Economy
& Energy 
No 43 Em Português 
Support: 
ECONOMIC DATA 
PREVIOUS e&e 
Capital Productivity in Brazil in the XX Century 
Annex 1: Brazil and the Additional Protocol of the IAEA Texto para Discussão: Opinião: O Brasil e o Protocolo Adicional ao Acordo de Salvaguardas Com a AIEA Legislação: Novas Leis Regulamentam o Setor Elétrico Download Texto das leis 10.848 (Comercialização de Energia Elétrica)
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Equivalente e BEN 49 x 46 (em Excel)

Annex to the Article:
Evaluation of the Capital
Productivity in Brazil in the XX Century.

Year 
Investment 
Investment depreciation in the period 
Accumulated capital stock due to investments in the period 
0 

0 
0 
1 



2 



3 



....... 



v 



v+1 
since we have

Since only the last v years influence depreciation


v+m 



According to the table above, dividing the depreciation by the stock, one gets the depreciation , for any year where , that is equivalent to a linear depreciation during v years, considering the annual investment growth rate j. The equivalent depreciation rate is given by:
or
that is, is constant in time for fixed values of v (time of life) and c (related to the investment rate growth j)
In Table A2.2 we show the equivalent depreciation rates for different lifes and different annual investment growth rates.
Table A2.2
Life
/ Investment growth 
0% 
1% 
2% 
3% 
4% 
7% 
10 years 
18,18% 
17,91% 
17,66% 
17,41% 
17,17% 
16,52% 
19 years 
10,00% 
9,71% 
9,44% 
9,19% 
8,96% 
8,35% 
20 years 
9,52% 
9,23% 
8,96% 
8,71% 
8,48% 
7,88% 
40 years 
4,88% 
4,58% 
4,33% 
4,11% 
3,92% 
3,50% 
48years 
4,08% 
3,79% 
3,54% 
3,33% 
3,16% 
2,80% 
50 years 
3,92% 
3,63% 
3,38% 
3,18% 
3,01% 
2,67% 
In the present applications we have considered the "equivalent" rates found in Table A2.3 where we also indicate the time of life and the investment growth rates per type of good in the period when the data is available (1901/2000 for construction and 1908/2000 for machines and equipment). We have considered investment growth rates obtained by exponential adjustment of IBGE (2003) data.
Table A2.3

Residential Construction 
Nonresidential Construction 
Machines and Equipment 
Life 
50 
40 
20 
Annual Investment Growth 
6,6% 
6,3% 
5,3% 
"Equivalent" Depreciation Rate 
2,7% 
3,6% 
8,2% 
Figure A2.2 shows the depreciation rates obtained using the linear function and the above expression for the “equivalent” rate
Figure A2.2: Equivalent depreciation rates and depreciation rate varying according to the capital stock age (Method of Permanent Stock) for different types of goods
and for the aggregated value (total).
Graphic Edition/Edição Gráfica: 
Revised/Revisado:
