Value & Capital, CHAPTER XII, Section 4

Following the previous section, which examined the simplified model of an economy with only "short lending," this section examines the case in which all lending is "long lending," i.e. with securities that pay a perpetual stream of payments where each payment's amount corresponds to the interest rate at the time of the payment.  There are, as before, n different prices, where one "price" is for the interest rate, and the other n - 1 prices are for the goods and services (and one of the goods plays the role of money).
As before, there are  n + 1 equations that match supply and demand for the  n - 1 goods and services, while also determining the supply and demand for money and determining the interest rate.  Again, as before, one of these equations is redundant and can be eliminated.  Because the process is somewhat different than in the previous model, the text spells out the details.  Where the discussion in the previous section  considered the possibility of an individual lending out money, the current model instead describes an individual as acquiring a security (which then pays the individual indefinitely).  Therefore the following equation holds for each private individual:

Acquisition of cash = Receipts (including interest from securities owned) 

- Expenditures - Value of securities acquired

For firms, instead of considering the possibility of repayment of loans, the long lending model considers the payment of interest on debts.  Thus for a firm we have the following:

Acquisition of cash = Value of output - Value of Input

- Interest on debts - Dividends 

 +Value of securities issued (or sold)

As before, adding these two equations will imply that net acquisition of cash = 0, by virtue of the following facts:

(1)  If demand equals supply in the output market, then

Net Expenditures by private persons = Value of net output.

(2)  If demand equals supply in the input market, then 

Net Receipts by private persons = Value of net input + Dividends + Interest payments

(3)  If demand equals supply in the securities market, then 

Value of securities bought = Value of securities sold

Therefore, for the community as a whole, net acquisition of cash by trading equals 0.  "As before, the system is determined with n unknowns and n independent equations."