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unit.To be more precise,the capital investment required for a 
given capacity decreases with increasing capacity ( Weintraub 
1939; Bain 1956; Haldi and Whitcomb 1967; Pratton 1971 ). This is 
largely the consequence of some of the same principles which are 
responsible for large scale economies: The dimensional scale 
effect which implies that the surface increases less than the 
volume with increasing size of a container. This gives rise to the 
two-third rule: If the surface of the container is linked to the 
cost and the volume to the capacity, then, since the first rises 
with the square and the second with the cube of the dimension, the 
cost will rise with a factor of 2/3 of a proportionate increase in 
the capacity. For the firm which uses the container the rule will 
be relevant, for example, for the fuel requirements; these are the 
current or ordinary large scale economies. In the production of 
the container the above considerations will be important for the 
cost of a larger or smaller capacity. Another consideration 
concerns the whole trend of technology which is typified by the 
conveyor belt (mechanisation): The unremitting continuity of the 
process not only saves labour but it at the same time also 
increases the output of a given equipment. 
2. It should be of considerable interest to analyse the relations 
between capital-output ratio,profit rate, profit margin and 
technology. To sharpen these concepts somewhat we shall talk of a 
capital-capacity ratio,and consider a profit margin at full 
capacity use. The idea is that we should distinguish between the 
economies of scale and those savings which automatically arise 
owing to the presence of fixed cost from a fuller utilisation of 
an existing equipment. In other words we should distinguish 
economies of scale and economies of utilisation. Again, we should 
distinguish the changes in the capital-output ratio which arise 
technology. To sharpen these concepts somewhat we shall talk of a 
capital-capacity ratio,and consider a profit margin at full 
capacity use. The idea is that we should distinguish between the 
economies of scale and those savings which automatically arise 
owing to the presence of fixed cost from a fuller utilisation of 
an existing equipment. In other words we should distinguish 
economies of scale and economies of utilisation. Again, we should 
distinguish the changes in the capital-output ratio which arise 
merely from varying utilisation of an existing equipment and 
infrastructure and the changes in the capital-capacity ratio. 
Another refinement needs to be made,too. Instead of gross value of 
output we shall use the concept of value added when we define 
capacity,that is, we shall talk of capacity in terms of value 
addegl; and in defining the profit margin we shall, instead of 
relating cost to output value consider the cost net of raw 
materials and other goods bought from outside the firm in relation 
to the value added. In this way different degrees of vertical 
integration will not, in principle, disturb the comparison between 
firms because a firm with raw material supplies integrated will 
not only have more capital but also a correspondingly greater 
value added and a greater profit. 
Let us now try to define the relations in terms of algebra. Let c 
be the cost exclusive of raw materials at full capacity use,and v 
the capacity output in terms of value added. The ratio of the two 
will be a function of the size z of the firm (measured in terms of 
real capacity -a quantity!): 
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