CAPITAL PRODUCTIVITY
ANNEX A
1. Some notation: Q is the value of output over some time period, K the value of the capital stock, I the value of investment (gross addition to the capital stock in a particular period). A change in Q, ie the increase over a particular period is denoted by AQ. 40.
2.
Paras 15 and 16 refer to various concepts of productivity. Average productivity of capital is 2/k or output per unit of capital. Marginal productivity is (roughly) the change in total output associated with a unit of investment (addition to the stock of capital) and is thus ΔΩ/Τ.
ΔΩ/Ι AQ/ is estimated in para 16 as 0.24 and 0.55 (the % signs are incorrect). Thus the claim is that each unit of new investment produced a quarter of a unit of output in 1981 and more than double that in 1984.
3. The marginal productivity of capital is usually referred to as the inverse of 40/1: 1/AQ or the Incremental Capital-Output Ratio or ICOR. This can be estimated from growth and investment share data as follows:
If we divide the investment
The percentage growth in GDP over a year is given by ▲0/0. The share of investment in GDP is 1/0.
I share by the growth rate, we have
1/0 ÷ 40/0
or
Q
1/Q
X
4.
which is
ΔΩ
I/AQ, the ICOR.
The following table presents these data for China:
Real growth rates (a-c)
1981
1982
1983
1984
a.
GDP
4.9
8.3
9.8
13.9
b.
Industry
4.1
7.7
10.5
14.0
C.
Agriculture
6.6
11.0
9.5
17.1
d.
Share of Investment in GDP
29.2
29.7
30.4
32.4
d/a: (1/0÷÷
ΔΩ
); ICOR
5.96
3.58
3.1
2.33
Q
a/a: marginal productivity
0.17
0.28
0.32
0.43
of capital
5.
While these figures are slightly different to those of the despatch (they are drawn from an IMF source) they show the same trend of 'improvement'. Can they indicate a real improvement in investment efficiency?
The IBRD's estimates for the ICOR in the period 1957-79 are in the range 4.8-5.4, deteriorating from around 3 in the 1950s to 5 in
6.
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