Question
17. After some consideration it has been decided to change the base year for the fuel index from 2000 to 2005. The old index numbers were:
(2000=100) (2005=100)
1998 90 A
1999 96 B
2000 100 C
2001 105 D
2002 110 E
2003 120 F
2004 110 G
2005 80 H
2006 140 I
Find the values of A to I in the table.
18. Consider the following two price index series:
1996 = 100
2000 110
2001 112
2002 120
2003 128
2004 130
2005 = 100
2004 93
2005 100
2006 104
2007 109
2008 115
Splice the two price index series to form one continuous series with:
18.1 2004 as the base year.
18.2 2006 as the base year.
19. The table below provides the GDP (in R 1 000 000) in real terms for each trimester during 2008 and 2009.
2008
I 66 593
II 67 003
III 66 838
2009 I 65 232
II 66 694
III 68 381
Determine the growth rate in the GDP during the first trimester of 2009 by using the method of current period on the:
19.1 Preceding period.
19.2 Preceding period at annual rates.
19.3 Same period of the preceding year.
(2000=100) (2005=100)
1998 90 A
1999 96 B
2000 100 C
2001 105 D
2002 110 E
2003 120 F
2004 110 G
2005 80 H
2006 140 I
Find the values of A to I in the table.
18. Consider the following two price index series:
1996 = 100
2000 110
2001 112
2002 120
2003 128
2004 130
2005 = 100
2004 93
2005 100
2006 104
2007 109
2008 115
Splice the two price index series to form one continuous series with:
18.1 2004 as the base year.
18.2 2006 as the base year.
19. The table below provides the GDP (in R 1 000 000) in real terms for each trimester during 2008 and 2009.
2008
I 66 593
II 67 003
III 66 838
2009 I 65 232
II 66 694
III 68 381
Determine the growth rate in the GDP during the first trimester of 2009 by using the method of current period on the:
19.1 Preceding period.
19.2 Preceding period at annual rates.
19.3 Same period of the preceding year.
Answers
GPT-4o mini
Let's work through each question step-by-step.
### Question 17: Index Number Conversion
To convert the old index numbers (2000 = 100) to the new base year (2005 = 100), we need to calculate the values for 1998 to 2006 based on the provided data.
Old base year index (2000 = 100):
- 1998 = 90
- 1999 = 96
- 2000 = 100
- 2001 = 105
- 2002 = 110
- 2003 = 120
- 2004 = 110
- 2005 = 80
- 2006 = 140
Now, let's establish the relationship between the two bases.
2005 in the old base year is not explicitly provided, but we can determine it using the fact that the 2000 index equals 100, hence:
\[
\text{Value for 2005 in old base} = 80 (2005 new) \times \frac{100 (old)}{100 (new)} = 80
\]
To find A to H, we transfer the values from the old base year (2000 = 100) to the new base year (2005).
**Conversion to New Index (2005 = 100):**
1. For **1998**:
\[
A = \frac{90}{80} \times 100 = 112.5
\]
So, A = 112.5.
2. For **1999**:
\[
B = \frac{96}{80} \times 100 = 120
\]
So, B = 120.
3. For **2000**:
\[
C = \frac{100}{80} \times 100 = 125
\]
So, C = 125.
4. For **2001**:
\[
D = \frac{105}{80} \times 100 = 131.25
\]
So, D = 131.25.
5. For **2002**:
\[
E = \frac{110}{80} \times 100 = 137.5
\]
So, E = 137.5.
6. For **2003**:
\[
F = \frac{120}{80} \times 100 = 150
\]
So, F = 150.
7. For **2004**:
\[
G = \frac{110}{80} \times 100 = 137.5
\]
So, G = 137.5.
8. For **2005**:
H = 100
9. For **2006**:
\[
I = \frac{140}{80} \times 100 = 175
\]
So, I = 175.
So the final indices are:
- A = 112.5
- B = 120
- C = 125
- D = 131.25
- E = 137.5
- F = 150
- G = 137.5
- H = 100
- I = 175
---
### Question 18: Splicing Price Index Series
**(18.1 Splicing with 2004 as Base Year)**
We need to retain the data with 2004 as the base year. Use the formula:
\[
\text{New Index} = \frac{\text{Index at year}}{\text{Index at base year}} \times 100
\]
**Series 1 (Prices 1996 to 2004):**
- 1996 = 100
- 2000 = 110
- 2001 = 112
- 2002 = 120
- 2003 = 128
- 2004 = 130
Convert this series (Base = 130):
- 1996 = (100/130) * 100 = 76.92
- 2000 = (110/130) * 100 = 84.62
- 2001 = (112/130) * 100 = 86.15
- 2002 = (120/130) * 100 = 92.31
- 2003 = (128/130) * 100 = 98.46
- **2004 = 100**
**Series 2 (Prices 2004 to 2008):**
- 2004 = 93
- 2005 = 100
- 2006 = 104
- 2007 = 109
- 2008 = 115
Convert this series (Base = 93):
- 2004 = 100
- 2005 = (100/93) * 100 = 107.53
- 2006 = (104/93) * 100 = 111.83
- 2007 = (109/93) * 100 = 117.16
- 2008 = (115/93) * 100 = 123.66
Now combine the two series into one series:
```
1996: 76.92
2000: 84.62
2001: 86.15
2002: 92.31
2003: 98.46
2004: 100
2005: 107.53
2006: 111.83
2007: 117.16
2008: 123.66
```
---
**(18.2 Splicing with 2006 as Base Year)**
Now, change the base year to 2006, using the fact that 2006 = 100.
From Series 1:
- 2004 = (130/100) * 100 = 130
(The values for earlier years will not change but must be converted to reflect their relative positions against 2006)
So Series 1 converts:
```
1996: 76.92
2000: 84.62
2001: 86.15
2002: 92.31
2003: 98.46
2004: 130
2005: (100/104)*100 = 96.15
2006: 100
2007: (109/104)*100 = 104.81
2008: (115/104)*100 = 110.58
```
### Question 19: GDP Growth Rate Calculation
**Given GDP values:**
2008:
- I: 66 593
- II: 67 003
- III: 66 838
2009:
- I: 65 232
- II: 66 694
- III: 68 381
#### (19.1 Preceding Period)
Growth from 1st Trimester of 2008 to 1st Trimester of 2009:
\[
\text{Growth Rate} = \frac{\text{GDP 2009 Q1} - \text{GDP 2008 Q1}}{\text{GDP 2008 Q1}} \times 100
\]
\[
= \frac{65 232 - 66 593}{66 593} \times 100
= \frac{-1 361}{66 593} \times 100 \approx -2.04\%
\]
#### (19.2 Preceding Period at Annual Rates)
To annualize this quarterly change, multiply by 4:
\[
\text{Annualized Growth Rate} = -2.04\% \times 4 = -8.16\%
\]
#### (19.3 Same Period of the Preceding Year)
Comparison between 2009 Q1 and 2008 Q1:
\[
= \frac{65 232 - 66 593}{66 593} \times 100 = -2.04\%
\]
All values are negative indicating decrease in GDP in Q1 of 2009 compared to both previous quarter and same quarter of previous year.
This concludes the solution for the problems presented.
### Question 17: Index Number Conversion
To convert the old index numbers (2000 = 100) to the new base year (2005 = 100), we need to calculate the values for 1998 to 2006 based on the provided data.
Old base year index (2000 = 100):
- 1998 = 90
- 1999 = 96
- 2000 = 100
- 2001 = 105
- 2002 = 110
- 2003 = 120
- 2004 = 110
- 2005 = 80
- 2006 = 140
Now, let's establish the relationship between the two bases.
2005 in the old base year is not explicitly provided, but we can determine it using the fact that the 2000 index equals 100, hence:
\[
\text{Value for 2005 in old base} = 80 (2005 new) \times \frac{100 (old)}{100 (new)} = 80
\]
To find A to H, we transfer the values from the old base year (2000 = 100) to the new base year (2005).
**Conversion to New Index (2005 = 100):**
1. For **1998**:
\[
A = \frac{90}{80} \times 100 = 112.5
\]
So, A = 112.5.
2. For **1999**:
\[
B = \frac{96}{80} \times 100 = 120
\]
So, B = 120.
3. For **2000**:
\[
C = \frac{100}{80} \times 100 = 125
\]
So, C = 125.
4. For **2001**:
\[
D = \frac{105}{80} \times 100 = 131.25
\]
So, D = 131.25.
5. For **2002**:
\[
E = \frac{110}{80} \times 100 = 137.5
\]
So, E = 137.5.
6. For **2003**:
\[
F = \frac{120}{80} \times 100 = 150
\]
So, F = 150.
7. For **2004**:
\[
G = \frac{110}{80} \times 100 = 137.5
\]
So, G = 137.5.
8. For **2005**:
H = 100
9. For **2006**:
\[
I = \frac{140}{80} \times 100 = 175
\]
So, I = 175.
So the final indices are:
- A = 112.5
- B = 120
- C = 125
- D = 131.25
- E = 137.5
- F = 150
- G = 137.5
- H = 100
- I = 175
---
### Question 18: Splicing Price Index Series
**(18.1 Splicing with 2004 as Base Year)**
We need to retain the data with 2004 as the base year. Use the formula:
\[
\text{New Index} = \frac{\text{Index at year}}{\text{Index at base year}} \times 100
\]
**Series 1 (Prices 1996 to 2004):**
- 1996 = 100
- 2000 = 110
- 2001 = 112
- 2002 = 120
- 2003 = 128
- 2004 = 130
Convert this series (Base = 130):
- 1996 = (100/130) * 100 = 76.92
- 2000 = (110/130) * 100 = 84.62
- 2001 = (112/130) * 100 = 86.15
- 2002 = (120/130) * 100 = 92.31
- 2003 = (128/130) * 100 = 98.46
- **2004 = 100**
**Series 2 (Prices 2004 to 2008):**
- 2004 = 93
- 2005 = 100
- 2006 = 104
- 2007 = 109
- 2008 = 115
Convert this series (Base = 93):
- 2004 = 100
- 2005 = (100/93) * 100 = 107.53
- 2006 = (104/93) * 100 = 111.83
- 2007 = (109/93) * 100 = 117.16
- 2008 = (115/93) * 100 = 123.66
Now combine the two series into one series:
```
1996: 76.92
2000: 84.62
2001: 86.15
2002: 92.31
2003: 98.46
2004: 100
2005: 107.53
2006: 111.83
2007: 117.16
2008: 123.66
```
---
**(18.2 Splicing with 2006 as Base Year)**
Now, change the base year to 2006, using the fact that 2006 = 100.
From Series 1:
- 2004 = (130/100) * 100 = 130
(The values for earlier years will not change but must be converted to reflect their relative positions against 2006)
So Series 1 converts:
```
1996: 76.92
2000: 84.62
2001: 86.15
2002: 92.31
2003: 98.46
2004: 130
2005: (100/104)*100 = 96.15
2006: 100
2007: (109/104)*100 = 104.81
2008: (115/104)*100 = 110.58
```
### Question 19: GDP Growth Rate Calculation
**Given GDP values:**
2008:
- I: 66 593
- II: 67 003
- III: 66 838
2009:
- I: 65 232
- II: 66 694
- III: 68 381
#### (19.1 Preceding Period)
Growth from 1st Trimester of 2008 to 1st Trimester of 2009:
\[
\text{Growth Rate} = \frac{\text{GDP 2009 Q1} - \text{GDP 2008 Q1}}{\text{GDP 2008 Q1}} \times 100
\]
\[
= \frac{65 232 - 66 593}{66 593} \times 100
= \frac{-1 361}{66 593} \times 100 \approx -2.04\%
\]
#### (19.2 Preceding Period at Annual Rates)
To annualize this quarterly change, multiply by 4:
\[
\text{Annualized Growth Rate} = -2.04\% \times 4 = -8.16\%
\]
#### (19.3 Same Period of the Preceding Year)
Comparison between 2009 Q1 and 2008 Q1:
\[
= \frac{65 232 - 66 593}{66 593} \times 100 = -2.04\%
\]
All values are negative indicating decrease in GDP in Q1 of 2009 compared to both previous quarter and same quarter of previous year.
This concludes the solution for the problems presented.