Introduction

This paper analyzes and examines the study approached by Deaton and Paxson (1998), their thesis was based on the test of Barten model, which explains positive relationships between the standard of livings and household size. The assumption of their phenomena was that larger households with constant per capita income save on the public goods, e.g. housing, that is they share the cost of it equally and it is free of charge and can afford to increase consumption of private goods, e.g. food or clothing.
In order to reveal and explore the concept of this empirical study, this assignment is divided into four main parts. The first section is dedicated to the utility maximization problem and demand function analysis. Further, the Engel curve regression analysis will be interpreted based on household’s consumption and demographic data. In its turn, third section will provide valid criticism and divulging drawbacks of Deaton and Paxson’ work based on the written documents of the scientists Horowitz (2002) and Vernon and Gan (2003). And the final chapter discusses the implication of the theoretical models and techniques for the government poverty measure and welfare issues.

Section 1. Derivation of individual food demand

For this task, it is given:

[pic] = Utility function
[pic] = Budget Constraint
Where: x - privately consumed good y – publicly consumed good m- income per capita
Thus the method of utility-maximization problem is essential here in order to get algebraic example of actual demand function. In common, there are two technique tools to resolve above task: first one is optimal-choice problem and the second one is Lagrange multiplier, that is the method of discovering the maximum function subject to the constraint. The latter one is more appropriate as there is no need to explicitly solve the conditions and use