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15.2 Productivity of Capital
(A) Physical and Value Productivity: Capital
is a productive agent; so it must result into an enhanced productive
efficiency in the act of production. The result of employment of
machines should lead to a sizable increase in the total output produced.
If a handloom factory produces 300 yards of cloth daily then, with
the introduction of the powerloom, there must be net improvement
in the cloth output produced such as of about 400 to 500 yards.
This is termed physical productivity of capital. According
to Bohm Bawerk, there must also be value productivity (in
terms of future utilities) of capital. This is necessary because
in the act of capital formation there is considerable time lapse.
Human valuation of present goods or their present consumption opportunity
is relatively larger than similar but uncertainopportunities in
the future. Therefore future enhanced size of goods must also compensate
for such value differences. This compensation is called agio
or discounting process.
(B) Stock and Flow: The concept of capital
is essentially a stock concept. Such a stock of goods produces income
for future consumption opportunities. A house purchased with an
investment of $15,000 today will bring in rent for the future 20
years or so. Investment in the house is the stock and future rent
is an income flow. Sir Irving Fisher has spoken in terms
of a cherry tree which is the stock and cherries that are collected
every day as the flow of income. Flow comes only when stock is present.
Therefore in order to enrich future income one has to build the
stock and improve it from time to time.
(C) Net Investment and Depreciation: Capital
formation is not a once for all activity. It needs to be continuously
sustained and improved. This can be possible only when the stock
of capital grows in size in the long run. Fresh addition made to
the stock annually or from time to time is called net investment.
However, total annual investment activity may not be fully realized
in the form of increase in the stock of capital. This is because
part of the present capital is likely to depreciate. Hence, additional
investment expenditure over and above depreciation charges makes
for the net investment and capital formation activity. As an illustration,
let a company that produces goods possess a total stock of capital
goods worth $10,000. These capital goods such as machinery, tools
etc. may have an average life span of 5 years. Therefore after 5
years the entire capital stock will be exhausted and no further
productive activity will be possible. In order to replace the present
stock after 5 years some amount of current income has to be set
aside. Such an allowance is called depreciation charge or
alternatively capital consumption or replacement charge.
In the above example, the firm has to set aside 1/5 or 20 percent
of the value of the stock every year. Hence the firm’s depreciation
charges will be $2000 per year (10,000 ¸
5 = 2000). If the annual investment activity of the firm is $3000
then it can add to the stock as well. In this case $3000 is the
gross investment. Out of this amount $2000 are required for
depreciation purposes; the remainder $1000 is the firm’s net investment.
We can conclude that the firm’s net investment or capital formation
activity will be positive and its stock of capital will increase
when its gross investment exceeds depreciation requirement. If gross
investment falls short of the depreciation allowance then net investment
will be negative.
GI - D = NE 3000 - 2000 = 1000 Positive
GI - D = NE 2000 - 2000
= 0 Nil
GI - D
= NE 1500 - 2000 = - 500 Negative
(D) Interest and Discount: Capital goods
are productive and they increase the future stock of goods. Therefore
capital is said to be an asset which brings net return or additional
income in the future course of time. Such net return on capital
is called its rate of interest. Rate of interest may be both
real as well as monetary in form. If we lend 500 quintals of wheat
to a farmer during the planting season to be used as seeds, he may
promise to return 550 quintals after the harvest season. The additional
50 quintals he returns is the real interest on the capital lent.
The rate of interest in this case is 10 percent. Since almost all
economic transactions today are performed in currency units the
rate of interest is charged and paid in monetary units. The farmer
in the above example may approach a banker for a loan of $1000 with
a promise to return $1100 after a year. In this case the farmer
pays an interest of $100 which is 10 percent of the loan but in
monetary units. It is easier and more convenient to compute and
charge interest in the form of money. This is because loan transactions
are carried out over a long number of years in which case, the compound
interest to be charged also increases in value.
As in the example above, if a bank lends an amount of $1000 at 10% rate of interest after one year the total amount repayable will be $1100 of which the capital or principal amount is $1000 and the interest amounts to $100. Further if we suppose the loan is extended over the second year the amount to be repaid will be more than $1200 because at the end of the first year $1100 were repayable and hence have been renewed as loan for the second year. 10% of 1100 will be equal to $110. Therefore at the end of the second year, the borrower would have to repay $1210.
1000 (principal) + 100 (first year’s interest) + 110 (second year’s interest) = 1210
This process is called compounding of interest charges. As the number of years of the borrowing period increase the compounded interest goes on increasing. In general, for n number of years, the mathematical formula used for compounding purposes is as follows:
V = K(l + r)n [V = K(l + r)1,
K(l + r)2…, K(l + r)n]
’V’ is the final value of the loan plus interest, ’K’ is the capital or principal amount borrowed, ’r’ is the rate of interest and ’n’ is the number of years of borrowing.
In our example, V = 1210, K = 1000, r = 10% or 0.10 and n = 2
Discounting is an opposite process. The
interest rate enhances the present value of the principal in the
future course of time. On the other hand, the discounting method
reduces future incomes or values at a certain rate to determine
their worth under present valuation. Since the future is uncertain,
price levels and other conditions may alter and therefore the lender
considers the future value to be lower under present valuation.
The rate of discount is calculated as the extent of difference in
valuation. Normally the rate of interest also acts as a rate of
discount. In the above example the amount of $1100 an year ahead
is equivalent to $1000 today. This way, the present value of the
future income has been discounted by 10 percent.
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