Economia
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PROJECTION OF ENERGY USE IN THE RESIDENTIAL SECTOR AGREEMENT MINISTRY OF SCIENCE AND
TECHNOLOGY The use of energy by Activity Sector is included in the National Energy Balance (BEN) since 1970. Data of years prior to 1970 can be obtained from Petrobrás, Eletrobrás, Electric sector Concessionaires and Companies of the productive sector publications, in most cases in a nonsystematic form. Data from BEN are in general sufficient for establishing reliable correlation. Projections concerning the Residential Sector have a special characteristic in the set of tasks given to Economy & Energy due to the nature of the variables that condition the use of energy. In the Industrial Sector, for example, economic factors, production technology, energy prices, payment forms, etc. are predominant. In the Residential Sector the predominant factors are those related to comfort, safety in use, absence of odour and smoke, etc. It is difficult to quantify these factors and they demand a treatment different from that of the industrial case, where the causal relationships are predominant. In principle, the size of the population, the fraction of the urbanized population and the income will be considered as relevant factors. In the preliminary projection exercises it was verified that the population and the fraction of urbanized population are described by the logistic law, developed by Verhulst as a support for analyzing the Malthus model and which has been successfully applied in the forecast of the evolution of selfreproducing closed systems (1,2, 3 – Prigoginee, Marchetty et alli) in a niche of finite resources (food, capital, information, etc.) Due to its frequent use in the present work, it is worth while to explain the sequence of procedures adopted in the application of the logistic law. The differential equation of the logistic law [ dN/dt = a N (N*N)] is fitted to the set of observed data concerning the rate (dN/dT) of the population evolution N, permitting the estimation of its final size, N*, as being twice the value of N corresponding to the maximum of dN/dT [ dN/dT is maximum when N=N*/2]. In this step, the average variation rates are used in time intervals that are long enough to absorb the fluctuations of N and short enough to supply a convenient number of rate values to be used in the dN/dT fitting. We have preferred to use fiveyear intervals when the historical series is about 30 years, as in the National Energy Balance. Once the value of N* is obtained, a change of variable F= N/N* is made and the linear form of the logistic law [ ln F/(1F)=at+b] is adopted in order to verify if the system under study follows this law; if the fitting of the linear form, using the method of least squares, produces correlation coefficients close to unity, the population can be described by the finite form of the logistic law [N/N* = 1/(1+ke^{at })], permitting extrapolation based on a law already tested in the population of people and other “populations”, in the large sense of the term. This procedure prevents errors due to mechanized fitting to arbitrary functions. POPULATIONData concerning the population are from the Census made by IBGE, complemented by evaluations carried out by this Agency in 1996. Projection for the year 2000 was made through the identification of the law observed until 1996, namely the classical logistic law. This behavior was the expected one for a practically closed population, since in the considered time interval the important migrations have been attenuated. The projection is based on demographic studies made by Neupert (1) which permit to evaluate that around 2100 the Brazilian population will differ from its stationary value of 250 million people by less than 1%. The details of this methodology can be found in issue n^{0} 1 of the electronic periodical e&e (http://ece.com) . Graphic 1 (table 1) is the representation of the population growth law that was transformed into a straight line by changing the variable P (number of inhabitants) to F= P/P*, where P/P* is the final number of inhabitants previously estimated. The table below summarizes the results of interest to the present work. Table 3  Projected population – million of inhabitants.
The linear interpolation in each quinquennium produces an approximation better than 0,1%. Graphic 1 Brazilian population. URBAN POPULATION.Using the Census data it is verified that the urbanization process in Brazil fits well to a logistic curve as shown in graphic 2. Graphic 2 – Urbanization index. The results of interest for the present work are shown in the table below .
GROSS NATIONAL PRODUCT.The values used were calculated in dollars of 1994 based on the exchange rate, according to a compilation carried out by e&e’s team, and using the purchase power parity concept published by the International Energy Agency, series “Energy Statistics & Balances“ 1998 edition, In all cases where comparison among countries were made, the substitution equivalent energy and the purchase power parity concepts were used. Graphic 3 shows the evolution of the Gross National Product using the Exchange Rate and the Purchase Power Parity (PPP) and compares the data compiled by e&e based on the National Accounts, expressed in 1994 dollars, with those of the International Energy Agency (purchase power parity concept PPP). It can be observed that the Brazilian GNP is about 50% larger that that evaluated using the exchange rate Graphic 3 – Gross National Product. In spite of the abrupt variations that began in the eighties following the so called petroleum “price shocks”, not yet completely absorbed, the GNP can be described by a logistic law with reasonable adherence to the observed data. It should be noted the elastic return to the logistic curve after financial crisis, already registered in other studies concerning closed systems. The methodology used to project the Gross National Product and the results of interest to this work are presented in the Macroeconomic Module, presented in a previous report. In the Reference Scenario adopted the GNP would grow according to the table below
Graphic 4 – Gross National Product Adjustement. 