Texts for Discussion
Follow-up of the Partnership Contract between e&e and MCT:
Text for Discussion
New Version of the Macroeconomic Module of projetar_e, Program Calculation
Approch and Results of the Reference Scenario
Carlos Feu Alvim, Frida Eidelman, Olga
The macroeconomic projection module of projetar_e, has been used in several studies of the Economy and Energy Organization e&e that were published in the periodical of the same name (http://ecen.com) or it is part of specific reports of projects developed by the Organization. It is a dynamic adaptation of the model developed in the book "Brasil: O Crescimento Possível" - Bertrand do Brasil 1996 – by Carlos Feu Alvim et al., and it is part of a set of programs aiming at subsidizing economic planning and helping the construction of scenarios.
This module maintains in its approach the Idea of “anchoring” projections in the historical behavior of quantities of the “real economy” as presented in IBGE’s National Accounts or in additional data that are coherent with its methodology. The future is projected considering the historical behavior of variables during 50 years. The experience of applying the model for more than 10 years has demonstrated that variables that have inertial behavior along the years tend to maintain the same behavior in the future. Sudden changes as those reached in the internal savings at the start of the 1990s tend to be reversed and the parameter resumes the previous historical path.
The initial development of the projetar_e module was carried out by Carlos Feu Alvim, Eduardo Marques e Aumara Feu. In the Economy and Energy periodical Nº 22 (http://ecen.com/matriz/matriz2/macro_ec.htm) a description of the macroeconomic module and of the variables involved as well as of the calculation procedure adopted are presented. This software has been continually improved and has been used in several economic and energy planning studies and in projections of greenhouse effect emissions. A reformulation of the calculation program was recently carried out to ECEN Consultoria by Rafael Macêdo under the orientation of Carlos Feu Alvim. The program can also be run in English (version made by Frida Eidelman). The present reformulation had the support of the Ministry of Science and Technology, through the Partnership Contract 0017/2005, and that of Eletronuclear.
The historical data base is periodically updated which permits the readjustment of the behavior functions according to the existing new historical values or revisions. A recent comparison of the forecasts made ten (the book itself) and five years ago (Emissions Matrix) has shown a good capacity of the model to project economic growth. It should be noticed that in both occasions the model’s forecasts were divergent regarding the expectations of the period.
On one hand the good capacity projection of the model using the inertial behavior of some variables is gratifying to the planner whenever his hypotheses are corroborated. On the other hand, when the planner does not indicate the possibility of economic growth required by society, the results are rather frustrating for the same planner.
For this reason it was introduced in the program the option of changing the historical trends due to changes in the economic policy or projected technologies. However, the transition always takes into account the previous historical behavior.
Since the program can be adapted to new policies, the model is less deterministic than that used in the book. Nevertheless, the model clearly points out to the fact that this change of the historical trend is only possible by paying the price of adopting a global policy that is coherent with the proposed objectives. On the other hand, connection with the historical trend brings difficulties regarding hypotheses that are incoherent with the past behavior. Whenever possible, comparisons with other countries are also made in order to orient the user’s choice.
However, the program served the purpose of making a diagnosis such as the hindering that the low capital productivity represents to Brazil’s development. The idea of the Partnership Contract between the e&e Organization and the MCT on the subject – that makes it possible improving the program – is precisely to try to intervene in one of the variables that have been identified as determining limits to growth.
In the present report we try at the same time to:
1) Show how the model works;
2) Present the relationship between the quantities that permit estimating the GDP and
3) Present the preparation of a reference run that can be a reference to other runs.
The model was made in Visual Basic language for Excel and Access data banks (all from Microsoft), what permits an easy use of its main results in other applications
Its initial presentation is shown below (Figure 1). The main module presents other options, not shown here, relative to other applications.
Figure 1: "Front page" of the program
Projections are made from a series of screens that permit to introduce some hypothesis regarding the evolution of variables that influence the economic growth in the structure of the program. The “front page” shown in Figure 1 is coupled with a series of modules (regional, energy source, emissions, etc.) and the further results now linked to the macroeconomic module. By choosing the “Macroeconomic” option (the only one shown) the program presents the initial screen that is the projection of internal savings shown in Figure 2.
Figure 2: Internal Savings Projection Screen with the menu of the program and projection screens
On the upper left corner is the menu of the program that is analogous to those available in other programs. This menu is shown in Figure 3 and it has ”Actions, Input, Graphics and Results” as main options.
The Actions item includes besides actions of the Present Scenario others from Excel. In Figure 3 some program Actions are included.
Figure 3: Example of items from the program’s menu. Actions corresponding to the macroeconomic module are opened and some actions relative to Excel were included
In this item of the menu there are some general actions that correspond to calculations that can be made from historical parameters or parameters supplied by the program. In a general way these actions are self-explanatory.
To make the projections, the program uses a series of results previously evaluated from historical data and those used in the projection. For example, the capital goods stock is calculated from historical investments (in % values of the GDP of the year converted to the 1980 GDP using an implicit GDP deflator), correcting scraping by using a logistic survival function, with different average life for investments in civil construction and machines and equipment (+ others). Scrapping considers the investment in each year and the time interval elapsed until the year when the capital stock is calculated. These graphics as well as others that are available can be accessed as indicated in Figure 4.
Figure 4:Choice of graphics display
For example, the option Survival of Goods Function produces the graphic shown in Figure 5.
Figure 5: Scrapping curves of goods regarding Civil Construction and Machines and Equipment (includes Others)
The program permits to see the results in graphics, as shown above and also in specific numeric worksheets to be chosen according to the options in Figure 6.
Figure 6: Options for numeric results of the menu
The program can be used with different scenarios that can be coupled to other programs such as regional projections or energy demand. For saving space in the computer’s disk and to facilitate the substitution of the economic scenario for other applications, only the fundamental data of these scenarios are saved. It should be emphasized that these data are sufficient to run the scenario again and obtain the resulting graphics and tables.
The revision of scenarios or the creation of new ones is carried out through the menu in the Actions indicated in the “Input” item, according to Figure 7.
Figure 7: Data input relative to scenarios
In what regards scenarios, the program permits three actions: introduction of a new scenario, revision of the scenario presently used or revision of an existing scenario. As illustrated in the following example, one can use an existing scenario to create a new one. For example, selecting the option Open Existing Scenario, a screen is shown where a scenario already saved can be chosen and where the date of its last change is indicated. When one of these scenarios are opened, the program revises all calculations of all steps and presents a screen with the summary of the different parameters used in the different scenarios. An example of this screen is shown in Figure 8.
Figure 8:The blue column presents the parameters used in the last scenario run and the other ones present the parameters of the previously recorded scenarios
By choosing the action “Revise Present One” According to Figure 9, we will start the revision of the present scenario that can be transformed in a new one at the end of the process. In what follows a practical example will show the program’s evolution.
As mentioned above, clicking on “Revise Present One” the program goes back to the first page of the scenario construction that corresponds to the Internal Savings.
It should be pointed out that the program’s screens permit to go back to the previous screen by clicking on the corresponding button. Normally, “Return” does not modify the previous action and “Next Data” introduces the new scenario information and then goes to the screen corresponding to the next step of the procedure. The title in blue points out the parameter that is supposed to be updated. The variable in question, as seen Figure 9, is the Internal Savings (P), which is the annual GDP share that is not consumed.
This "consumption renunciation" was a “well-behaved” variable in the past as can be seen in the graphic of the figure below and its strong oscillation (upwards) at the end of the 1980s can be assigned to variations of the relative prices. The internal savings rate is fundamental for projecting investments as will be seen in what follows. As already pointed out, the past is used for the choice of its future evolution.
Figure 9: First screen for data input the main variable to be changed refer to the Internal Savings behavior
The Internal Savings value was growing in the last decades and indicated a positive factor for economic growth. Apparently the interests rate increase and the Real Plan have discouraged the internal savings. Resuming the initial trend can be observed from 2000 on.
In the worksheet used, the year 2005 was considered as the last year in which data are known. As far as estimates, even partial ones, of data relative to 2006 are available, it may be convenient to use them as a base for projection. This is made through the “Last Year” link.
One can also change the “Present Year” and it changes the intermediate years in result tables as will be further indicated. This flexibility of reference years permits to introduce new years in the historical series whenever they become available.
For the projection it was assumed that the internal savings would tend to be a fixed fraction of the GDP. This limit value was used to adjust a logistic curve. The scenario, that may be considered biased, assumes a saturation value of 25% of the GDP that represents the best fit to past data. Even when this value is 3% higher than those of 2002 and 2003 it results in annual growth of the GDP between 2% and 4% in the next two decades.
In the reference scenario it was assumed that the internal savings would resume the growth behavior it had before the Real Plan and would tend to a value of 30% of the GDP. This change is made by changing the limit value in the window shown in the blue title in Figure 9. The new result is shown in Figure 10.
As can be seen in Figure 10, the variation of the Internal Savings implies a disposition of changing from consumption to real investment (in fixed capital goods). To “match” the adjustment with the historical data a Poisson function was used and its parameters may be changed in order to smooth the transition between the last data and the projection, with different delay times.
Figure 10: The option for a limit of 30% of the GDP for the territorial savings leads to Internal Savings that are coherent with those of years before the Real Plan and it generates a larger economic growth. It should be emphasized that this change in the series’ behavior implies corresponding action in the economic policy.
The maximum value of the Capital/Product ratio is introduced in the cell indicated in Figure 11 and then the fitting and the projection are shown in the graphic, whose transition regarding the last data is carried out using a Poisson curve. In the present case, the limit value of 2.7 was adopted (graphic capital productivity shown in Figure 11).
Figure 11: Capital/Product ratio data input
The Capital/Product ratio can be seen as the inverse function of the global capital productivity. That is, as can be observed in Figure 12, the capital productivity has been decreasing in the last decades. When the Capital/Product ratio value is equal to 3 it means that it is necessary a stock of capital goods of 3 thousand dollars for each thousand dollars of the product. In the “reference” scenario it was assumed that the capital productivity would tend to a value of 39% (Capital/Product = 2.7) that is very close to the value measured in the last years. To obtain Figure 12 one should click on the Graphics/Capital Productivity menu.
One of the false premises regarding the Brazilian situation analysis is the one that assumes that opening the economy in the 1990s implied an immediate increase of insertion in the international trade. What actually happened, in a conjuncture of lower petroleum prices and less pressure on external accounts, was that Brazil could increase the volume of its exports. Since the exports volume relative to the GDP was reduced to satisfy internal demand, external trade – here considered as the average of imports and exports relative to the GDP – did not grow and it was even reduced relative to the previous decades. There has been in the last years an overvaluation of the Brazilian currency that brings some distortions to the GDP calculations and that has also contributed to reducing the external trade value as a percentage of the GDP. Anyway, opening the economy in the 1990s was rather an opening to imports than to external trade.
In the last years there has been an expressive reaction of the Brazilian exports from the point of view of quantity and value. An analysis of the historical data shows a notable stability in the average behavior of this parameter that does not permit very optimistic forecasts regarding the external trade expansion.
In the book “Brasil: O Crescimento Possível” we have tried to explore the natural expansion limits of the Brazilian trade. It was concluded that it has limitations connected with the Brazilian geographic extension and with the relatively modest size of our neighbors’ economy. Nevertheless, the Brazilian economy in the nineties continued to be relatively closed, presenting a foreign trade that was 7% of the GDP when, according to the book’s evaluation, there existed an external trade potential of about 13% of the GDP of which 5% referred to the trade with our neighbors.
In the exercise presented here we have projected an average evolution of 12% in the 2026 horizon; see Figure 13.
Figure 13: The Brazilian external trade presents a historical value around 7% of the GDP but has the potential to reach 12%. It is shown the adjustment adopted in the projection that was obtained by linear extrapolation and the 12% value was exogenously fixed for 2026. The coupling with the last year was made using a Poisson curve.
The commercial balance behavior is exogenously introduced in our model and it takes into account the possibility of indebtedness of Brazil and the penetration of external capital in the country’s capital goods stock.
The exogenous values input is made in the next worksheet where the years are indicated: starting in the last known year, some intermediate years, the present year, the following year plus the 4 future years with intervals of 5 years between them starting in the present year. When creating a new scenario, the user must supply the Commercial Balance values starting in the last known year, as shown in Figure 14. The results for exports and imports consider the external trade extrapolation shown in the previous figure and the interpolation of the Commercial Balance values between the values exogenously supplied.
Figure 14: Worksheet where the commercial balance values are introduced starting in the year that follows the last known year. The input data are exogenously introduced so that it will reach an external liability limit. The program evaluates the transfers abroad considering their historical behavior.
Using the commercial balance data the program endogenously calculates the transfers abroad that include non factors goods and services of the debt. The correspondence between these parameters is obtained through the behavior of the previous data. Roughly, there is a deficit of 1% of the GDP in the services balance. The transfers abroad are used to evaluate investments, as will be shown in what follows.
The flow of external investments, real or financial, is effective in the actual economy only when there is input (or output) of goods and services in the economy. Since the country does not issue external circulation currency and the indebtedness capacity is limited, the historical flow of real goods coincides – with some gap - with the financial flow in what concerns the accumulated value due to variation in the reserves.
The so-called productive investment presents a behavior similar to that of the financial investment. The difference is who administers the investments. For cumulative control purposes, one can consider the net external liability that includes the net debt and the accumulated investment in capital goods in the country.
For practical or strategic reasons, there exists the option of trying to impose some limit for this liability. In the example it is marked the 70% GDP line that corresponds to about 27% of the capital stock. Naturally, the absolute limit would be when all the capital stock would be in foreign hands. For this reason, we assume that the Capital/Product ratio is progressing to 2.7 – in the example shown here – and this absolute value would be 270% of the GDP. When this limit is attained, Brazil would have literally a new owner.
The way of evaluating the external liability has been changed in the present version of the program. This was possible because the Brazilian Central Bank has carried out a census regarding external investments and Brazilian assets abroad. Besides that, there has been a significant variation of the components of the net liability. Actually, the remuneration of direct (mainly profits and dividends and interests among enterprises) and portfolio (mainly remuneration of fixed income bonds and profit and dividends) investments have grown in importance in our payment balance in the last years, as shown in Figure 15.
In the projection the actual interest rate (discounting the international inflation) paid in the country was used as a determining parameter of this accumulation. For direct investments and the so-called “portfolio” investments (stock exchange and fixed income bonds) it was adopted 11% remuneration rate considered as representative of the last years (average from 1995 to 2005, 10.2% annually with growing trend). For actual interests on the net external debt it was considered the value of 5% annually. Rigorously, there is no reason for these investments to receive remuneration very different from the financial ones. In fact, there was in the past a disproportionate remuneration in the opposite sense..
Figure 15: Remuneration of external investments transferred abroad (net values) showing the reduction of importance of interests of the foreign debt and large growth of remuneration of direct and portfolio investments
The results for the external liability of the last years consider as the starting point the values of foreign investments stock in Brazil supplied by the Central Bank and that they include the deficits and surpluses of the payment balance. In order to calculate the amount of the debt it is still necessary to define which share of the payment balance surplus (or deficit) would be assigned to pay (or increase) the external debt. This value is introduced as input data. The external liability values are shown in Figure 16; it considers a limit value for the external liability that is fixed relative to the capital stock (26% in this case) or 70% of the GDP.
Figure 16: The net external liability is used as a control variable; once a reference interest rate is established, the transfer of resources is adjusted to a desirable rate of the net liability. The limit fixed for this liability is arbitrary and corresponds in the present case to 26% of the total capital stock of the country that is in the hand of the external capital
The evolution of the net external liability from 1995 on and its projection until 2026 are shown in Figure 16. The results are within the fixed limits. If it is considered convenient, the values of the external trade could be modified so that one would obtain another path for the external liability. It should be pointed out that whenever a value is expressed in dollars as a function of the GDP one is excessively dependent on the exchange rate. For this reason in Figure 16 are also shown the values corresponding to the GDP expressed in real values (at the 2005 exchange rate).
Excessive interest rates or excessive capital remuneration can hinder the GDP growth. In effect, in order to cope with remittance of resources abroad and at the same time keep the external liability stable, it is necessary to increase the remittance of goods abroad. Since the internal savings is limited, investments are smaller. The alternative of obtaining loans or more external investments can aggravate the medium or long term problems since they mean larger remittance of profits and dividends or more payment of interests.
As an illustration, it is shown in Figure 17 the Net External Liability that would result in a commercial balance as the one considered (tending to a surplus slightly higher than 1.5% of the GDP) and real interest rate of 12% for the external debt and 12% for external investments.
Figure 17. The use of a reference rate of 12% interest rate and 12% for investment would produce external liability values higher than those fixed as limit
Growth in the model assumes the use of the productivity capacity in the future according to the average value used in the past. The production capacity is based on the capital stock of the year and on the projected Capital/Product ratio of that year.
In the production calculation it is also considered the effects of imports that complement the production capacity whenever demand requires it (example: imports of components for cars production) and interruption of the productive chain whenever demand is reduced (example: additional exports of steel not absorbed by the car industry). In economies fundamentally directed to the internal market like the Brazilian one, this effect produces an increase or decrease of the GDP according to the flow of transfers, predominantly in or out. 
In Figure 18 are shown the shares of external and internal savings in the investment. It can be noticed that from 2002 on Brazil became a net capital exporter. Therefore, the internal savings recovery has no effect on the investment rate. On the other hand, the inflow of external resources between 1995 and 2001 (average value: 1.75% of the GDP) did not compensate the decrease of the internal savings that was 7% of the GDP.
Figure 18: Contribution of the internal and external savings to investment in Brazil
Not all variables that influence the GDP are treated by the model. The difference between the model’s projection and the effective economic activity measured by the GDP reflects the factors not treated by the model. This is assigned to the use of the installed capacity relative to its average utilization. The graphic of Figure 19 shows that it can be associated with conjuncture factors that increase or decrease the GDP level around its long term trend. One can compare it to the year 1973 – that would be the year of maximum utilization of this capacity (scale of the left vertical axis) – or to the average value (scale of the right vertical axis). In the first, 100% corresponds to the 1973 value, in the second, 100% corresponds to the average value.
It can be observed that most of the GDP recovery in the last five years was not due to production capacity increase but rather to a more intense use of this capacity. As the utilization factor in 1999 would be 7 percent points below the average value, one could forecast a recovery of this factor that tends to come close to the historical average value. The utilization factor in 2004 was 4% above the average. For the future it is projected that the factor will return to the normal value.
The evolution of the utilization factor relative to the average is shown in Figure 1. In the screen shown it is possible to observe that the past behavior of the factor utilization as well as to specify some conjuncture aspects that have influenced it. One can indicate the expected values in years when there are partial results about the economy’s performance that can be taken into account in the extrapolation. In the present case, this resource was not used.
Figure 19: The factor utilization indicates the installed capacity use relative to the historical average. The values of the GDP growth in the first projected years can be introduced when a partial evaluation already exists
From the factor utilization projection one can obtain corrections for the GDP values. On the screen shown in Figure 19 one has the GDP values initially projected by the model and the estimated one (they include correction relative to transfers) that now also incorporate the influence of the factor utilization variation. By the evolution of this projected factor itself it results that the growth rates of the series’ last years are practically not affected since this factor has already reached the value 1. It is permitted to introduce GDP growth values in the first projected years that will be taken into account in the projection and the adjustment will be compensated in the GDP growth projected for the following years.
The results are presented in the following worksheet. The worksheet shown in Figure 20 shows the graphic of the GDP evolution. The relevant results – and other complementary ones – can be checked in specific worksheets or graphics. It is also possible to change the unit of results by changing the year of the reference dollar (it is used the average exchange rate indicated by the Brazilian Central Bank).
Figure 20 : Worksheet of the GDP results. The scenario can be confirmed (adoption of the revised values) or recorded as a new scenario, using the button close to the data that opens the specific worksheet. One can also change the year of the of the reference dollar.
Several other results are available in the form of graphics or tables. Some values can be used as additional control mechanism, for example the GDP data and the per capita consumption shown in Figure 21. In effect, internal savings growth means relative consumption decrease. The scenario assumes as boundary condition that the per capita consumption parameter – of true social importance – at least does not present negative rates due to savings resuming. This boundary condition is not automatically verified by the program.
Figure 21: GDP, per capita consumption and its annual growth rate, that is, the variables and their growth rates. In 2026 the per capita GDP would be about 6700 US$/inhab, at constant 2004 dollar
The worksheets of results can be seen through the Results menu as shown in Figure 22.
Figure 22: Choice of macroeconomic results summary for selected years (synthesis values). Data in Structure are in general data in percent values of the GDP. Data for all projected years are also presented (Annual Results)
The results for "Synthesis Values" are shown in Table 1. The years in red can be changed by the user if he wants other projection years. The default years shown are the last known year, the present one and the years: present year +1, +2, +5, +10, +15 and + 20.
Table 1: Synthesis Values for the Reference Scenario
The new version of the projetar_e proved to be very useful for testing the impact of changes concerning the evolution of parameters that determine economic growth in the present model.
It has not been mentioned in the present report that the time for running a new scenario in the new version of the program has been reduced by 80%. In the new software the data bank is external to the program and can be easily updated by the user. Some adjustments and improvements are still necessary but the program is entirely operational
 This report is part of the Partnership Contract No 0017/2005 between e&e and the MCT and corresponds to the specific item: Improvement and supply (to MCT) of the software for economic growth projection.
 In the book were studied limitations to the Brazilian economic growth, adopting a methodology analogous to that used in the program. The program was transformed into the macroeconomic module that gives support to projections in different areas. The book’s model uses as an anchor the historical behavior of some macroeconomic variables that presented strong inertia in the past. On the other hand it deals with "the real economy" and, as a first approximation, it does not consider financial factors such as: inflation, interests and currency flow. The analysis concentrates on capital goods accumulation, on physical production and on the transfer of goods and non-financial services, as they are presented in the National Accounts. Because of this approach the currency, corrected by the GDP is used to present these values in a common unit. The financial limitations – accumulated debt and interests rate – are introduced as a consequence of changes in the real economy (transfers abroad) and as parameters for establishing a limit to indebtedness that might restrict or determine the flow of resources.
 The program is registered in the Brazilian Patent Institute by ECEN Consultoria Ltda.
 See Economy and Energy No 55, http://www.ecen.com/eee55/eee55p/poupanca_interna.htm
 As mentioned in the preceding article “Evaluation of the Capital Productivity Increment Impact on Economic Growth”.
In the present case, as opposed to what generally happens, by selecting "Return" the program goes to the screen where the last year with known data is chosen and whose worksheet is normally retrieved when it necessary to change the referred year.
 That is, GDP ( Y ) data and consumption ( C ) then:
P = (Y-C)/Y = 1 - C/Y
 As the values in constant prices have shown, it is only due to the relative prices variation.
 It should be noticed that the high interests rate policy as an instrument for controlling inflation has the expected effect of reducing consumption. Almost inevitably this policy reduces the savings applied on real goods. In the actual economy the predominant effect was the reduction of the internal savings only partially compensated, as will be seen further, by external resources resulting from the privatizations and overvaluation of the Real. The global result was a decrease of the investment rate and the consequent smaller growth .
 The values of this demonstration run differ slightly from the reference scenario published in the No 55 issue of the e&e periodical and adopted as the reference scenario for energy studies.
 This deficit has grown in the 1990s and it seems to be related to modifications in the exchange area. In 1991, the smaller difference between the parallel and the official exchange rate which increased the volume of official transactions connected with traveling and remittances and in 1994 the overvaluation of the Real that stimulated traveling abroad.
 In the mentioned book “Brasil: O crescimento Possível” it was made an evaluation until the first years of the nineties.
 A note about this re-evaluation will be soon be published by e&e. Now the calculated values of the net external liability should be considered as preliminary.
 This disproportion is due in part to the difference between the external and external interest rates. In what regards the past, it should be considered that there is presently a greater liberty concerning the remittance of profits and dividends. On the other hand, the survey of foreign capital stock invested in Brazil has shown that 2/3 of these investments are made in the services sector (mainly telecommunications, commerce and financial services) that, in principle, do not favor export of profits and dividends that are comprised in the products, since most of the services are provided in the country itself.
 The conversion uses the trend of the capital/product ratio value, namely, K/Y= 2,7; the corresponding GDP % would be (2,7×26%=70%)
 Investment I in one year is the sum of the internal savings and the external inflow represented in the real economy by the net transfers abroad. That is, I = P – T where T represents the transfers abroad or external savings in real terms (External Savings = - T).
The program estimates the share of investment in machines and equipment and in Civil Construction using a historical correlation that shows that in a larger growth rate period, investments in machines and equipment have a larger share in the global investment.
Using the scrapping curves previously shown and considering the previous capital stock one can determine the capital stock of future years from the new investments. One gets the first product projection given by Y1 = K/v, where v is the projected Capital / Product ratio for the year and K is the capital stock in that year .
 Because of that, the correction factor g is introduced that is proportional to the GDP deviation. The projected GDP becomesY2 = Y1 . (1+ g .T. More details about the calculation, see the No 22 e&e periodical, previously mentioned.
Graphic Edition/Edição Gráfica:
Tuesday, 11 November 2008.