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.

An Application of Dynamic Programming Principle in Corporate International Optimal Investment and Consumption Choice Problem

This paper is concerned with a kind of corporate international optimal portfolio and consumption choice problems, in which the investor can invest her or his wealth either in a domestic bond (bank account) or in an oversea real project with production. The bank pays a lower interest rate for deposit and takes a higher rate for any loan. First, we show that Bellman's dynamic programming principle still holds in our setting; second, in terms of the foregoing principle, we obtain the investor's optimal portfolio proportion for a general maximizing expected utility problem and give the corresponding economic analysis; third, for the special but nontrivial Constant Relative Risk Aversion (CRRA) case, we get the investors optimal investment and consumption solution; last but not least, we give some numerical simulation results to illustrate the influence of volatility parameters on the optimal investment strategy.