The Relationship Between Capital and Waste Accumulation: An Application of Dynamic Input-Output Approach



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The Relationship Between Capital and Waste Accumulation:

An Application of Dynamic Input-Output Approach*

By

Shigemi Kagawa


Research Center for Material Cycles and Waste Management,

National Institute for Environmental Studies,

Onokawa 16-2, Tsukuba, Ibaraki, 305-0053, Japan,

Phone: +81-298-502843, Fax: +81-298-502840,

E-mail: kagawa.shigemi@nies.go.jp.
First version: November 2001

Second version: July 2002

This version: September 2002

*This revised paper was prepared for the Society for Environmental Economics and Policy Studies, Hokkaido, Japan, 28-29 September, 2002, and for the Fourteenth International Conference on Input-Output Techniques, Montréal, Canada, 10-15 October, 2002.



The Relationship Between Capital and Waste Accumulation:

An Application of Dynamic Input-Output Approach

Abstract

In the long run, we cannot examine the dynamic path of waste accumulation without evaluating a path of capital accumulation (investment decision) at the same time. This paper explores the dependent relationship between capital and waste accumulation. Through this exploration, I find some important conditions in terms of both balanced growth paths and finally reveal a functional relationship between capital and waste accumulation process.


Keywords: Dynamic input-output models; balanced growth paths;

capital accumulation; waste accumulation; Frobenius roots

JEL Classification Numbers: O41, Q00, Q01, Q32


1. Introduction

Examining the dynamics of waste accumulation is fundamental to evaluating the relationship between environmental externalities related to waste generations and recycling technology innovations.1 What are the structural determinants of the dynamic path of waste accumulation? And what are the economic and environmental impacts of the structural determinants?

In order to analytically answer these questions, I (2001) recently proposed a simple dynamic multi-sector model for waste analysis by following Leontief’s dynamic tradition (1953, 1970b). The crucial point of the model is that a technical coefficient matrix of intermediate waste was definitely incorporated into the traditional Leontief dynamic system and it was indicated that a dynamic path of waste accumulation largely depends on a recycling technology of the intermediate waste. More concretely, assuming that the number of ordinary marketable commodities, and non-marketable wastes is n,2 the continuous dynamic equilibrium for waste distribution can be described by

Intermediate waste inputs for production of intermediate goods and services at time t

Intermediate waste inputs for production of additive capital stock at time t

Intermediate waste inputs for production of final goods and services at time t

Final waste disposal

at time t



Total waste outputs at time t
(1)
or
(1)’
where is the physical total output of waste


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