APPENDIX TO CHAPTER XII 357

APPENDIX TO CHAPTER XI
§1 (ro Cu. XI, § 2)
Dimensions of Income-capital Ratios

If we indicate time by ¢ and distinguish the quantity and
value of services by the letters ¢ and v, and the quantity and
value of capital by @ and V;, the four ratios mentioned assume
the form: —

Physical productivity, = e.g. bushels per acre per year.
i

Value productivity, T e.g. dollars per acre per year.

Physical return, 2 e.g. bushels per dollar’s worth of
Vv capital per year. -
Value return, _Y, e.g. dollars per dollar (i.e. per cent)
Ve per year.

APPENDIX TO CHAPTER XII
§1 (ro Ca. XII, § 2)

Mathematical Relations between Rates, Annually, Semi-annually, ete.,
when conceived in the Sense of the Price of Capital

If #' represents the rate of interest per annum when the
income is payable semi-annually (such as 4 9% in the example
in the text) and i the rate which would be its equivalent when
the income is payable annually (such as 4.04 9 in the example),
the relation between i’ and 7 is, —

12

facta
emt

e observe that under our hypothesis as to ©

To show this w .
1 income of either

and i', a capital of $1 will buy a perpetua
Let us suppose, as in the

each year, or : each six months.
preceding example, in six months the holder of the latter

. 1
annuity, after receiving his first installment of income, 4, sells

 

  
 
 
 
 
   
  
  
  
    
 
 
  
  
    
 
  
  
   
      

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