r may be considered to remain constant

The coefficients j3 and r may be considered to remain constant throughout the trade cycle; i is the rate of interest at a given

time. The anticipated gross profitability ; may be estimated from

the actual gross profitability of existing plant. We have already denoted the volume of capital equipment at a given time by K and the aggregate gross profit by P; consequently the gross profita-

bility of existing plant is ;. Thus we may conclude that r is estimated on the basis of ~, and that the investment orders at a given time depend on the gross profitability ; and on the rate

of interest i. It should be added that it is not the investment orders I that

should be considered a function of ; and i, but rather the ratio

of I to the volume of capital equipment K, i.e. ~ ; indeed, if P and K increase in the same proportion, ~ wi1l remain unchanged, while I is likely to increase in the same proportion as P and K. Thus we arrive final'ly at the relation:

It is known that in die course of the trade cycle the rate of interest rises in the upswing and falls in the downswing. When we come to develop our theory, we shall try to explain this connection (see page 15), At the moment we shall accept it a priori, and on this basis we shall make the following simplifying assumption, The rate of interest i is an increasing function of the gross profitability p K'

From this assumption and the equation (7) it follows that ~ . f . f P IS a unction 0 K:

Since, as was shown above, the gross profit P is proportionate to Bo + A where B is the constant part of capitalists' consumption and the gross accumulation A is equal to the production of invest-

ment goods, : is proportionate to Do; A and the equation (8) may be written as follows:

The constant m must be positive since <p is an increasing function. Equation (10) may be written in the form:

1= m(Bo + A) - nK (lOa) We shall now show that n must be positive. From the equation

(lOa) it follows that m(Bo+A)-1

I representing the orders for goods used for the reproduction and expansion of capital equipment remains always positive; it may, however, possibly approach the zero level. Let us imagine that I falls below the positive value mBo. For values of I less than mBo h . m (Bo + A) - I . h rnA. mA t e expressIon IS greater t an K I.e. K K K K

will be then less than n. Since, however, the coefficient m is positive, as shown above, and since A (production of investment goods) and K (volume of capital equipment) are also positive, it follows that the coefficient n must be positive.