This book provides an analytical and computational approach to solving and simulating the Mahalanobis model and the papers surrounding it. The book comes up, perhaps for the first time, with a holistic examination of an important growth model that emerged out of India in the 1950s. It contains detailed derivations of the Mahalanobis model and the several critiques and extensions surrounding it with an organized synthesis of the main results. Computationally, the book simulates the model and its many variants, thus making it accessible to a wider audience. Advanced undergraduates and beginning graduate students in the fields of Economics, Mathematics, and Statistics will gain immensely from understanding both the mathematical aspects as well as the computational aspects of the Mahalanobis model. In the absence of a single 'go-to' source on all aspects of the model -- analytical and computational -- this book is a definitive volume on the Mahalanobis model that has all the derivations of all the papers surrounding the model, its dissents and critiques, and extensions as in the wage goods model suggested by Vakil and Brahmananda.
Author(s): Chetan Ghate, Pawan Gopalakrishnan, Srishti Grover
Publisher: Springer
Year: 2022
Language: English
Pages: 215
City: Singapore
Acknowledgements
Contents
About the Authors
List of Figures
List of Tables
1 Introduction
1.1 Why Do We Need This Book?
1.2 MATLAB/Octave
1.3 Where Does This Book Fit into the Field of Growth Theory?
1.4 Who Is the Ideal Reader?
1.5 Descriptions of Chapters
1.6 What Is the Relevance of the Mahalanobis Model Today?
1.7 Summary
2 The Mahalanobis Two-Sector Model
2.1 The Harrod-Domar Model
2.2 The Mahalanobis Model
2.2.1 Production Structure
2.2.2 Solving the Baseline Model
2.2.3 Growth Rate of Output in the Mahalanobis Two-Sector Model
2.2.4 Critical Level of λi: A Knife-Edge Result
2.3 Comparing the H-D Model with the Mahalanobis Model
2.4 Similarities between the Mahalanobis Model and the Fel'dman Model
2.4.1 Model Setup
2.4.2 Level Equations
2.4.3 Rate of Growth in the Fel'dman Model
2.4.4 Optimum γ: The Maximization of Consumption and the Short-Run Versus Long-Run Trade-Off
2.5 Summary
2.6 Technical Appendix
3 The Stochastic Two-Sector Mahalanobis Model
3.1 Introduction
3.2 The Model
3.2.1 Case 1: µ=0
3.2.2 Case 2: µneq0
3.3 The Mahalanobis Model with Changing β
3.3.1 Time-Varying β: ch3Mahalanobis1953
3.3.2 A One-Time Step-Function Progression in β
3.4 Summary
3.5 Technical Appendix
4 Critiques of the Two-Sector Mahalanobis Model
4.1 Introduction
4.2 The Bronfenbrenner Model: Capital Malleability
4.2.1 The Model
4.2.2 A Dilemma
4.2.3 Comparing the Mahalanobis Model and the Bronfenbrenner Model
4.2.4 Summary
4.3 Ezekiel's Critique of the Bronfenbrenner Model
4.3.1 Bronfenbrenner's Rejoinder
4.4 Bettelheim's Critique: A Role for Replacement Requirements
4.4.1 The Model
4.4.2 Comparing Output in the Mahalanobis Model and the Bettelheim Model
4.4.3 Revisiting Bettelheim's Original Critique
4.4.4 Evolution of National Income
4.4.5 Critical Value of λi
4.5 Haldane's Critique: the Need for Targeted Investment Allocation
4.6 Summary
4.7 Technical Appendix
5 Open Economy Extensions of the Mahalanobis Model
5.1 Introduction
5.2 The Harris (1972) Model
5.2.1 The Model
5.2.2 The Growth Paths of the Sectoral Capital Stocks
5.2.3 Growth Rate of Capital in the Economy
5.2.4 Growth Rates in the Economy
5.2.5 Comparison with ch5Mahalanobis1953
5.3 The ch5Ezekiel1965 Model
5.3.1 The Model: x-Pattern Versus the y-Pattern
5.3.2 Solving the Model
5.3.3 Growth Rates in the Economy
5.3.4 Comparing Alternative Patterns
5.3.5 Incremental Savings Ratio
5.3.6 Domestic Production of Capital Goods
5.3.7 Impact on Employment
5.3.8 Conclusion
5.4 Technical Appendix
6 The Mahalanobis Four-Sector Model
6.1 Introduction
6.2 The Model
6.2.1 Parameter Values
6.2.2 Solving the Model
6.2.3 Some Counterfactuals
6.3 Growth in the Four-Sector Model
6.4 Open-Economy Version of the Four-Sector Model
6.4.1 The Level Equations in the Open-Economy Model
6.4.2 Calculating the Parameter Values
6.4.3 Comparison with the Closed-Economy Mahalanobis Model
6.5 Two Criticisms of the Four-Sector Model
6.5.1 The Shenoy Critique
6.5.2 The Komiya Critique
6.6 Summary
6.7 Technical Appendix
7 Optimal Savings Plough-Back and the Wage-Goods Model
7.1 Introduction
7.2 The Model
7.2.1 Growth Rates in the Economy
7.2.2 Steady-State Growth Rate and the Optimal Plough-Back Ratio
7.2.3 Asymptotic Growth Rates
7.3 Comparing Growth Rates Under the Mahalanobis Model and Wage-Goods Model
7.4 Summary
7.5 Technical Appendix
Index
Index
