1 Abstract—This project investigates the relationship between economic, demographic, and environmental systems using engineering controls concepts and modeling tools. A variable tax feedback loop is added to previous work in order to obtain greater performance. A rapid government response rate is determined to yield the best results. Index Terms—control systems, growth economics, sustainable development. I. INTRODUCTION Economic development and sound environmental management are complementary. Development can contribute to improved environmental management, and a healthy environment is essential for sustaining development. - World Bank, 1992 ne of the most important problems of the 21st century will be sustainable development. The World Commission on Environment and Development defines sustainable development as “development that meets the needs of the present without compromising the ability of future generations to meet their own needs” [1]. Given the environmental and ecological constraints of the earth, it is uncertain whether the current levels of growth and poverty alleviation will be achievable in 50 or 100 years. Unfortunately, it is difficult to get a clear picture of how environmental and economic systems will interact and impact development, and there are a wide variety of viewpoints and opinions on this issue [2]. In order to gain greater certainty with regards to sustainable development, modeling and controls concepts will be utilized. The Wonderland model of the economy and the environment will be used as a starting point for analysis [3]. Any model of a complex system will involve considerable simplifications, and this model is no exception. However, the Wonderland model offers insight into sustainable development and how it can be attained. Specifically, this Manuscript received December 18, 2003. This paper was written as a final project for Calvin College’s Engineering 315 Control Systems class. M. J. Bloem is with the Calvin College Engineering Department, Grand Rapids, MI 49546 USA (e-mail: [email protected]). S. L. Schoofs is with the Calvin College Engineering Department, Grand Rapids, MI 49546 USA (e-mail: [email protected]). paper will evaluate the role of pollution taxes in achieving sustainable development. II. DESCRIPTION OF PREVIOUS WORK A. The Wonderland Model The Wonderland model was developed to investigate the relationship between economic, demographic, and environmental systems. The model has four subsystems: the economy, population, the environment, and pollution. All of the variables in the model are shown in Table I. TABLE I. MODEL VARIABLES Variable DescriptionY Per capita outputI Net per capita outputB Crude birth rateD Crude death rateN PopulationF Flow of pollutantsK Natural capital stockC Pollution control expenditureP Pollution per unit of output 1) Economy: The equations representing the economy are shown below. ])1()(1[1ληγγtttKYY −⋅+−+⋅=+ (1) tttCYI −= (2) The economy is modeled to grow exponentially, and depends on the level of natural capital. The stock of natural capital includes the forests, streams, oceans, and air that allow our economy to operate. If the stock of natural capital is 1, indicating that the environment is undiminished by pollution, then economic growth is unhindered. If the stock of natural capital is depleted to a level lower than 1, however, economic growth begins to slow. Once the stock of natural capital has been totally depleted (K = 0), the economy collapses and output falls to 0. Note that net per capita output, I, is the output that is left after per capita expenditures on pollution controls have been subtracted from the gross level of output per capita. 2) Population: The equations representing the population level are shown below. Controlling Wonderland (Dec. 2003) Michael J. Bloem and Samuel L. Schoofs, Student Member, IEEE O2 +−=⋅⋅ttIIteeBβββ11 (3) ()[]θαααααtIItKeeDtt−⋅+⋅+−⋅=⋅⋅111210 (4) −+⋅=+100011ttttDBNN (5) The population level is determined by considering the difference between the death rate (Dt) and the birth rate (Bt) in Wonderland. As income increases, death rates and birth rates decline. Also, as the stock of natural capital becomes depleted, the death rate begins to rise. This occurs because a decline in natural capital can have negative impacts on health as well as economic performance. 3) Environment: The equations representing the environment are shown below. +⋅−⋅⋅=⋅⋅⋅⋅NCNCtttttteePYNFεεκ1 (6) ttttttttFKKKFKKKteeKωωρρ−⋅+−−⋅+−++=51ln51ln11 (7) ()tttYKC ⋅−⋅=µφ1 (8) Equation 6 gives the flow of pollutants, F. This depends on the population, per capita output, pollution per unit of output, amount spent on pollution control measures, and the effectiveness of pollution control measures, κ. The relationship between the flow of pollution and the stock of natural capital is explained by equation 7. Natural capital is depleted as the flow of pollution increases, but natural capital can regenerate to offset earlier damages. The pollution control expenditure in Wonderland, C, is determined by the stock of natural capital and the income per capita level (equation 8). As the stock of natural capital is diminished, pollution control expenditures grow. Higher income levels also correspond to greater pollution control expenditures. 4) Pollution: The equations representing pollution are shown below. ttPP ⋅=+χ1 (9) The amount of pollution per unit of output, P, is assumed to decrease at a rate χ. Note that as long as χ is less than 1, pollution per unit of output declines exponentially. As will be shown later, χ is an important parameter for this model. The parameter values used in this model are shown in Table II. TABLE II. MODEL PARAMETERS (FOR DREAM SCENARIO) Parameter Value Sectionγ 0.04 Economyη 0.04 Economyλ 2.00 Economyα 0.09 Populationα010.00 Populationα12.50 Populationα22.00 Populationβ 0.08 Populationβ040.00 Populationβ11.38 Populationθ 15.00 Populationκ 1.00 Environmentδ 1.00 Environmentε 0.02 Environmentρ 0.20 Environmentω 0.10
View Full Document
Unlocking...