space travel firm’s production function, which is also transformed into the consumer’s utility function. Thus, the market equilibrium occurs at the equivalence of supply and demand functions, like the GRT, which presents the equivalence between the spatial geometric tensor and the energy–momentum tensor, explaining the principles of gravity and the motion of space matter in the spacetime framework. The mathematical axiomatic set theory of the accounting equation explains the equity premium effect that causes a short-term accounting equation inequality, then reaches the equivalence by suppliers’ incremental equity through the closing accounts process of the accounting cycle. On the demand side, the consumption of space travel can be assumed as a value at risk (VaR) investment to attain the specific spacetime curvature in an expected orbit. Spacetime market equilibrium is then achieved to construct the space travel pricing model. The methodology of econophysics and the analogy method was applied to infer space travel pricing with the model of profit maximization, single-mindedness, and envy-free pricing in unit-demand markets. A case study with simulation was conducted for empirical verification of the mathematical models and algorithm. The results showed that space travel pricing remains associated with the principle of market equilibrium, but needs to be extended to the spacetime tensor of GRT. Full article

The Northeast State-owned Forest Areas comprise the largest region of resources in China. The transformation of the Northeast State-owned Forest Areas is due to various stimuli, such as policies, systems, and markets. In the context of ecological construction and the reform of the state-owned forest system in Northeast China, these have undergone a transformation in terms of economy, society, and ecology. However, a mismatch persists between employment and industrial structures, leading to hidden unemployment. This study employs the framework of hidden unemployment theory, utilizing the Cobb–Douglas production function to quantify the hidden unemployment rate, revealing the relationship between transformation and hidden unemployment. Through this analysis, the underlying causes of hidden unemployment in Northeast China’s state-owned forest regions are scrutinized. There is a bidirectional causal relationship between ecological transformation and hidden unemployment, while there is a unidirectional causal relationship between economic transformation and hidden unemployment. Variance decomposition analysis highlights the substantial contribution of social transformation, followed by economic transformation, with ecological transformation playing a comparatively smaller role. Based on the above research, this article proposes expediting the reforms within the forest industry groups, facilitating the separation of governmental and corporate interests. Additionally, it advocates for strategic forestry development planning to effectively absorb surplus labor, and proposes three policy directives aimed at supporting forest area employees, including provisions for job transfers and reemployment opportunities. Full article

This study utilizes a Cobb–Douglas production function and an instrumental variables regression approach to analyze the impact of quality certification and product diversification on asset productivity at the firm level. Analyzing a panel dataset of approximately 2500 firms from 2011, 2013, and 2015 showed that regional norms significantly influence adoption behaviors, which vary across industries and business types. The study reveals that firms employing computers and those with a larger scale are more inclined to adopt these strategies. The results showed that quality certification enhances asset productivity by approximately 26%, highlighting its positive role. In contrast, firms with diversified products exhibit about 18% lower asset productivity than mono-product firms, suggesting a trade-off inherent in diversification. The study concludes with policy recommendations emphasizing the promotion of quality certification while carefully considering the complexities and potential inefficiencies arising from product diversification strategies. Full article

This study examines the impact of renewable energy on sustainable development in the Kingdom of Saudi Arabia from 2000 to 2019 and analyzes the kingdom’s most essential practices in this field to achieve sustainable development. The Cobb–Douglas production function is used in this study to investigate the impact of renewable energy on sustainable development using ordinary least squares (OLS) estimation. According to the findings, renewable energy consumption has a negative but insignificant effect on GDP. Additionally, traditional energy consumption has a major negative influence on GDP. The findings also demonstrate that fixed capital formulation and technical progress have a significant positive impact on Saudi Arabia’s sustainable development. Furthermore, while the labor force has a positive impact on GDP, this effect is not statistically significant. This report provides some recommendations for Saudi government policymakers to reform the country’s energy efficiency and consumption technologies in order to reduce energy waste and satisfy the goals of sustainable development. While the labor force is recognized as having a positive influence on GDP, it is notable that this result lacks statistical significance. The suggestions of these findings are mainly applicable to Saudi policymakers, and we present recommendations to improve energy competence and utilization technologies. Specially, our suggestions are intended to reduce energy dissipation and to support the objectives of sustainable development. Full article

Sustainable development of the state implies a proportional change in the key macroeconomic indicators described by standard models, one of which is the exponential production function (a special case of the Cobb-Douglas function), where the number of employees (labor) and the value of fixed assets (capital) acts as factor inputs, and GDP becomes the output, and output elasticities of production factors are estimated. This function is successfully used to analyze and predict macroeconomic processes in both developed and developing economies. The purpose of the study is to use econometric modeling—applying the exponential Cobb-Douglas production function—to identify the presence or absence of dependencies of production factors (labor, capital, etc.) on the final product output in Russia. The study shows that in Russia, GDP does not significantly depend on fixed assets. The authors hypothesized that this discrepancy is due to underutilization of production capacities and proved that to reveal the real dependence of Russian GDP production on the value of fixed assets it is necessary to adjust the indicators published by Rosstat for utilization of production capacities, which made it possible to fully use the methodological capabilities of production functions for the analysis and forecasting of macroeconomic processes in Russia. Full article

This study reports the results of farmers’ production via irrigation resources utilization and efficiency parameters of technical efficiency and allocative efficiency by way of sustainable environmental economics. The hypothesis is that factors of farmers’ production affect technical efficiency and allocative efficiency in the irrigation scheme as sustainable environmental economics. Data from cross section and panel data were used and then the productivity parameters measurement of the production function are outlined in two scenarios: first, the data report that the parameters such as output elasticity determine factors of inefficiency and technical efficiency. Second, it presents the scores for the allocative efficiency to explain whether production factors (resources) are optimally, under- or over-allocated by farmers in the irrigation systems under environmental sustainability. This paper presents the productivity and efficiency parameters estimated using stochastic frontier analysis for the translog production function, which was estimated by the MLE method, and the allocative efficiency for the factor inputs allocation in the irrigation systems estimated by ordinary least square for the Cobb-Douglas production function. This study concludes that collective farmers lead into technical inefficiency and over use of factors of production. Full article

For one variable–supply currency in isolation, one player’s Cobb–Douglas utility depends on the current supply divided by the initial supply, multiplied by the inverse of the accumulative inflation/deflation. With equal weight assigned to both factors, money printing outweighs inflation, and money withdrawal outweighs deflation. The study design is to analyze how competition between one variable–supply and one fixed–supply currency impacts the player’s choice of currency. Applying the 1959–2021 US M2 money supply data and the 1635–2021 US inflation data, the player’s utility increases over time when assigning high weight to money printing/withdrawal and increases less or decreases overall when assigning high weight to inflation/deflation. With different player support for the two currencies, depending on each currency’s backing, convenience, confidentiality, transaction efficiency, financial stability, and security, replicator dynamics is used to determine the player’s volume fraction of transactions in each currency. Low, high, increasing, and decreasing support of a currency are analyzed. Each fraction may increase, decrease, be inverse U–shaped, U–shaped, and approach low or high levels over time. For example, high weight assigned to money printing may cause the player to eventually prefer the variable–supply currency unless the player supports the fixed–supply currency highly and increasingly. Full article

This study analyzed the relationship between energy trilemma (ET) and economic growth in 109 countries between 2000 and 2020 across income levels and regions. This study constructed an extended Cobb-Douglas production function including three elements of ET such as energy security, energy equity, and environmental sustainability as their effects on economic growth differ by income level and region. The methodology of this study differs from that of previous studies, which utilized the representative value of ET based on principal component analysis. To analyze the panel series, this study utilized econometric procedures, panel regression of pooled ordinary least squares (OLS), feasible generalized least squares (FGLS), fixed effects, and dynamic panel analysis of generalized methods of moments (GMM) by three income levels. In addition, this study undertook a time series analysis between ET and economic growth for each country. The results showed that each element of ET is not balanced. Moreover, each element can contribute differently to economic growth due to differences in income levels and regions. This study suggested that a balanced environmental policy reflecting various aspects of ET is required and can contribute to the economic growth. Full article