A Model For The Quality Of Life As A Function Of Electrical Energy Consumption
Global Issues >> Energy >> A Model for the Quality of Life Energy Vol. 16, No.4, pp.739745, 1991 03605442/91 $3.00 + 0.00
Abstract We present a mathematical model for the physical quality of life as a function of per capita electrical energy consumption. This model is based on data for 112 countries. Our equation may be used to assess the physical quality of life as a guideline for national planning.
INTRODUCTION
For the remaining threequarters of the human population, conditions are painfully different. The overwhelming majority of these people are illiterate or semiliterate poor villagers surviving on less than adequate diets, whose infant mortality is an order of magnitude higher than in the developed world and whose life expectancy is as much as three decades shorter. The difficult present and less than promising future of this developing world, or as some prefer, the less developed countries (LDC) or underdeveloped Third World is, to a very large extent, the result of relatively low consumption of commercial energy.^{1} In developing countries, agriculture is the main source of biomass fuel, as well as one or the main energyconsuming sectors. The energy captured through agriculture in crops and crop residues provides food for people and fodder for draft animals, Dung and crop residues are used for cooking and heating.^{2,3} During the past two decades, these traditional energy sources have been supplemented by the use of coal, oil and electricity in agriculture, transport, industry, and the domestic sectors. The most striking feature of energy use in the Third World is that the amount of useful work which the poor obtain from the energy they use is relatively small.^{4} When the inputs to agriculture (including directly applied energy) are increased properly, the energy outputs per worker and per unit of land increase. Energy obtained from the consumption and sale of crops is, in turn, needed to increase the input to agriculture to raise crop yields, extend irrigated land, increase multicropping, mechanize construction and repairs of water projects, build modern roads, and, in general, improve the quality of life of the peasants. The rate with which the developing countries move toward the distant goal of rural modernization is largely determined by the direct and indirect energy flows into agriculture, which may be expected to make up a larger fraction of energy consumption in the future than at present. The standard of living or quality of life achieved in any community and for any group of people may be measured, for practical purposes, by the quantity of total energy used per capita.^{5} It has been widely recognized that the preceding statement is more appropriate for societies in which the production and distribution of energy is secure and widely spread than for LDCs. Several studies have been reported on increasing energy requirements for economic development and enhancing the quality of life, Smil^{6} reports that economic growth and energy consumption are closely related. Smil and Knowland^{7} state that energy is the prime mover for economic growth and development. Revelle^{8} comments that men and women in rural areas are tied to poverty and misery because they use too little energy and use it inefficiently. In addition, Rahman and Huq^{9} claimed that there was a distinct correlation between energy consumption and the overall economic conditions in any country. Brisco and Bari^{10} pointed out that the socioeconomic position of rural people will deteriorate rapidly unless increased inputs of technology and energy are made into agriculture. Friedlander^{11} noted that in order to achieve an Improved standard of living, developed countries have encouraged the consumption of energy at a very fast rate Dalal^{5} emphasized that electrical energy consumption is an indicator of economic condition. Hoque et al^{12} state that the total energy produced and obtained from all possible sources is an index of the physical quality of life. Forrester^{13} estimated the physical quality of life by using pollution, population density, food consumption, and resources as indicators. Islam^{14} quantified the quality of life by using 28 variables. Alam et al^{15} reported that the physical quality of life in developing countries depends on fundamental needs and energy consumption in various forms and quantified it in terms of cooking energy (in the form of biogas) and population density. Martin^{1} calculated the physical quality of life index for different countries by using an average life expectancy (LE) at age 1 year, infant mortality (IM), and literacy rates (LR). In this paper, we present an empirical equation showing the relation between the physical quality of life and the per capita electrical energy consumption in kilowatt hours. DEVELOPMENT OF THE MODELMartin^{1} defined the physical quality of life in terms of LE, IM, and LR and estimated the physical quality of life for 147 countries. However, we postulate that Martin's suggested approach of basing it on a variety of statistical socialcondition indices related to population for the parts of the world under investigation leads to some vague data. Instead, we postulate that the electricity consumption figure per capita will implicitly include and also reflect the overall physical condition of people carrying on their various activities and passing their lives at a certain stage of development. We have obtained the per capita electrical energy consumption (kWh/cap) for 112 countnes.^{16}
Fig. 1. Comparison of reported ( + ) and correlated values ( ) of LE vs ln(kWh/cap). Fig. 2. Comparison of reported ( + ) and correlated values ( ) of LR vs ln(kWh/cap). In Fig. 1, we show the correlation (line) together with actual data for LE as a function of per capita energy consumption and the regression equation is: Fig. 3. Comparison of reported ( + ) and correlated values ( ) of IM vs ln(kWh/cap). Fig. 4. Comparison of reported ( + ) and correlated values ( ) of PQLI vs LE. Fig. 5. Comparison of reported ( + ) and correlated values ( ) of PQLI vs LR. Fig. 6. Comparison of reported ( + ) and correlated values ( ) of PQLI vs IM. In Figs. 2 and 3, we also show the correlation (line) together with actual data for each or the variables LR and IM as a function of per capita energy consumption respectively and the corresponding regression equations are: IM = 256.05  29.41(ln(kWblcap)) r = 0.88 (3) Again, we show the correlation (line) together with actual data for physical quality of life as a function of each of the variables LE, LR and IM in Figs. 4, 5 and 6 respectively and the corresponding regression equations are: PQLI = 15.65 + 0.79(LR), r = 0.98 (5) PQLI 99.32 0.44(IM), r = 0.97. (6) Martin's estimation and examination of Figs. 1 6 and of Eqs. (1) (6) suggests the following functional relations: kWh/cap = f2(LE, IM, LR), (8) where PQLI = physical quality of life. Equations (7) and (8) suggest the relation where A may be taken as a technological constant. This technological constant depends on the form and mode of energy use and on energyuse efficiency. The technological constant will increase in value with technology advancement. The parameter A may be estimated by regression analysis. We find: The utility of Eq. (10) may be checked.^{1719} From T tests, t = 61.10 and the tabulated value is 1.98 at the 5% level of significance.^{18} This large value of t leaves little doubt that PQLI and ln(kWh/cap) are linearly related as specified.
Fig. 7. Comparison of reported ( + ) and correlated values ( ) of PQLI vs kWh/cap. Other measures of the utility of our model are the coefficient of correlation r and rank correlation coefficient r(rank), where r = 0.89 and r(rank) 0.98. These large values confirm the conclusion that PQLI and ln(kWh/cap) are highly correlated. Figure 7 shows the correlation between PQLI and kWh/cap. The agreement is fairly good. Figure 8 shows the residuals (PQLI_{i}  PQL1_{i}) vs ln(kWh/cap). Since the residuals are randomly scattered about the reference tine, we have additional evidence that our regression model correlates the data well. Fig. 8. Residuals (PQLI_{i}  PQL1_{i}) from Eq. (10) and random scatter. REFERENCES
