Page 218 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes If p and q denote the price and the quantity of the commodity during the base period (0) and if p n
0
0
and q denote the corresponding price and quantity during a given period (n), then the total value v 0
n
= p q and v = p q , and the value relative of the period n w.r.t. the base period 0 is defined by
0 0 n n n
v n
value relative in percentage (of period n w.r.t. period 0) = v 0 × 100

pq
nn
= pq × 100 ... (3)
00
and is denoted by v .
0|n
Properties of Relatives
Let p , p , p , ... denote the prices, in the periods a, b, c, ... respectively, q , q , q , ... denote the quantities
a
c
c
b
a
b
and v , v , v , ... the volumes for the corresponding periods.
a b c
The relatives satisfy some properties which are directly obtained from the definitions. We shall state
the results for price relatives and write similar results for the quantity and value relatives :
1. Identity property :
The price relative of a given period w.r.t. the same period is 1, that is
p a/a = 1.
2. Time reversal property :
If the base period and the reference period are interchanged, then the product of the
corresponding relatives is unity (one is the reciprocal of the other). That is :
p a|b × p b|a = 1

1
or p b|a = p a|b

Here
p b p a
p a|b = p a and b|a = p b and so the result follows.
p
3. Circular or Cyclic property :
We have
p p p
p
p a|b = p b a , b|c = p c b , c|a = p a c
p
and so p a|b × p b|c × p c|a = 1
That is, if the periods a, b, c, are in cyclic order then the product of the three relatives w.r.t. the
preceding period as base period is unity.
This holds for any number of periods in cyclic order.
4. Modified Circular or Cyclic property :
We have
p p p
p a|b × p b|c = p b a × p b c = p c a = a|c
p
More generally
p
p a|b × p b|c × p c|d = a|d .

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