Knowledge that Transforms

THE ESSENTIAL ARGUMENT of this paper is that the new capital acquired by all the traders in a closed economy in a given period is given a putative or constructive turnover of once for the period by typical accounting procedure. It is possible to demonstrate the truth of this argument in a very convincing way in the case where unit prices are imagined to be constant over time, for in that case the concept of increase in cost value of all traders' stock of goods is clearly seen to be a construct itself in the sense that it is not really an excess of input at cost over output at cost. In any case the output of a given trader in physical units is the same as the physical input of the trader to whom he sells; so in any case the physical rate of output of all traders by trade is equal to their physical rate of input by trade. Moreover, the cost price of one trader at a given time is the selling price of a trader at an earlier stage of production at the same time if there is no price change. Let X, 2, 3, ... , represent the physical outputs (and inputs) at various stages of the productive process, while p1 2, 3, ..., i are the unit prices respectively. Then the money value of total inputs may be stated as Xipi+Xi_pi_-+ · , while the money value of the outputs are Xipi_l+Xi-pi-2_2+ Thus if Xi units of ore, limestone, labor, etc., in the form of pig iron are sold for pi dollars per ton, and the iron was made of cost elements worth p2 dollars per equivalent composite unit, the input of the buyer would be Xlpl dollars, and the output of the seller would be Xlp2 dollars. The difference between the value of total input at cost and total output at cost for all traders would be EXipi -Xipi_l. But this difference may be restated as follows:

A PROBLEM COMMONLY TREATED in monopoly theory is the effect of a shift in demand on monopoly price and output. In most instances attention centers upon the positive or negative character of the shift, and on occasion the accompanying change in elasticity is considered. The direction of shift in demand is usually ignored, however. This would appear to be a serious omission. The following analysis indicates that the direction of shift in demand may have significant bearing on the results and that it is advisable in all cases to give it explicit consideration. 1 That the addition of a constant increment to the quantities that will be taken at various prices (a horizontal shift in demand) is not in general the mathematical equivalent of the addition of a constant increment to the prices that will be paid for various quantities (a vertical shift in demand) is readily demonstrated. Geometrically one need only shift a demand curve to the right by a constant amount at all levels and then shift the same curve upward by a constant amount for all abscissa points to note that the two new demand curves are not the same. Algebraically it may be shown as follows: Let x = F(p) be the equation of the demand curve in which the quantity is expressed as a function of the price and let p =f(x) be the inverse relationship. Then if a small constant amount is added to the quantity that will be taken at any price, the first equation becomes x' = F(p) +Ax and if Ax is small, the inverse becomes approximately p'=f(x) -f'(x)Ax. Hence the amount that would have to be added to the price at each quantity level to yield the practical equivalent of adding a constant amount to the quantity that will be taken at each price depends upon the slope of the demand curve f'(x) at each point. A linear (constant slope) demand curve is thus the only instance in which the addition of a constant amount horizontally is the equivalent of adding a constant amount vertically. The frequent use of linear demand curves in graphic analysis is possibly one reason why the direction of shift in demand has not been given more consideration.