#### Date of Submission

2-28-1972

#### Date of Award

2-28-1973

#### Institute Name (Publisher)

Indian Statistical Institute

#### Document Type

Doctoral Thesis

#### Degree Name

Doctor of Philosophy

#### Subject Name

Mathematics

#### Department

Economic Research Unit (ERU-Kolkata)

#### Supervisor

Mukherjee, Moni (ERU-Kolkata; ISI)

#### Abstract (Summary of the Work)

International variation in national product is a subject of considerable interest, and any meaningful comparison of national product or per capita national income has to be in termo of a common currency. An intertemporal comparison for the same country at two points of time is mote meaningful in real terms, or in other words when the currency unit is adjusted for change in the general price level between the two points of time. In the same manner, the level of output or of consumption of a group of persons belonging to a region or to a particular socio-economio group can be meaningfully compared with another such group, when an appropriate adjustment is made for the variations in the purchasing power of the monetary unit used in the two groups to obtain the measures of the aggregates at current prices. This results in the need fet suitable index number formulae fer price comparisons. Research in this line together with the availability of numerous index number formulas made the problem of choice of a system of index numbers, for a given comparison problem, more acute.This has led to the formulation of some restrictions which are intuitively justified, so that the index numbers not satisfying these restrictions may be discarded. These are termed as 'consistency tests' in the literature of index numbers It is Irving Fisher who introduced the idea of consistency tests and brought them into prominence. We focus our attention on the circularity test which is the generalization of Fisher's time reversal test and this test gives the basic problem of the thesis.Let us formulate the problem of multilateral price and quantity comparisons, given the price and quantity vectors concerning each country. This discussion can be made more general by replacing the countries by any set of well defined population groups. The groups may refer to different countries or different sections of the population of a country defined according to certain social and economic characteristics, and it may be convenient to talk in terms of groups from now on. The analysis works in all cases without loss of generality. Ijk represent the price index for the k-th group with the Let j-th group as base.In this set-up, the circularity test requires that the price change between any two groups can. be expressed as the product of price change measured through a third group. Hence the test stipulates that Ijk=ijÎ»+IÎ»k for all groups 1, jk k and k. This test makes use of the assumption that the price changes are multiplicative. The condition becomes Ijk=ijÎ»+IÎ»k in the case of addictive set-up.

#### Control Number

ISILib-TH13

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

#### DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

#### Recommended Citation

Rao, Dodla Sai Prasada Dr., "Contributions to Methodology of Construction of Consistent Index Number." (1973). *Doctoral Theses*. 72.

https://digitalcommons.isical.ac.in/doctoral-theses/72

## Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28842848