E pHV rfV0 PY2 ptvn [1

is the cost of the basket in year 0, and

E = +P? v2)+• • •+Prvn) Pi i=i is the cost of the basket in year t. A price index for year t, with year 0 as the base year, is defined as

If the cost of the basket is 1032 in year 0 and the price of the same basket in year r is 1548, then the price index is (1548/1032) • 100 = 150.

In case the quantities q(!) are levels of consumption in the base year 0, this index is called the Laspeyres price index. But if the quantities q{l) are levels of consumption in the year t, this index is called the Paasche price index.

Problems

1. Evaluate the following:

2. Expand the following sums:

3. Write these sums by using summation notation:

a. 4 + 8+ 12+ 16+ ■■■+4n b. I3 + 23 + 33 + 43 +----\-n?

d. anb]j + ai2b2j H-----h ainbnj e. 3x + 9x2 + 21 x2 + 81;c4 + 243x5 + 129x6

f. afbi+3 + afbi+4 H-----1-af bi+p g. afbi+3 + af^bi+4 + • • • + a^bi+p+3

4. Compute the price index [B.l] if n = 3, p(0l) = 1. p(02) = 2, Pq} = 3, p™ = 2, pi2) = 3, p?] = 4, * <» = 3, = 5, and q® = 7.

5. a. Expand (x/ — i), and prove that it is equal to xi ~ b. Prove in general that

6. Consider a country divided into 100 regions. For a certain year, let c,7 be the number of persons who move from region i to region j. If, say, i = 25

and j = 10, then we write c25.10 for ct]. Explain the meaning of the sums:

100 100

j=1 ¿=i 7. Decide which of the following equalities are generally valid:

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