Value of total output
We shall investigate here the composition of income when households spend only a fraction of wages paid at the beginning of January. We shall also study the value of total output when investment is effective. Finally, some conclusions shall be drawn.
Consider the case where the saving rate of January wages is positive. We compute output value at the end of January as the value of sold and unsold goods. January income is given as the sum of the following values:
 (a) The value of sold chowder ($40 in the example).
 (b) The value of unsold chowder which could have been sold if workers had spent the totality of wages ($40 in the example).
 (c) Realized profit ($10 in our example). It is not known yet whether this profit will be invested or not in the production of instrumentalgoods.
 (d) Unrealized profit ($10 in the example). Had workers not saved, this profit would have been realized by the company, together with (c).
The sum of values (a) to (d) is given as follows:
Y, = Hs^oW, + s„^W,
The sum of (b) and (c) is households’ saving out of wages ($50). Observe also that (a) + (b) equals aW_{{}, that is, real wages, the value of chowder that could have been sold if the totality of wages paid on January 20 had been spent by workers ($80). Observe also that (c) + (d) is equal to TtWj, that is, profit that could have been made if workers had spent the totality of wages paid on January 20 ($20). (c) + (d) is also equal to the value of chowder that would remain unsold if all wages were spent (namely, to the value of real profit). Notice also that (b) + (c) + (d) is the value of chowder warehoused in January, UWG_{t} ($60):
UWG^s^+P,
Recall that (a) is the value of chowder sold in January, C, + S_{uii} + P_{t}, while (b) + (d) is saving out of wages in January, S_{u4}, and (c) is profit formed, P„ that can be invested in the production of fishing rods:
V, = C, + S_{H?]} + Pj
Assuming that one half percent of profit is invested in producing instrumentalgoods (fishing rods), we compute output value at the end of February as the sum of wages paid in January and February. In other words, the value of total output is equal to the value of chowder produced in January plus the value of fishing rods produced in February. We obtain that total output is:
Xofa/ = WJl + SpC^TT)
The expenditure of nominal wages worth $50 (out of total wages worth $100) has generated a profit of $10. In January, households have purchased chowder valued at $40. Fifty percent of the profit ($5) has then been invested in the production of instrumentalgoods and the other 50% ($5) has been distributed as dividends, taxes, and interests. Remaining bank deposits have then been finally spent by households on purchasing chowder.
To sum up, the value of total output is given as:
being investment equal to invested profit
/ = S =
As Keynes (1936 [1964]: 18) wrote:
From the time of Say and Ricardo the classical economists have taught that supply creates its own demand;  meaning by this in some significant, but not clearly defined, sense that the whole of the costs of production must necessarily be spent in the aggregate, directly or indirectly, on purchasing the product.
This applies to the monetary theory developed here, whatever value the saving rates from wages and from profit may have.
The consequences on the theory of capital accumulation are farreaching. According to Smith (1776), accumulation consists of the accumulation of a capital that is necessary for production of consumptiongoods to be carried out. From the viewpoint of the theory of profit developed here, instead, the existence of capital does not precede, at least in logical terms, the productive process. We must observe that the sine qua non condition of fixed capital formation is the investment of part of the income formed by the production of consumptiongoods.
A final consideration is in order. In an economy where profit has been invested in the production of instrumentalgoods, and wagegoods have been entirely sold, income is equal to the value of wagegoods plus the value of instrumental capital, that is, invested profit:
which is tantamount to asserting that the value of output is identical to the value of consumption plus the value of investment.
In this respect, new light is thrown on Keynes’s ‘truisms’ resulting ‘from the equality between aggregate Income (Y) [...] and aggregate Disbursement (D) which is the sum of Consumptionexpenditure (C) and Investment (I)’ (1933 [1979]: 689): income arisen with the production of consumptiongoods and instrumentalgoods is necessarily equal to the income spent by households and companies to purchase such goods. The value of total output can be defined as the value of consumptiongoods plus the value of instrumentalgoods, namely the sum of wages paid for the production of consumptiongoods and invested profit.
Profit and interest
Hereafter, we shall investigate the relation between profit and interest. Specifically, by the term interest, we shall mean interest on consumption loans and interest on fixed capital. We shall also comment on the relation between natural and market interest rates. Interest has largely been the object of inquiry of a great number of economists. Keynes, for instance, in 1930, made ‘the rate of interest and its relation to saving and investing the central problem of monetary theory’ (Hayek 1931: 270). It was true then, as it is true at present, that the reason for the existence of interest lies in saving and in investment.
Interest on consumption loans
Interest on consumption loans (Leihzins, as Eugen BohmBawerk called it) is an income whose existence alters the way in which national income is shared among households, although its total sum remains unchanged. We shall understand better this concept through the following example.
Suppose that Andy receives wages for $80 and that Anna receives wages for $20:
Andy’s $80 + Anna’s $20 = $100
If a part of Andy’s deposits, corresponding to $10, is lent to Anna, Andy’s deposits decrease by $10, from $80 to $70; on the other hand, Anna’s deposits increase by $10, from $20 to $30:
Andy’s $70 + Anna’s $30 = $100
The total sum of deposits remains unchanged and corresponds, both before and after lending, to $100. For simplicity, suppose that the income deposited in the bank accounts of Andy and Anna is not spent.
The following month, Andy receives further wages worth $80 and Anna receives wages worth $20:
Andy’s $80 + Anna’s $20 = $100
If Anna repays $10 to Andy, plus interest, suppose of $2, Andy’s deposits increase by $12 and Anna’s deposits decrease by $12. The total sum for deposits remains unchanged. Supposing the new income not be spent, the total for bank deposits amounts to a temporary capital (bank deposits) of $200. Andy and Anna are therefore free to dispose of a total income of $200.
Andy has received wages of $160, and has also received an interest of $2, deriving from Anna’s wages:
$(8010)+ $(80+ 10+ 2) = $162
On the other hand, Anna has received wages for a total of $40, $2 of which corresponds to the interest paid to Andy.
$(20 +10) + $(20 10  2) = $38
Obviously, the example given is for didactic purposes. In reality, borrowers spend their own income, together with the shortterm loan received, to purchase goods and services. The previous example appears more plausible once we assume that Anna spends almost immediately her wageincome and the loan initially granted ($20 + $10, respectively). For a certain period, Andy waives the expenditure of $10 of his initial income ($80). Andy shall be able to spend the $10 at a later date, once the debitcredit has been extinguished. Once he has received the interest of $2, Andy will also be able to spend this interest on the purchase of further goods and services.
Any consumption loan does not generate new income, since it exclusively modifies the sharingoutofincome among individuals. The entire income is definitively spent, sooner or later. Interest on consumption loans has no linkages with investment and is to be distinguished from interest paid on fixed, or instrumental, capital.
Following Wicksell, BohmBawerk had already contemplated the existence of a difference between interest on consumption and interest on fixed capital. ‘[I]nterest on pure consumption loans [. . .] is no part of the large social income categories: wages, rents and (with respect to the whole economy, as derived from [. . .] production) interest’ (Wicksell 1912 [1997]: 234). We shall therefore make a few observations concerning the relationship between interest and fixed capital.
Interest on fixed capital
Besides the interest on consumption loans, another type of interest deserves attention: the interest paid to the owners of capital (BôhmBawerk used to call it Urzins). Interest on capital is an income distributed to the owners of fixed capital. The analysis undertaken so far has shown that capital is a means of production. That is, capital increases the physical production of labor but is not a productive factor of value in the same way as labor. Fixed capital has its own value, inasmuch as it is a product of labor, yet it does not directly create economic value.
As with profit, interest may also correspond to a portion of the wages intercepted by companies. Above, a numerical example was proposed, in which households spent their entire income of $100, thereby giving rise to a profit of $20. In that example, other incomes, including interest and revenue, were supposed to be null. If we now assume that interest must be paid to capitalists, we immediately note that, as long as the Urzins is positive, the macroeconomic price of wagegoods should be initially greater than their value. That is, their price should be inclusive of the price of interestgoods. In fact, the general rule holds, according to which the price of wagegoods is inclusive of all other, nonwage, goods, such as profitgoods, dividendgoods, interestgoods, etc. Indeed, nominal wages initially paid include the value of consumptiongoods and the value of all other goods, such as profitgoods, dividendgoods, interestgoods, etc. Schmitt (1984) argued that interest on fixed capital, contrary to interest on consumption loans, is therefore a macroeconomic type of interest, with features of its own.
Natural and market interest rates
Keynes must be included among those scholars who preeminently investigated the nature of natural and market interest rates (especially in his A Treatise on Money). Another economist is worth mentioning, though. In fact, ideas of great interest can be found in the writings of Johan Wicksell.
Wicksell defined the natural interest rate as ‘the rate of interest which would be determined by supply and demand if no use were made of money and all lending were effected in the form of real capital goods’ (1898 [1965]: 102). The monetary, or market, interest rate is, instead, the interest rate fixed for credit transactions between individual savers and companies. If the two rates diverge, then the level of production and its price will vary until natural and market interest rates coincide. To explain this adjustment of the two interest rates, Wicksell resorted to the concept of equilibrium.
It has been previously noted that interest is the compensation paid to the capitalists for having undertaken investment activity. Therefore, the interest rate is defined as the ratio of interest over fixed capital. According to an interesting intuition (to be found in Schmitt 1996: 38), if full employment were achieved, and monetary anomalies entirely disposed of, interest rate or natural interest rate would equal what has been called Euler’s number, e  as a percentage the mathematical constant discovered by the Swiss mathematician Jacob Bernoulli, an expert in interest theory. Interest on loans, which is called instead market interest, is influenced by the central bank. According to Schmitt, the market interest rate would depend on the natural interest rate even though the level of the latter would line up with that of the former. In fact, in order to be granted a consumption loan, borrowers must offer a market interest rate that is higher than, or equal to, the natural interest rate. Were this not the case, investment activity would always be more advantageous than lending activity.
Even though Wicksell considered it as an equilibrium variable, the natural rate of interest can be considered as the rate determined in any given economy between interest and capital or, since interest is derived from profit, between profit and capital. In other words, it is licit to interpret Wicksell’s natural rate of interest as the rate of profit. Quite interestingly, a correlation between the market interest rate and the natural interest rate would appear to be confirmed through the observation of modern monetary economies. Market interest rates are increasingly lower, due to the intervention of the central bank in favor of industrial activity (and to the detriment of financial activities). Following central bank intervention, the market rate usually tends to fall short of the natural interest rate. However, the natural interest rate (the profit rate) is increasingly lower, for the profitaccumulated capital ratio decreases over time. The very reason of this tendency of the ratio to decrease is that profits can never be greater than wages. The decrease in the market interest rate follows, as an attempt by the central bank to limit the damages to the real economy by the tendency of the profit rate to decrease. Traditional theories does not convincingly explain this tendency to decrease toward the usual lowest limit (zero).
Profit and capital growth
Economic activities are influenced both by the ability of incomeearners (households and companies) to purchase the macroeconomic product (demand), and by the effective availability of the product (supply). Indeed, it can be argued that there is a symmetrical relationship between supply and demand. Such a symmetry should be evident by a simple look at bank books: produced output is the object of the debt incurred by firms to banks and is entered on the assets side of banks’ balance sheets; the debt incurred by companies as a consequence of the payment of wages is always and necessarily matched by the deposits, entered on the liabilities side, resulting from the loan granted by wageearners to banks. Demand and supply turn out then to be the two terms of an identity (see, for instance, Cencini 2005, 2015; Cencini and Rossi 2015).
Hereafter, we shall analyze the payment of wages over infinite periods. Assuming constant saving rates out of wages and out of profits, we shall seek to find the price of domestic output, as divided into consumption (or wage) and instrumentalgoods, produced over infinite periods of time.
Suppose that wages are always fully spent in the purchase of consumptiongoods, and profit is always fully invested in the production of capitalgoods. Households’ expenditure of $100 wages in the purchase of consumptiongoods at a price of $125 gives rise to a monetary profit of $20 and to corresponding physical goods temporarily stocked in the company. Profit is then fully invested by the company. Following the production of investmentgoods, households are credited with new wages. Assuming, for the sake of simplicity, a constant price/value ratio, the $20 stock is sold then at a price of $25. A stock worth $4 is still left unsold, and company’s bank deposits are still credited with $4. 5upposing that a new production of investmentgoods takes place, households are credited with $4. Repeating the reasoning infinite times, wage payment takes place over infinite periods of time. Wages shall follow a decreasing trend approaching zero (see Table 4.11).
Table 4.11 The infinite horizon
T 0 I 2 3 ... oo
W, 100 20 4 0.8 ... 7>0
The process follows a geometrical progression. In particular, total investment over the infinite horizon has a value amounting to $25. Wages follow an exponential decay. In particular, wages follow a trend expressed by W_{t}=W_{o}e^{u}, where t = 0, 1, 2, 3, . . ., +oo. In our study case, 2 = 1.6094. For instance, $4 = $100e'^{2,i}; 2 = (ln25)/2 = 1.6094. Total output value over the infinite horizon ($125) is:
^{Y}i = ELW = W^, where
q = = 7t, where 7t is the rate of profit. The initial price of consumption
goods ($125) includes the value of consumptiongoods and the value of capitalgoods produced over the infinite horizon.
So far we have dealt with one single payment of wages, starting from which an infinite number of other wage payments has followed (through profit investment over infinite timeperiods). In realworld economies, the creation of a net wageincome takes place every accounting period (the month, for instance), thanks to the credit lines granted by the banking system to firms. In fact, it is thanks to credit lines that companies, without disposing of previous funds, pay wages to their employees. This amounts to saying that a process of income distribution and investment starts every time an initial payment of wages is made. Table 4.12 might help understand this issue.
Consider ten timeperiods (from t = 0 to t = 9), supposing that each timeperiod is equal to the solar month. Every month, thanks to banking intermediation, $100 wages are paid for the production of consumptiongoods. We also suppose that the profit rate is constant and equal to 0.2, and that profit is always fully invested in several productions of fixed capital. This means that, besides the payment of wages for the production of consumptiongoods, every month further wage payments also take place for the production of capitalgoods. The overall process leads to a monthly increase in the deposits level (as shown in the last row or, equally, in the last column, of Table 4.12): in particular, deposits approach the upward limit of $125.
For the sake of clarity, observe also Figure 4.1, which shows the deposits levels over ten timeperiods. At the beginning (i = 0), the first payment of wages gives rise to deposits amounting to $100 (nominal wages measure a physical stock of consumptiongoods). The following month, wages for $100 are paid for a new production of consumptiongoods. Meanwhile, $20 are paid for the production of capitalgoods. The total deposits level equals $120. A similar reasoning can be extended to an infinite number of
Table 4.12 Deposits growth (per month, in dollars): an upward limit
0 
/ 
2 
3 
4 
5 
6 
7 
8 
9 

100 
20 
4 
0.8 
0.16 
0.032 
0.0064 
0.00128 
0.000256 
0.0000512 
124.9999872 
0 
100 
20 
4 
0.8 
0.16 
0.032 
0.0064 
0.00128 
0.000256 
124.999936 
0 
0 
100 
20 
4 
0.8 
0.16 
0.032 
0.0064 
0.00128 
124.99968 
0 
0 
0 
100 
20 
4 
0.8 
0.16 
0.032 
0.0064 
124.9984 
0 
0 
0 
0 
100 
20 
4 
0.8 
0.16 
0.032 
124.992 
0 
0 
0 
0 
0 
100 
20 
4 
0.8 
0.16 
124.96 
0 
0 
0 
0 
0 
0 
100 
20 
4 
0.8 
124.8 
0 
0 
0 
0 
0 
0 
0 
100 
20 
4 
124 
0 
0 
0 
0 
0 
0 
0 
0 
100 
20 
120 
0 
0 
0 
0 
0 
0 
0 
0 
0 
100 
1 00 
1 00 
120 
124 
124.8 
124.96 
124.992 
124.9984 
124.99968 
124.999936 
124.9999872 
Notes: Months (0 to 9) are shown in the first row. Deposits, expressed in dollars, are shown in the other rows. Bold numbers are the sums of deposits over time.
Figure 4.1 Deposits growth (per month, in dollars): an upward limit
timeperiods. It is of particular interest, indeed, that, after the first three to four months, the deposits level approaches the upward limit already.
In particular, the deposits level at time t can be found as follows:
Deposits, = Deposits,, 1 +
where 7t is the rate of profit.
The analysis conducted here confirms that firms’ access to bank credit is crucial for sustainable capital growth. Indeed, the functional relation between banks and firms allows for the creation of net values. Thanks to such a relation, whenever consumptiongoods and instrumentalgoods are produced, the population is provided with the income necessary to purchase the totality of consumptiongoods. The profit made by any company, which defines the total for bank deposits belonging to the company, allows for the payment of dividends, taxes, and interests, but it allows especially for investment activity. The latter leads to the creation of a new value; that is, to the value of capitalgoods.