Qualitative analysis of cases 1 and 2 Just as we have done a numeric analysis of cases 1 and 2, to understand the value → price connection, here we will do the same, but in their qualitative aspect. To do this we present table 5: Table 5 Qualitative analysis of the relation → price Case Um Stocks Prices Utilities q Which theory Explains it Umq Um$ .q $ .Pq$ P$q αTIq αIq αFq Umq∩Um$ O∩D Case 1 = ↑ = ↓ ↓ ↑ = ↓ ↑ YES NO Case 2 = ↓ = = ↓ ↑ = ↑ ↓ YES NO In table 5 we have a reflection of the behavior of each case relative to the position of origin of the Um, the quantities of stocks available for exchange, and the prices corresponding to each economic good. The behavior of each variable is symbolized with: = (constant), ↑ (increase) y ↓ (decrease). In the last column we summarize which theory explains the behavior of the variables and which does not. From 5 we derive these conclusions, comparing each case with the position of origin: (q and $) versus prices (Pq$ and P$q) in of Uq and U$: Quantities (q) and prices (Pq$). Ie, ∆q versus ∆Pq$: In both the quantities of q remained constant (= q), while their price (Pq$) decreased. It is evident, as the two last columns show, that the theory based on Umq ∩Um$, can explain it, not so the theory based on O∩D. Quantities ($) and prices (P$q), i.e., ∆$ versus ∆P$q: In the first case the quantity of $ decreased (↓$) and its prices increased (↑P$q), in the second case the quantity of $ remained constant (=$), and its price increased (↑P$q). It is evident that: while the theory based on Umq∩Um$ explains both cases, with the theory based on O∩D we cannot explain either case, though in the first case the correlation coincides with O∩D but it does not explain. Marginal utilities (Um) versus prices (P): Marginal utilities (Umq) of q and prices (Pq$) of q, i.e., ∆Umq versus ∆Pq$:
A concomitant increase of prices (↑Pq$) and of exchanged quantities (↑qI) can only be explained in of Umq∩Um$. Therefore, in the microeconomic sphere an increase of exchanged quantities (↑qI), in conformity with the law of decreasing marginal utility of an economic good, explains the behavior of total (αI) and marginal (Uq) exchanged utilities: ↑αI con ↓Uq. Our considerations about q are also valid for the behavior of currency ($) as an economic good. As to it being a currency, means of exchange of common use, it is important to ratify: Currency is an economic good. As an economic good it is governed by the axiom of the permanent positivity of prices (P$q˃ 0) to which we add the axiom of permanent positivity of marginal utility (U$˃ 0). An excessive expansion of $ implies the possibility of P$q → 0 as a consequence of U$ → 0. In this manner, we have duly demonstrated that: What explains value and prices are not quantities or costs, but utility. Utility is governed by the marginal laws of decreasing utility, with that of wealth determining prices (macroeconomics) and the corresponding law for economic goods determines the behavior of economic units (microeconomics) Currency as an economic good falls within the domain of the theory that explains value and prices and the marginal laws of decreasing utilities of any economic good. This denies the validity of any attempt to produce a special theory of currency and any quantitative theory that tries to explain currency prices and the price of currency. Variation of non-currency wealth We now analyze the variations of non-currency wealth, and for this we present graph 7. Graph 7 was built following the methodology of the preceding graphs: We have two of manifestations of wealth: q that represents all the stock available for exchange of “non-currency” wealth, and $ that represents the stock available for exchange of currency wealth. We must bear in mind that our curves of marginal utilities (Uq y U$) are different ―because they represent the decreasing marginal utility obtained by the demander― from the traditional curves of demand by Marshall ―variation of demand according to the price-data.