This unit discusses the concept of investment theories in which the amounts of investable funds are related to the level of interest rate and income.
At the end of this unit, the student should be able to;
i. Understand the concepts of Investment Expenditure
ii. Explain different investment theories.
iii. Relate investment at a certain time to level of profit..
THE ACCELERATOR THEORY OF INVESTMENT
The accelerator principle states that an increase in the rate of output of a firm will
require a proportionate increase in its capital stock. The capital stock refers to the desired or optimum capital stock, K*. Assuming that capital-output ratio is some fixed constant, v, the optimum capital stock is a constant proportion of output so that in any period t,
Kt
* = vYt ………………………………….. 1
Where Kt
* is the optimal capital stock in period t, v (the accelerator) is a positive
constant, and Yt
is output in period t.
Any change in output will lead to a change in the capital stock. Thus
Kt
* - K*
t-1 = v (Yt – Yt-1) ………………….2 and
Int = v (Yt – Yt-1) ……………………………. 3
[ Int = Kt
* - K*
t-1] = v Yt ……………….4 where
investment.
Yt = Yt – Yt-1 and Int is net
In the above equation, the level of net investment is proportional to change in
output. If the level of output remains constant ( net investment would be zero. For net investment to be a positive constant, output must increase.
Self Assessment Exercise (SAE)
i. Discuss major determinant of investment in accordance to accelerator theory
THE FLEXIBLE ACCELERATOR THEORY OR LAGS IN INVESTMENT
The flexible accelerator theory removes one of the major weaknesses of the
simple acceleration principle that the capital stock is optimally adjusted without
any time lag. In the flexible accelerator, there are lags in the adjustment process
between the level of output and the level of capital stock. This theory is also
known as the capital stock adjustment model. The theory of flexible accelerator
has been developed in various forms by Chenery, Goodwin and Koyck. But the
most accepted approach is by Koyck. Junankar has discussed the lags in the
adjustment between output and capital stock. He explains them at the firm level
and extends them to the aggregate level. Suppose there is an increase in the
demand for output. To meet it, first the firm will use its inventories and then
utilise its capital stock more intensively. If the increase in the demand for output is large and persists for some time, the firm would increase its demand for capital
stock. This is the decision-making lag. There may be the administrative lag of
ordering the capital. As capital is not easily available and in abundance in the
financial capital market, there is the financial lag in raising finance to buy
capital. Finally, there is the delivery lag between the ordering of capital and its
delivery. Assuming ―that different firms have different decision and delivery lags
then in aggregate the effect of an increase in demand on the capital stock is
distributed over time … This implies that the capital stock at time t is dependent
on all the previous levels of output, i.e.
Kt = f (Yt
, Yt-1, …., Yt - n).”………………… 5
The Koyck’s Approach
Koyck‘s approach to the flexible accelerator assumes that the actual capital stock depends on all past output levels with weighs declining geometrically.
Accordingly,
……. 6 …
Where, 0 < < 1. If there is no change in income and it is equal to ̅ , the
expected volume of output also remains unchanged, then
̅ ̅ ̅ ̅ ̅ = ̅ ……………………….. 7
Where = 1/ are the weights in geometric series
and equation (7) becomes
̅̅…………………………………………… 8
Or ̅ ……………………………………………………… 9
If equation (6) is valid, then is also true. Therefore, we can rewrite equation
(6) as
………. 10
Multiplying by we have
…
Subtracting equation (10) from equation (6), we get
Since the term tends to zero, the above equation becomes
……………………………….. 13
or …………………… 14
This process of rewriting equation (6) as equation (11) is called the Koyck
transformation.
Net investment is the change in the stock of capital, Therefore,
subtract from both sides of the equation to get the expression net
investment,
………………………….. 15
Int =
or Int = ………………………….. 16
The net investment ( is called the distributed lag accelerator which is
inversely related to the capital stock of the previous period and is positively
related to the output level. On the other hand, gross investment equals net
investment plus depreciation. Depreciation is proportional to the capital stock
and is estimated by . By adding this to net investment, gross investment is
………………………………………………………………
17
By substituting the value of in the above equation, we have
……………………………………..
18
…………………………………… . 19
The above equation reveals that ―gross investment will rise when the level of
income rises because in that case more capital is required. It also shows that the
existing capital stock plays a dual role. Since the term is negative, a large existing capital stock implies excess capacity and therefore less investment.
On the other hand, is positive so that the larger the existing capital, the greater
the required amount of replacement investment.‖
In the long run equilibrium, the capital stock reaches its optimal so that
Kt
* = ………………………………………………………… 20
Substituting equation (14) in equation (11), we have
Kt
* = …………………………………………………………… 21
Substituting equation (15) in equation (12) we get
or ………..............................… 22
This equation represents the flexible accelerator or the stock adjustment
principle. This suggests that ―net investment is some fraction of the difference between planned capital stock and actual capital stock in the previous period ….
The coefficient tells us how rapidly the adjustment takes place. If
[i.e. = 1] then adjustment takes place in the unit period‖..
Self Assessment Exercise (SAE)
i. Differentiate between accelerator theory and flexible accelerator theory.
FINANCIAL THEORIES OF INVESTMENT
Some economists have laid emphasis on the effects of financial factors on investment and by implication on economic growth. These include Profits
Theory of Investment and the Cash-Flow Theory of Duesenberry among others.
THE PROFITS THEORY OF INVESTMENT
The profits theory regards profits, in particular undistributed profits, as a source of internal funds for financing investment. Investment depends on profits and profits, in turn, depend on income. In this theory, profits relate to the level of
current profits and of the recent past. If total income and total profits are high,
the retained earnings of firms are also high, and vice versa. Retained earnings are of great importance for small and large firms when the capital market is
imperfect because it is cheaper to use them. Thus if profits are high, the retained
earnings are also high. The cost of capital is low and the optimal capital stock is
large. That is why firms prefer to reinvest their extra profits for making
investments instead of keeping them in banks in order to buy securities or to give
dividends to shareholders. Contrariwise, when their profits fall, they cut their
investment projects. This is the liquidity version of the profits theory.
Another version is that the optimal capital stock is a function of expected profits.
If the aggregate profits in the economy and business profits are rising, they may lead to the expectation of their continued increase in the future. Thus expected
profits are some function of actual profits in the past,
Kt
* = ………………………………………………… 23
Where Kt
* is the optimal capital stock and is some function of past
actual profits.
Edward Shapiro has developed the profits theory of investment in which total
profits vary directly with the income level. For each level of profits, there is an
optimal capital stock. The optimal capital stock varies directly with the level of
profits. The interest rate and the level of profits, in turn, determine the optimal
capital stock. For any particular level of profits, the higher the interest rate, the
smaller will be the optimal capital stock, and vice versa.
DUESENBERRY’S FINANCIAL THEORY OF INVESTMENT
Duesenberry in his book Business Cycles and Economic Growth has presented
another variant of the financial theory of investment, known as the cash-flow
theory. In his version, he integrates the profits theory and the acceleration theory
of investment. He emphasizes that the aggregate cash flow is the main
determinant of investment. Duesenberry has based his theory on the following
propositions: (1) Gross investment starts exceeding depreciation when capital
stock grows (2) Investment exceeds savings when income grows (3)The growth rate of income and the growth rate of capital stock are determined entirely by the ratio of capital stock to income. Duesenberry regards investment as a function of income (Y), capital stock (K), profits (π) and capital consumption allowances (R). All these are independent variables and can be represented as
………………………………. 24
Where t refers to the current period and (t – 1) to the previous period. According
to Duesenberry, profits depend positively on national income and negatively on
capital stock,
……………………………………………25
Taking account of lags, this becomes
………………………………………26
Where refers to profits during period t, and are income and capital
stock of the previous period respectively and a and b are constants. Capital
consumption allowances are expressed as
…………………………………………………27
The above equation shows that capital consumption allowances are a fraction (k)
of capital stock (
Duesenberry‘s investment function is a modified version of the accelerator
principle,
… (1)
Where investment in period t is a function of income (Y) and capital stock (K) of
the previous period (t – 1). The parameter ( represents the effect of changes in
income on investment, while the parameter ( represents the influence of capital stock on investment working through both the marginal efficiency of investment and profits.
Since the determinants of investment also affect consumption, the consumption
function can be written as,
Where dt stands for dividend payments in period t. Since π = f(Y, K), R = kY and
d = f(π), these independent variables can be subsumed under Y and K. Thus
… (2)
The parameter (a) in equation (2) is MPC and it also reflects increase in profits.
This increase is reduced by the effect of profits on dividends and the effect of
changes in dividends on consumption. The influence of changes in capital stock
on consumption is reflected by the parameter (b).
The capital stock is represented by the following equation which is an identity,
It is derived as under:
The capital stock equation can be written as
=
=
Or = … (3)
The national income identity can be written as
= [From equations (1) and (2)]
=
= ( …(4)
By substituting the value of in equation (4), we get
= (
= (
… (5)
Again, the national income equation (4) can be written as:
=
Or ( ) =
Having obtained the value of , substitute it in equation (5),
= (
By taking common factors, we have
= [(
= [(
… (6)
This is a generalized version of a multiplier-accelerator process.
Next Duesenberry compares his formulation with a simple multiplier-accelerator process. In a simple model of the multiplier-accelerator, investment equation takes the following form
Whereas in his model, the investment equation is in this form
Where the value of parameter = -1 and investment is regarded as net
investment so that k = 0. Depreciation is not considered. The influence of
changes in capital stock on consumption is also neglected so that b = 0.
Substituting all these values in equation (6), we obtain the simple form of the
equation for the multiplier-accelerator process. Thus
= [(
Or = (
To conclude, Duesenberry‘s cash-flow version of the financial theory and the
acceleration theory are surely not as remote in ultimate derivation as they are
usually made to appear … Although the simple acceleration principle makes no
reference to the price and profit system, this is merely a short-cut. The
technological relationships that underlie the accelerator actually guide behaviour
through their effect on prices, costs, volume, and ultimately profits. And profits
affect firm‘s ability to finance investment both directly through cash flow and
indirectly by improving the borrowing capacity of profitable firms‖.
Self Assessment Exercise (SAE)
i. Discuss Duesenbbery financial theory.
ii. Explain clearly the profit concept of financial theory.
CONCLUSION
This unit looked at concept of investment expenditure and those theories that
served as the foundation or bedrock of investment analysis, it also explain that
some of the theories are indeterminate because of the exclusion of income level
in determining the level of investment at any given point in time.
SUMMARY
This unit explore the major theories of investment expenditure and equally
examined the determinants of investment theoretically through the selected
theories discussed. The study unit also expresses relationship between rate of
interest, level of income and investment
MARKED ASSIGNMENT
i. Explain any theory of your choice.
ii. Evaluate the Koyck investment model
iii. Differentiate between financial theories of investment and the
accelerator theory.
iv. Examine the similarities and dissimilarities between accelerator theory
and flexible accelerator theory.
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