With this distinction between volume of money and volume of money-income[347] clearly held, we are prepared to go further in our attack on the quantity theory, granting the quantity theorist all his most rigorous assumptions, and still demonstrating that prices can vary independently, without prior change in quantity of money, volume of trade, or velocity of money. Let us assume the extreme case of the quantity theory: a closed market; no credit; no barter; a fixed supply of money; a fixed volume of trade; a fixed set of habits affecting velocity, namely, that everyone spends, in the course of the month, all that he has accumulated by the first of the month. The quantity theorist could not ask a more iron-clad set of assumptions than this! If the quantity theory is not valid here, if the price-level is not absolutely fixed, helpless to change, with these assumptions, then the quantity theory, even as a minor tendency, must be surrendered, and the quantity theorist must admit that the whole line of thought has been fallacious. But is the price-level passive? Suppose we assume a combination of employers of maid-servants, which forces down the wages of maid-servants from $20 to $10 per month. Assume further that there is no alternative employment for the maid-servants, so that they all remain at work.[348] So far, we have made a change in _one_ price, the price of domestic service. What of the general average of prices, the price-_level_? Well, so far, the price-level is down. If nothing else takes place, we have reduced the price-level by reducing one price. What else can take place? Two things: (1) the masters now have $10 per month each more to spend for other things than before. That tends to raise prices in their other channels of expenditure. (2) The maid-servants now have $10 each less to spend,--the same ten dollars! That lessens prices in the lines of their expenditure. These last two changes exactly neutralize one another. The first change, in the price of domestic service, remains unneutralized. The general price-level is, then, lowered--by a cause acting from outside the equation of exchange, directly on prices. The first change comes in one price. In the final adjustment, that change remains unneutralized. How is this possible? Is the equation of exchange still valid? As a mathematical formula, yes. As expressing a causal theory, in which prices are effect, and money, trade, and velocity causes, no. The equation is kept straight by a reduction in velocity. _Because_ the wages of maid-servants are reduced, _less_ money goes through their _hands_; $10 per month per maid are short-circuited. But the _cause_ is with the _prices_. The price-level, even under these absolutely rigorous assumptions, is not passive.