INTRODUCTION…………………………………………………………………………………….3

SECTION 1

Individual demand for Private good……………………………………………………………...4

SECTION 2

Engel Model OLS Estimtion………………………….………………………………………….6

Empirical Results explanation………………....………………………………………………….8

Analysis of Scale Economies across Different Income Groups……..………………………..…10

SECTION 3

Economies of Scale and Poverty Measure……………………………………………………….12

Economies of Scale and Welfare Comparison…………………….…………………………….13

Implication of Economies of Scale to the Government Welfare Policy..……………………….14

CONCLUSION………………………………………………………………………………………17

REFERENCE….…………………………………….………………………………………………18

APPENDIXES

Appendix1. Explanation of Variables…………………………………………………………21

Appendix2. Estimated Results of Engel Curve……………………………………….……….22

Appendix3. Estimated Results of Engel curve

without control variables for performing F-Test……….…………………………………22 Appendix4. Estimated Results of Engel Curve for 5 Income Groups…………………………23 Appendix5. OECD Equivalence Scale………………………………………………………...26

INTRODUCTION

The paper discusses household resources allocation between jointly consumed goods (public goods) and those consumed individually (private goods); and implication of household scale economies to the government welfare policy. The first section focuses on the derivation of the individual demand function for private good, and the effect of change in household size on private good consumption. The second section provides OLS estimation of the Engel curve borrowed from Deaton and Paxson (1998) for clothing (purely private good). For the purpose of estimation and analysis the sample data of 2948 Uzbek households from World Bank’s Living Standards Measurement Survey was used. In addition, the sample was divided into 5 income quartiles and the variation in household economies of scale across income groups is discussed in the second section. Section three explains the implication of economies of scale to poverty measure, welfare studies, and government welfare policy.

SECTION 1

Individual Demand for Private Good

Suppose that a household has n identical members, and individual preferences are represented by a utility function of the form: u(x,y) =

where x and y are quantities of goods X (private good) and Y (public good) respectively. The consumer preferences are assumed to be monotonic; hence the consumer is expected to spend all income between these two goods. Each household member has income m, and as they share the cost of public good, the individual budget line is:

where are prices of goods X and Y accordingly

The utility maximization problem of the individual is:

Max u(x,y) =

S.t.

The Lagrangian for this problem is

L=x2+y-λ(pxx+pyny-m)

Differentiating gives us the first-order condition:

∂L∂x=2x2x2+y-λpx=0∂L∂y=12x2+y-λpyn=0∂L∂λ=-pxx-pyyn+m=0 => xx2+y=λpx (1)12x2+y=λpyn (2)pxx+pyyn=m (3)

Divide equation (1) by equation (2)

2x=pxpynpxx+pyyn=m => x=pxpy*n2pxx+pyyn=m

Hence the demand functions for private good X is

x=n2*pxpy

Once we have the demand function for good X, the demand function for good Y comes from the budget constraint:

y=n*mpy-n*px22py2

Taking into account that consumption can not be negative, and when income m is zero, the demand is also zero; the demand function for good Y takes the form:

y=0 when m≤px22pyn*mpy-n*px22py2 when m>px22py

The derived demand function of private good X has the interesting feature that the demand for X is dependent from a number of members in household.

x=n2*pxpy

Thus, keeping the individual income and prices constant, it is clear that the only factor, which may cause the demand of X to change is increase or decrease of the numbers of household members. The logic behind this is that as a number of household members increases, they...