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# Index Number Deflating Assignment Help

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Index Numbers - Index Number Deflating
Index Number Deflating

By the term deflation we mean making allowances for the effect of changing the price levels. A rise in price level means a reduction in the purchasing power of money. To take the case of a single commodity assume the price of rice rises from $ 500 per quintal in 1999 to $ 1,000 per quintal in 2009, it means that in 2009 one can buy only half of rice if the spends the same amount which he was spending on wheat in 1999. Thus the value or the purchasing power is simply the reciprocal of an appropriate price index written as a proportion. If prices increase by 60 percent the price index is 1.60 and what a rupee will busy is only 1/1.60or 5/8 or what it used to buy. In another words the purchasing power of dollar is 5/8 of what it was or approximately 63 cent. Similarly, If prices increase by 25 percent the price index is 1.25 (125 per cent), and the purchasing power of the dollar is 1/1.25 = 0.80 or 80 cent.

This is the same as the purchasing power of money is the reciprocal of the price index. The general expression may be given as,

Purchasing power of money = 1 / price index

It shall be clear from the above that as the value of money goes down with rising prices the workers or the salaried people are interested not so much in money wags as in real wages not how much they earn but how much their wage or income will buy.

For the calculation of real wages we can multiply money wages by a quantity, measuring the purchasing power of the rupee or better we divide the cash wages by an appropriate price index. This process is known to as deflation. In principle it appears to be very simple but in practice the main difficulty consists in finding the appropriate index to deflate a given set of values or appropriate deflators. The procedure of deflating can be expressed in the form of a formula as follows:

**Real wage = money wage / price index x 100 **

Real wage or income index no. = index of money wages / consumer price index

** Illustration:**

The following table gives the annual income of a worker and the general index numbers of price during 2001 - 2009 prepare index number to show the changes in the real income of the teacher and comment on price increase:

**Year **

2001

2002

2003

2004

2005

2006

2007

2008

2009

**Income ($)**

36000

42000

50000

55000

60000

64000

68000

72000

75000

**Price index No.**

100

120

145

160

250

320

450

530

600

** Solution:**

Index number showing changes in the real income of the worker

**Year**

**Income ($)**

**Price index No.**

**Real income**

**Real income index No.**

2001

36000

100

36000/100x100=36000.0

100.000

2002

42000

120

42000/120x100=35000.0

97.22

2003

50000

145

50000/145x100=34482.7

95.78

2004

55000

160

55000/160x100=34375.0

95.49

2005

60000

250

60000/250x100=24000.0

66.67

2006

64000

320

64000/320x100=20000.0

55.56

2007

72000

530

72000/530x100=13584.9

37.74

2008

75000

600

75000/600x100=12500.0

34.72

The technique discussed above is frequently used to deflate individual values, value series or value indices. Its special use is in problems dealing with such diversified things as rupee sales, dollar inventories of the manufacture's wholesaler and retailer income wages etc.

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**Real wage = money wage / price index x 100**

Real wage or income index no. = index of money wages / consumer price index

**Illustration:**

The following table gives the annual income of a worker and the general index numbers of price during 2001 - 2009 prepare index number to show the changes in the real income of the teacher and comment on price increase:

**Year **

2001

2002

2003

2004

2005

2006

2007

2008

2009

**Income ($)**

36000

42000

50000

55000

60000

64000

68000

72000

75000

**Price index No.**

100

120

145

160

250

320

450

530

600

**Solution:**

Index number showing changes in the real income of the worker

**Year**

**Income ($)**

**Price index No.**

**Real income**

**Real income index No.**

2001

36000

100

36000/100x100=36000.0

100.000

2002

42000

120

42000/120x100=35000.0

97.22

2003

50000

145

50000/145x100=34482.7

95.78

2004

55000

160

55000/160x100=34375.0

95.49

2005

60000

250

60000/250x100=24000.0

66.67

2006

64000

320

64000/320x100=20000.0

55.56

2007

72000

530

72000/530x100=13584.9

37.74

2008

75000

600

75000/600x100=12500.0

34.72