Sensitivity Analysis between Lagrange Multipliers and Consumer Budget: Utility Maximization Case

In this paper sensitivity analysis between Lagrange multipliers and total budget is discussed. The method of Lagrange multipliers is a very useful and powerful technique in multivariable calculus. In mathematical economics, utility is the vital concept that increases or decreases overall happiness of the consumers. This study tries to discuss utility maximization policy of an organization by considering two constraints: budget constraint and coupon constraint. In this article, an attempt has been taken to achieve the best result through the application of scientific method of optimization

Utility Maximization Analysis of an Emerging Firm: A Bordered Hessian Approach

In this paper, method of Lagrange multipliers is used to investigate the utility function; subject to two constraints: budget constraint, and coupon constraint, and to verify that the utility is maximized. An economic model of an emerging firm has been developed here by considering four commodity variables. In the study, determinant of the 6×6 bordered Hssian matrix is operated to verify the utility maximization. Two Lagrangian multipliers are used here, as devices of optimization procedures, during the mathematical calculation. In this article, an attempt has been taken to achieve optimal result by the application of scientific method of optimization

Economic Investigation of Lagrange Multiplier if Cost of Inputs and Budget Size of a Firm Increase: A Profit Maximization Endeavor

In this study method of Lagrange multiplier is considered to investigate profit maximization policy. In the twenty first century global economy faces serious complexities. Sensitivity analysis of economic firms becomes essential part of sustainable economic environment. The method of Lagrange multiplier is a very useful and powerful technique in multivariable calculus that is applied in economic models to obtain higher dimensional unconstrained problem from the lower dimensional constrained problems. This paper proceeds with Cobb-Douglas production function, where 6×6 bordered Hessian and 6×6 Jacobian are used to examine sensitivity analysis efficiently and elaborately

UTILITY MAXIMIZATION OF BANGLADESHI CONSUMERS WITHIN THEIR BUDGET: A MATHEMATICAL PROCEDURE

A consumer is considered as a person or a group of people who uses purchased goods, products, or services only for personal use, and not for manufacturing or resale. Consumers usually purchase valuable and useful commodities or goods by spending all or partial of their income. The property of a commodity that enables it to satisfy human wants is called utility. Producers must be conscious to increase the utility among the consumers. This study has considered the maximization of utility problem of consumers of Bangladesh subject to two constraints; namely, budget constraint and coupon constraint. Consequently, in the study two Lagrange multipliers are used and interpreted these with mathematical analysis. Prediction of consumer behavior will help both producers and consumers to take decision of their future economic productions and consumptions, respectively. This article is ornamented with sufficient theorems and economic analyses. So that all the readers find interest when go through the economic analysis of utility maximization

Utility maximization analysis of an emerging firm: a bordered Hessian approach

In this paper, method of Lagrange multipliers is used to investigate the utility function; subject to two constraints: budget constraint, and coupon constraint, and to verify that the utility is maximized. An economic model of an emerging firm has been developed here by considering four commodity variables. In the study, determinant of the 6×6 bordered Hessian matrix is operated to verify the utility maximization. Two Lagrangian multipliers are used here, as devices of optimization procedures, during the mathematical calculation. In this article, an attempt has been taken to achieve optimal result by the application of scientific method of optimization

Utility Maximization Analysis of an Organization: A Mathematical Economic Procedure

In the society utility is the vital concept, especially in mathematical economics. It is considered as the tendency of an object or action that increases or decreases overall happiness. In social sciences, the property of a commodity that enables to satisfy human wants is called utility. This paper has tried to operate utility maximization policy of an organization by considering two constraints: budget constraint and coupon constraint. To develop the maximization policy of utility function, the techniques of multivariate calculus are used. In this study four commodity variables are used to operate the mathematical analysis efficiently. In this article Lagrange multiplier technique is applied to achieve optimal result throughout the study

Sensitivity Analysis between Lagrange Multipliers and Consumer Budget: Utility Maximization Case

In this paper sensitivity analysis between Lagrange multipliers and total budget is discussed. The method of Lagrange multipliers is a very useful and powerful technique in multivariable calculus. In mathematical economics, utility is the vital concept that increases or decreases overall happiness of the consumers. This study tries to discuss utility maximization policy of an organization by considering two constraints: budget constraint and coupon constraint. In this article, an attempt has been taken to achieve the best result through the application of scientific method of optimization

Learning Personalized Risk Preferences for Recommendation

The rapid growth of e-commerce has made people accustomed to shopping online. Before making purchases on e-commerce websites, most consumers tend to rely on rating scores and review information to make purchase decisions. With this information, they can infer the quality of products to reduce the risk of purchase. Specifically, items with high rating scores and good reviews tend to be less risky, while items with low rating scores and bad reviews might be risky to purchase. On the other hand, the purchase behaviors will also be influenced by consumers' tolerance of risks, known as the risk attitudes. Economists have studied risk attitudes for decades. These studies reveal that people are not always rational enough when making decisions, and their risk attitudes may vary in different circumstances. Most existing works over recommendation systems do not consider users' risk attitudes in modeling, which may lead to inappropriate recommendations to users. For example, suggesting a risky item to a risk-averse person or a conservative item to a risk-seeking person may result in the reduction of user experience. In this paper, we propose a novel risk-aware recommendation framework that integrates machine learning and behavioral economics to uncover the risk mechanism behind users' purchasing behaviors. Concretely, we first develop statistical methods to estimate the risk distribution of each item and then draw the Nobel-award winning Prospect Theory into our model to learn how users choose from probabilistic alternatives that involve risks, where the probabilities of the outcomes are uncertain. Experiments on several e-commerce datasets demonstrate that our approach can achieve better performance than many classical recommendation approaches, and further analyses also verify the advantages of risk-aware recommendation beyond accuracy