Man, economy and state, original chapter 5: producer's activity.
Y = 100 - (2/5)X (7)
This is Jones' constant outlay curve for 1000 ounces.
All constant outlay curves for two factors have the shape of a straight line. The slope of the line is negative, and is the ratio of the prices of the two factors, which is also equal to the rate of outlay substitution between them. When X is zero (even though such a choice will never arise in practice), Y is equal to the constant outlay sum divided by the price of X; and when Y is zero, it is easily seen that the value of X is the constant outlay divided by the price of Y.
This algebraic analysis enables us to establish a whole series of constant outlay curves for different values of k for different constant outlays. Whatever the constant outlay, the curve can be determined: it again will be of the same slope as the other curves, while the difference will be in its position. Thus, say the constant outlay is 800 ounces of gold. In this equation, when X is zero, Y will be equal to 800/10, or 80. When Y is zero, X will be equal to 800/4, or 200. And the constant outlay curve for 800 will connect the two points.
In this way, we can establish a whole family of constant outlay curves. All that is needed is the knowledge of the prices of the two factors, which are assumed to be given; and then for each possible constant outlay, the combinations of the factors can be determined. Some of the members of the family of constant outlay curves in Jones' case are as follows:
[FIGURE 3 OMITTED]
Now, it is important to realize that the prices of the factors are the sole determinants of the family of constant outlay curves. These prices are always approaching uniformity on the market. Therefore, the constant outlay curves are not only applicable to Jones; the very same ones are applicable to all producers who use these two factors. Thus, the given set of constant outlay curves and the given rates of outlay substitution are the same for all the firms producing with these factors, not just for one firm alone. At any one time, then, the family of constant outlay curves for any two factors is the same for all producers on the market. This family of constant outlay curves is a series of regular, similarly sloped lines, easily determined by anyone once the prices are given, and the same for all producers.
The production function, on the other hand, is not a given data to all producers. The production function is the estimate of the maximum quantity that could be produced from each combination of factors. Although this is technological rather than catallactic knowledge, it by no means follows that it is "given" to all prospective producers. This knowledge is not simply of engineering formulae; it involves numerous minute details of individual skills, correctness of estimates, judgment of materials and location, etc. (37) It is far more likely that each individual's production function differs than that it is the same, even with the same product and the same factors. As we will see below, this likelihood is made a certainty when there are many more than 2 factors of production, and, when, as is almost always the case, some of these factors are unique (specific), in some ways to the individual firm. Production functions, therefore, are irregular, and differ from one producer to another. Furthermore, they are not "objectively" given; they are only estimates in men's minds.
What is the shape of the production function? Some might be of fixed proportions, i.e. only one combination of factors can produce each possible quantity of output. We have seen in the text that this is practically never the case, but if it were, a diagram would be as follows: the quantity of one factor on the horizontal axis (say X), and the quantity of the other factor on the vertical axis (say Y):
[FIGURE 4 OMITTED]
The numbers designate the quantity of output yielded at the various points. These quantities can be of any amount, but they must increase as the quantities of X and Y increase, by the nature of production.
With the existence of varying proportions of factors, so that there are alternative factor combinations for each quantity of product, we can draw up constant product schedules, and therefore constant product curves. If we assume that there are many possible combinations for each possible product, then we may ask the question: suppose for example that 1 unit of X and 10 units of Y combine to produce 10 units of product:
[FIGURE 5 OMITTED]
At this combination (1X; 10Y) there is very little of X and a great deal of Y. Now suppose that X is increased to 2; what will be the loss in Y to compensate and maintain production at 10 units? We cannot know the answer except for the concrete case, but it is clear that since the two factors are imperfect substitutes for each other by their very nature, where the quantity of X is low a slight addition of it will compensate for a big loss in Y to maintain constant production. Let us say that the constant production combination is (2X; 6Y). In the diagram we may connect the two points for the sake of convenience. Now, what if X is increased to 3 units? Since X has been increased and Y has diminished, it will now take a lesser loss of Y to compensate for an increase of X. Thus, the point (3X; 4Y) might be on the constant product curve. Between the first and second points, the loss of Y was 4 and the gain of X was 1 unit; the ratio of the two is 4/1, or 4. From the second to the third point, Y lost 2 and X gained 1; the ratio was 2. This ratio is the marginal rate of product substitution between the factors, or the rate of substitution of X for Y. It is evident that as X increases, this rate diminishes. As X increases and Y diminishes, more and more gain of X is needed to substitute for less and less loss of Y. Thus, the succeeding points on the constant product curve above may be (4X; 3Y), (7X; 1.5Y), with marginal rates of substitution at those points 1 and .5 respectively.
We have arrived at one constant product curve. At each constant product, it is evident that there will be a similar shape, in that the marginal rate of substitution diminishes throughout. However, it is obvious from the nature of production that the larger product calls forth a larger quantity of both factors at each point. Thus, suppose that we are interested in a constant product curve at 20 units. Suppose X is 1 unit; it is obvious that Y will have to be more than 10 in order to produce these 20 units. What amount this will be we do not know; we only know it will be greater. Let us suppose that the point will be (1X; 15Y). We can now draw in a set of succeeding points, assuming only a diminishing marginal rate of substitution. It is clear that all these points will be above, or to the right of, the corresponding points on the lower constant product line.
Thus, we see that there is a family of curves for each constant product. The higher products are above (to the right of) the lower ones. The property of diminishing rates of marginal substitution make these curves tend to be convex to the origin. As the product gets lower and lower, the curves get closer to the origin, finally reaching that point itself at zero product; since zero quantities of factors yields zero product. On the other hand, the curves never cross the X or Y axes. Since both factors are assumed to be necessary ones for the production of the product, and hence the imperfect substitutability of the factors, no increase in the one factor, however great, can compensate for the loss of the whole supply of the other. A common classical example is the case of a wheat farm where no amount of labor, however great, can produce wheat when there is no land available; on the other hand, no amount of acreage can produce wheat without any labor. The point applies, however, to all types of production.
The point has come when this information can be consolidated. For any process of production using two factors, there are two families of curves: constant outlay curves, and constant product curves. Constant outlay curves hold for all producers who use the two factors, since they depend solely on the market prices of the factors. Constant product curves are estimates by the enterprising producers, and will differ from firm to firm. While the former are regular straight lines determined by the ratio of prices and total outlay in view, the latter are irregularly spaced, their only condition being the diminishing rate of substitution between the factors. The two families of curves will be somewhat as follows:
[FIGURE 6 OMITTED]
As we have seen in the text, at any given outlay, the actor will produce at the maximum product. What does this mean in graphic terms? Let us take, as in the figure below, a typical constant outlay line, and start at the top.
[FIGURE 7 OMITTED]
This diagram has seven constant product curves, marked 1 to 7, in ascending order of the size of the product. As the constant outlay curve begins at the top it intersects constant product curve 1 at point A. At point A, that combination of factors X and Y yield a total product of order 1. Proceeding further along the constant outlay line, (further in the sense of increasing X and decreasing Y), we intersect point B, at which point X the factors will produce products of size 2. So as we proceed along the constant outlay line, we arrive at higher and higher products--at curves further and further to the right. Finally, we arrive at the point with the highest size product, and the point of production that will be chosen with this outlay. This is point E of size 5, the point of tangency between the constant outlay line and the highest constant product curve obtainable with that outlay. Beyond this point, the constant outlay line again intersects the lower-sized product curves.
For any constant outlay line then, the entrepreneur will strive to act so that his combination of factors will be at a point tangent to the constant product curve. Of course, the entrepreneur in practice does not need to know about such tangencies and curves; he is only concerned with maximizing his output for the given outlay. But we have seen that mathematically this is implied by such maximum output. It must be cautioned that in practice, the constant production curves are a series of dots, of discrete points, rather than continuous lines. A continuous curved line implies that the distance between the points of decision by the actor are infinitely small; actually, this can never be the case--human action of necessity deals with discrete objects and distances. However, in the realistic case, the choice of the maximum product is the closest approximation to such tangency that could be, or should be, achieved.
It is clear that this elaborate analysis of families of curves and tangencies is of no particular aid in this problem; however, it provides analytic tools that will be handy in later analyses of the pricing of factors of production. (38) For one thing, we know geometrically that the marginal rate of product substitution, which is always diminishing, is equal to the slope of the constant product curve, when the latter is a continuous curve. At a point such as E, of tangency with the constant outlay line, elementary geometry tells us that the slopes of the curve and the line are equal. The slope of the line equals the marginal rate of outlay substitution, which is constant throughout and equal to the ratio of the factor prices, and therefore, at the point of tangency, the marginal rate of outlay substitution equals the marginal rate of production substitution. Under real conditions, this is only an approximation rather than an actual fact, but this proves the assertion in the text that the producer sets his production so that these two marginal rates tend to be equal. And this means, furthermore that, for each producer's decision, the marginal rate of product substitution between the two factors tends to equal the ratio of their prices.
This equality is only an approximation, since for the universal case of more or less discrete points; the point of decision will only be the nearest approach to such equality. However, because of the divisibility of money, the constant outlay curve tends to be (although never will be) a continuous line, while the more advanced the production structure and the more complex the alternative combinations, the nearer will the constant production schedules approach being continuous curves. The more highly developed the market economy, therefore, the greater will be the tendency to approach equality between the ratio of the prices of factors and the marginal rates of product substitution between them.
At each possible constant outlay line, therefore, the producer will pick his preferred combination of factors at the point of maximum output, or approximate tangency to a constant product curve. The higher the amount of money to be spent, and therefore the higher the constant outlay line, the higher and the further to the right will be the constant product curve, and the various points of tangency. Thus, a typical family of constant product and outlay curves may have points of tangency as follows.
[FIGURE 8 OMITTED]
In this figure, we depict constant product curves, P1, P2, ,...P7, and constant outlay lines, O1, O2, ... O7. They have points of tangency at A, B, C, D, E, F, and G. The zero point is also a point of tangency, at zero input of factors. The points of tangency enable to producer to determine his maximum product outlay curve. For at any given outlay, the tangency points will yield the size of the maximum constant product curve. Thus, O1 will be tangent to P1 at point A. The same is true to every other alternative. Thus, the decision points A, B, C, etc., reveal to the producer: 1) the maximum product for each outlay, and 2) the best combination of factors for this production.
SECTION 4: THE OUTPUT AND INVESTMENT DECISION OF THE PRODUCER
We must now return to Jones and his outlay of 1000 ounces. We have already seen that, given an investment of 1000 ounces, Jones will select one combination which will yield him a maximum product. Out of a group of alternative combinations, he will select the best combination. We could diagram this situation as follows:
[FIGURE 9 OMITTED]
This diagram shows that, at an outlay of 1000 ounces of money, different alternative combinations could yield various amounts of product, namely 110, 107, 105, 100, 97, and 96, as listed in Table 8 above. The highest production, or the top dot on the line, will be the one that is chosen, and the combination of factors will be picked accordingly. This dot is crossed to represent the product of the combination that will be chosen. The same sort of process will be undertaken regardless of the amount that the producer has to invest. Thus, if he has 990 ounces to invest, he will choose the combination yielding him the maximum product, at 105 units. At each possible investment of money outlay, the producer will choose that factor combination which yields him the maximum product. Thus, the diagram of such a situation will be as follows:
[FIGURE 10 OMITTED]
For each straight line, the top crossed dot will be selected. Thus, we see a series of possible vertical straight lines, representing the constant outlay, with units of product on the vertical axis, and money outlay on the horizontal axis. Each vertical straight line is a constant outlay line, and the crossed top dot is the maximum product that would be selected in each case. The crossed dots can be joined for convenience to give us a connected line of potential products for each money outlay:
[FIGURE 11 OMITTED]
Each producer will try to determine the various points on this product outlay curve. As we have seen, he estimates the various alternative factor combinations for producing each particular quantity of product, and using these and the prices of the factors, the producer will be able to judge his constant outlay combinations, and which combination will yield him the maximum product for each outlay. This will give him the series of crossed top dots for each outlay, and yield him the above diagram, which represents the maximum product schedule for each outlay.
What can economics say about the shape of this important curve? In the first place, it is obvious that a greater outlay can never produce a lower maximum product. We have seen above that the 1000 ounces will yield a maximum product of 110 units. A greater outlay, say 1050 ounces, cannot produce a maximum product of less than 110 units. This is obvious from the very nature of production and of factors. At the very least, the 110 units could be produced, even if the excess factors purchased with the other 50 ounces cannot be used. Thus, the maximum product schedule always slopes upward or remains horizontal when the money outlay increases. It never slopes downward.
Another characteristic of the maximum product outlay curve is an obvious one: it must pass through the zero point, since no expenditures will obviously result in no production. A typical product outlay curve might therefore look like this:
[FIGURE 12 OMITTED]
We notice that we may conveniently omit the crossed dots from the final connected line. From the line, we may read off the maximum product which would be yielded by the expenditure of any given outlay.
Without discussing at this moment when the curve is likely to be horizontal, it is obvious that no producer knowing the situation will pick any outlay along the horizontal except the cheapest: i.e., the point on the extreme left of each horizontal line. Thus, if 1000 ounces of outlay will produce 110 units maximum and 1050 ounces of outlay will also produce 110 units maximum, it is clear that there will be no hesitation in choosing the 1000 ounces, and not the more expensive outlays. Any other decision would be a pure waste of money by the producer. Therefore, without yet fully answering how much money will the producer decide to invest, we can immediately answer that he will never decide to invest that amount which lies along a horizontal line. Thus, if 1000 ounces will produce 110 units, and all greater expenditures up to 1100 ounces will only produce 110 units (with expenditures of over 1100 ounces yielding more units), we can be sure that Jones will not decide to invest a sum of between 1001 and 1100 ounces. He will either invest more or less. In Figure 12 above, we cross the horizontal lines with vertical marks to designate those sums that are ruled out from the producer's decision.
So far, from Figure 10 we know two definite points on Jones' maximum product outlay curve: 1000 ounces netting him 110 units of product and therefore 1100 ounces of money revenue; 990 ounces netting him 105 units of product and therefore 1050 units of revenue (selling prices are assumed to be 10 ounces per unit). In the former case, he makes a net money income of 100 ounces, equaling 10% of his outlay; in the latter case, he makes 60 ounces net, equaling about 6% of his outlay. Now, we must directly pursue the question of how much Jones, or any other producer, will decide to invest in any particular line of production, and how much he will decide to produce. It is clear that the determining influences are the expected net income, its amount and its percentage. Their exact nature, however, must wait on a more elaborate explanation of the relation between outlay, product, and revenue, in table and figure.
Before finally analyzing which point on the maximum product outlay curve will be chosen, it is necessary to extend the analysis to remove the restrictive assumption of 2 factors. What will be the situation with n number of factors? This is a vital consideration, since it is very rare to find an actual case where only two factors are used to produce any given product.
If there are n number of factors, with market prices assumes to be given, the producer's investment decision turns out to be almost identical with the case of two factors. The situation may not be diagrammed as in the case of two factors, but the greater mathematical difficulties in the description of the case of n factors does not by any means signify difficulty for the producer. The producer is, again, confronted with a complex of technological alternatives, for producing various amounts of output. Now, the production functions will be combinations of various quantities of factors X, Y, Z, etc. Once again, a constant outlay will enable a certain set of factors to be chosen, in accordance with their market prices. The producer may draw up the list of alternative factor combinations and corresponding outputs, plus a list of factor combinations that can possibly be bought at each given outlay. And, once again, the producer will choose the maximum product combination for each outlay. The fact that there are now many factors does not change the desire of the producer to maximize his product for each possible outlay. The shape of the maximum product curve does not change; it is still true that a greater outlay cannot yield a lower product, and that those greater outlays which will not increase product will not be chosen. It is evident that the analysis based on the maximum product curve is not changed by permitting any number of factors.
What of the interrelationships between the factors and the factor combinations that will be chosen as points on the maximum product curve? Here, it is clear that the situation, with n factors, is more complicated. It is, however, essentially the same, and does not materially alter the analysis. It is still true that we can represent the producer as adjusting, and substituting, all of his factors for each other. Each factor is an imperfect substitute for each other factor, the degrees of imperfection varying with the data of each concrete case. There can be no perfect substitutes for different factors, and there are few or no cases of absolute fixed proportions between all factors, so that, within limits, more of one factor can be substituted for less of the others. The marginal rate of substitution between any two factors diminishes as one factor increases. The rate of outlay substitution between any two factors is equal to the ratio of their prices and the producer will still tend to approximately equalize the rate of outlay substitution and the rate of product substitution between any two factors. Even if ten factors are involved, if, for any two factors, for example, the rate of product substitution is greater than the rate of outlay substitution between them, it will pay the producer to keep substituting, say X for Z, until the rates are approximately equal. For this is equivalent to saying that substituting more X for less Z at constant outlay will yield a greater total product. Conversely, if the rate of product substitution is less than the rate of outlay substitution, it will pay to use less of X and more of Z until the rates are equal.
Therefore, for a case of n factors, the producer will always tend to produce at the point where the marginal rate of substitution for any two factors is equal to the ratio of their prices. There is a simultaneous balancing and adjusting in order to find the maximum product for each outlay. It must be emphasized that there is still one maximum product for each outlay, that there is still an array of different products for the alternative combinations at each outlay. Out of this array, the producer selects the maximum product combination; the number of factors involved does not change this.
Now let us turn to the final production decision of the producer who has arrived at his maximum product schedule. How much does he decide to invest and to produce? For convenience, let us take the case of another producer, Smith, [who can invest in a different firm that produces Product Pi. In addition to his maximum product outlay schedule, he estimates his future selling price, and this enables him to estimate his revenue outlay schedule. Thus, assume that his maximum product outlay schedule is as follows (assuming, for convenience, steps of 10 ounces of money outlay):
Table 11 SMITH--PRODUCT P TOTAL MONEY OUTLAY TOTAL MAXIMUM (GOLD OUNCES) PRODUCT 0 0 10 0 20 10 30 18 40 28 50 40 60 50 70 55 80 55 90 65 100 70
This product outlay schedule is shown below in Figure 13.
Now Smith estimates the future selling price of his product. It is quite possible that, as Smith's prospective product decreases, his selling price will rise. This estimate depends on his idea of the market demand schedule for his individual product.
At this point we must broaden slightly our application of the concept of monopoly and competitive price. A monopoly price situation will occur not only if less produced from a given money investment yields a greater profit, but also if a lower money outlay, and its lower product, yields a greater profit because of the higher selling price. It is clear, however, that this does not materially change our analysis of competitive and monopoly price. In the previous section we assumed a given investment and a lower than maximum product; here, a lower outlay can also yield the same goal of a lower product, and without the waste of the former. This, then, is the actual case. If the demand for the firm's product is inelastic, so that a lower product, thrown as stock on the market, will so raise the price that money revenue is increased, the firm acts as a "monopolist" to cut back production and outlay to the lower figure. Thus, suppose that at a money outlay of 60 ounces, and at a maximum product of 50 units, as in Table 11, the price of the product per unit is 2 ounces. The money revenue, then, will be 100 ounces, for a net income of 40 ounces. If the demand schedule for the firm's product is inelastic above this range, then, for example, a sale of 10 units will raise the price to 20 ounces, and a total revenue of 200 ounces. Now obviously, Smith will not invest 60 ounces, produce 50 units, and then throw 40 of these units away in order to acquire 200 ounces. We assumed this above, because we were dealing with the assumption that money outlay is fixed at a certain amount. Obviously, he will rather choose the minimum money outlay required to produce 10 units, i.e. 20 ounces. There will therefore be no need for him to throw away 40 units, and he will save 40 ounces which he would have needlessly expended.
There is therefore no change in our analysis of the demand curve for the firm, and its relation to the incidence of monopoly price. This curve depends only on the quantity sold, and bears no relation to how this quantity is produced. The change in our analysis of the monopolist is, that even he will choose the maximum product for the money outlay that he spends. Even the monopolist will choose a point on his maximum product outlay schedule, and therefore even he strives to gain further profits producing whatever units he makes as efficiently and as productively as possible. If his demand curve is inelastic, he will simply reduce his money outlay from the amount that he would have invested under a competitive price. The reduction of his outlay will reduce his product to the most profitable amount.
On the other hand, there is no reason to restrict the definition of competitive price to a situation where the amount the firm produces has absolutely no effect on the price. It is clear that a change in the amount a firm produces always does change the market stock of the product, and therefore tends to affect the price. It may well be, of course, that, within the relevant range; the action of the firm is not large enough in relation to the product as a whole, to change the market price. There is no need, however, to restrict the discussion of competition to this limited case. The only criterion is that the demand curve is not such as to raise revenue for a restriction of output to a price above the competitive one.
The following is a tabulation of Smith's productive situation, [and the firm producing P that he can invest ini, with the above total outlay and total product schedules, plus an expected selling price schedule for each quantity produced and sold of P. The selling price declines as the stock increases, but are not such as to yield a monopoly price situation (i.e. an increased total product for the firm does not lower its gross revenue). From these three columns we can deduce three others, which are also presented: expected total money revenue (which equals expected selling price times product); net money income (which equals money revenue minus money outlay); and percentage net money income (which equals net money income as a percentage of money outlay). These three schedules are derived from the primary three:
Table 12 TOTAL OUTLAY TOTAL PRODUCT EXP. PRICE EXP. REVENUE (1) (2) (3) (4) (=2*3) 0 0 -- 0 10 0 -- 0 20 10 2 20 30 18 1.8 22.4 40 28 1.7 47.6 50 40 1.6 64 60 50 1.5 75 70 55 1.5 83 80 55 1.5 83 90 65 1.4 91 100 70 1.4 98 TOTAL OUTLAY EXP. NET INCOME EXP. RATE OF NET INCOME % (1) (5) (6) (=4-1) (=5/1) 0 0 0 10 -10 negative 20 0 0 30 -7.6 negative 40 7.6 19 50 14 28 60 15 25 70 13 18.5 80 3 3.75 90 1 1.1 100 -2 negative
[FIGURE 13 OMITTED]
[FIGURE 14 OMITTED]
Figures 13 and 14 illustrate Table 12. In Figure 13, total units of product are plotted on the vertical axis, as against corresponding money outlay on the horizontal axis. The figure reveals the amount of maximum total product that could and would be produced at different amounts of monetary outlay. The result is the product outlay curve, which is read vertically. There is a dotted line bypassing the point at the money outlay of 80, because here the product curve is horizontal, and no producer would consider such a waste of his resources as to produce at such a point.
In Figure 14, the product schedule is multiplied by the expected selling price at each quantity of product, to yield the expected total revenue for each point of outlay. This yields the total revenue schedule of Column 4. In this figure, money revenue is plotted on the vertical axis, and money outlay on the horizontal axis, the result yielding a revenue outlay curve, which expresses the expected revenues for each amount of invested money outlay.
It is clear that there is a direct resemblance between the shape of the revenue and product curves, since the former is derived from the latter. At a 45 degree angle between the two axes, there is a diagonal straight line. Since the units on each axis of Figure 14 are exactly the same (money in gold ounces), with the same distances, such a 45 degree line can also (vertically) represent money outlay on the diagram. Thus, let us take a money outlay of 60 ounces. This is given by the distance 0A on the horizontal axis. However, if we read vertically upwards from point A, we find that the distance between A and the intersection point B on the money outlay line is also precisely 60 ounces. Therefore, AB, and other such vertical distances, may be read as equaling money outlay on the chart.
This device makes figure reading a very easy task. At the outlay of 60 ounces, the money outlay equals AB. What is the money revenue? This can be read off from the revenue curve, and will equal AC, or 75 ounces. This permits a clear portrayal of net income, which will be the difference, or the vertical line BC.
Similarly, the expected net income can be read at any desired point. It becomes evident, for example, that there is a negative money income at such outlays as 10 ounces, 30 ounces, or 100 ounces.
Such a chart also permits the facile portrayal of the expected percentage net income, or rate of net income. This will equal the net income divided by the money outlay. On the figure, for example, it will be the ratio of BC divided by AB, or alternatively, BC divided by DB.
Now, armed with this portrayal of the alternatives and their expected consequences, what amount [of P] will Smith decide to produce [in this firm]? It is obvious that this problem is a central one in the analysis of productive activity on the market. For the question is applicable to all producers, whatever the product or whoever the individual involved.
Smith has a list of alternative courses of action from an investment of 0 to 100 ounces. It is clear that he will not decide on 80 ounces, since this will be a wasteful act with 70 ounces able to produce the same number of units. It is also clear that he will not choose to invest: 10 ounces, 30 ounces, or 90 ounces, since he will suffer monetary loss from such investments. He will not invest 20 ounces, where there would be no income from his investment. Which alternative will he choose of the ones remaining?
Most writers on this important subject have gone astray in their answers to this question. They look at the schedules and simply assume that every producer is interested in "maximum money profits," or, in better terminology, "maximum net income." Almost invariably, they would conclude in Smith's case that Smith would choose a money outlay of 60, and the expected money revenue of 75, since this yields the highest expected net income, i.e. 15 ounces. This is greater than any of the other alternatives. At first sight, this assumption seems plausible. Further analysis, however, reveals the unsoundness of such a simple assumption. It is true that if Smith invests 60 ounces, he expects a return of 75, and a net income of 15. Yet compare this with the alternative of investing 50 ounces and obtaining a net income of 14. In the former case, his percentage net income, [or rate of net income], is 25%, while in the latter case it is greater, 28%. Isn't it plausible that Smith could invest 50 ounces at 28%, and then find a better and more rewarding way of investing the remaining 10 ounces? If we look at the marginal rate of net income, it becomes clear that, on the added 10 ounces of outlay, Smith is only making an extra 1 ounce in net income, a percentage net income of only 10% on these last 10 ounces. If, as seems plausible, Smith can find a greater rate of net income on these 10 ounces, it is clear that he will only invest 50 ounces in this product, and will invest the other 10 ounces elsewhere.
How many ounces [in this firm for Product P] then, will Smith invest? Will he invest 60 ounces to earn a net income of 15, and a rate of net income of 25%; or will he invest 50 ounces to earn a net income of 14, and a rate of 28%?
It is clear from out discussion that, in fact, there is no precise theory of the determination of the investment in, and output of, the firm. There is no theory of investment or output of the firm, because on firm cannot be considered in isolation from the other firms in the economy. Whether or not Smith will invest 50 ounces or 60 ounces in this firm depends, for example, on whether he will be able to invest the remaining 10 ounces elsewhere to yield more than 1 ounce of net income. The prospective investor considers, in various possible firms, the net returns that he will earn from various amounts of outlay in various possible firms. He must consider which alternative will be more remunerative: to invest 50 ounces here and 10 ounces elsewhere, or 60 ounces here. His marginal rate of return on the last 10 ounces is 10%; if he can earn 15% or 1.5 ounces elsewhere, he will invest them there, and invest only 50 ounces in this firm. Furthermore, the investor might invest nothing at all in this firm, for he might be able to earn a 30% return for 60 ounces in some other firm, producing some other product. It is impossible, therefore, to consider a firm in isolation, and attempt to determine how much will be invested in it, or how much it will produce.
Each investor, in a free economy, can range among a myriad of possible enterprises and invest in them. Indeed, by means of the device, to be examined more fully below, of parceling out parts of ownership of a firm's assets to different investors in various shares, each individual can invest a few ounces of money in one firm, a few in another, and several in a third, the investors hiring managers to supervise the actual production. (39) In all of his actions, psychic factors being equal, he will attempt to maximize the rate of net income from each unit of money that he invests, thereby maximizing his total net income from his entire investment in all branches. To pursue this approach will lead us to a theory of the savings and investment of the investor, rather than of the output of the firm, and thence to the theory of the savings and investment of all the investors, indeed all the individuals, in the economy. This will be inextricably connected with the problem of time preference, which we have already seen in Chapter I to play a determining role in the decision of the individual as to how much he will save and invest compared to the amount he will consume. (40) This will be discussed in a later chapter. (41)
It is evident that, in the pursuit of the maximum possible rates of net return, the investors will invest each sum of money, large of small, in that firm or in those firms where the rate of net return, for each size of money invested, will be at its maximum. Investors will spurn 2% return projects to invest in expected 20% return projects.
At this point we must make a crucial distinction in our analysis of investment and production--the distinction between the investor or investors considering investment in new firms, and those contemplating the extension or continuance of investment in old firms. New firms are those which are starting from the beginning. If Smith is a new investor, he will decide as follows: [with a given 60 ounces to invest], he will invest 50 ounces so as to produce 40 units [in this firm for Product P], and earn an expected 28% net income [and invest 10 ounces elsewhere to try to earn more than a 10% marginal rate of net income]. However, if he cannot earn [more than] 10%, or 1 ounce, on 10 ounces elsewhere [in another firm], he will invest 60 ounces to produce 50 units [of Product P], and earn 25% on the investment.
It is clear that there prevails on the market a tendency toward equalization of expected net income rates on new firm investments. Suppose that in one firm or product, the rate of net return is expected to be unusually high compared to other investments, say 28%. It is clear that the new investors will flock to invest in this firm, or in competing firms producing the same product. If the data on the market remain the same, then this flood of investments will tend to lower the price of the product, and raise the price of the factors, particularly those specific to that product, until the expected rate of return will be drastically lowered. Furthermore, in unusually unprofitable firms, such as those earning 2%, the old investors, given enough time, will allow their capital goods to wear out, and shift their investments to the more profitable investments. Suppose we postulate, then, an evenly rotating economy, such that the data never change, i.e. on each day consumer demand, saving and investment, tastes and resources and technological knowledge, will be the same. In this case, given enough time, the rate of net return will be equalized in every firm and every branch of production. This will be an economy of certainty-since there will be no uncertainty of future price, demand, or supply. In this case, the expected rate of return will invariably be the realized rate of return, and this will be equalized for every firm and investment. This rate of return is called the pure rate of interest. What rate will it be, and how will it be determined, we must leave to further chapters. (42) In the evenly rotating economy, then, every firm will earn the same net return, say 5%. Since there is no uncertainty, every firm will be built and arranged to produce at its optimal level.
[Returning to the individual investor, Smith, in the above example we assumed that he was going to invest 60 ounces in one or more firms. But how does Smith choose the amount of money that he is going to invest at all? We have shown above that we cannot simply concentrate on maximum net income on an investment, but must also pay attention to its rate of net income.] Can we then say that Smith will invest that sum which will yield him the largest percentage, or rate of net income? No, we cannot simply make such a plausible statement either. Suppose, for example, we consider the investment of 40 ounces, yielding a percentage net income of 19%. An additional investment of 10 ounces would yield an additional net income of 14 minus 7.6 ounces, which equals 6.4 ounces, [for a rate of net income of 28% on his 50 ounces]. This is a return of 6.4 ounces on an outlay of 10 ounces, a marginal rate of return, or marginal rate of net income, of 64%. Yet, circumstances are conceivable when Smith would not make the additional investment. We must never forget, as we pointed out in Chapter III above, (43) that every individual is always engaged in balancing his various consumption, and his various investment expenditures, and additions or subtractions from his cash balances. Suppose, now, that Smith has a money stock of 200 ounces, which he is in the process of allocating. It is entirely possible that, while he may choose to invest 40 ounces in factors of production yielding him a 19% net income, even so high an additional return of 64% on the next 10 ounces will not induce him to restrict his consumption further. In such a case, Smith prefers present consumption spending with these 10 ounces to the 64% rate of income; therefore, his marginal rate of time preference for these 10 ounces is higher than 64%, and he does not make the investment. His investment in the product will then be 40 ounces and his level of output will be 28, producing an expected revenue of 47.6, a percentage of 19%.
In every case, therefore, the amount of money investment by the producer, and consequently the amount of product made, depends on the interrelationship between the expected rate of net income and the individual's rate of time preference.
This interrelationship, specifically, is most important in its marginal aspects. The reader is referred again to Chapter I, the basic foundation for the later analysis. (44) There we saw how man allocates his stock of goods in accordance with their marginal utility in the various uses. (45) We also saw how man allocates his labor in accordance with the marginal utility of the expected products in the various uses, and with the marginal disutility of the foregone leisure. (46) This is particularly relevant. We recall that each man allocates his labor in units, say hours, to that particular use which provides the greatest value of marginal product on his value scale.
This analysis, in its essence, is applicable to the present problem. Smith is choosing, not between the utility of labor and its product versus leisure forgone, but between the utility of an expected future net money income, and between the disutility of present consumer goods forgone, by investing in factors of production. Again, his decision in every case is marginal, i.e. he deals with divisible units of a good. In this case, he is dealing with units of a money commodity used to purchase factors. He knows, or believes that he knows, the various technological alternatives by means of which certain quantities of factors will yield him certain quantities of product, and from this he estimates the expected money revenue that will accrue from the sale.
Thus, let us consider an expansion of Smith's choices [for the firm producing Product P] as shown in Table 12 above:
Table 13 TOTAL OUTLAY MARGINAL EXP. NET EXP. MARGINAL EXP. RATE OF OUTLAY INCOME NET INCOME MARGINAL NET INCOME % (1) (5) (6) (7) (8) (=7/8) 0 0 10 -10 20 0 30 -7.6 40 40 7.6 7.6 19 50 10 14 6.4 64 60 10 15 1 10 70 10 13 -2 negative 80 10 3 -10 negative 90 10 1 -2 negative 100 10 -2 -3 negative
Money outlay and expected net money income are taken from Table 12. The other columns require extended explanation. The purpose of the added columns is to better analyze Smith's final investment decision in production. Column 7 sets forth the addition in net money income which will be yielded by an addition to Smith's monetary investment in factors. This is the marginal net income expected from his various decisions. However, an investment of 10 ounces will immediately be rejected by Smith; the net income itself is negative. Similarly, an investment of 20 ounces, or 30 ounces, will be rejected for the same reasons. The first possible investment is that of 40 ounces; there is no choice for Smith between 0 and 40. Therefore, the space above that in Column 7 is left blank. Marginal decisions, and their features, refer only to actual choices confronting the actor. The differential in which we are interested in is the differential that is significant to the human actor, and not the convenience of algebraic manipulation. Therefore, for example, the marginal net income at an outlay of 40 ounces is not the difference between 7.6 and -7.6, equaling 15.2, since there is no possibility that Smith would ever consider an outlay of 30 ounces, yielding a negative return. The margin is not between 0 and 10, 10 and 20, etc., but between 0 and 40 only. The marginal net income at 40 then, equals 7.6 minus 0, which equals 7.6. From then on, the margin occurs every 10 ounces, for that is the decision unit, so to speak. Smith estimates that the next 10 ounces of investment will increase his net income from 7.6 ounces to 14 ounces--giving him a marginal net income by these 10 ounces of 6.4. From 50 to 60, the 10 new ounces only increase the net income from 14 to 15 ounces, a marginal net income of 1 ounce. After this point, the net income declines; therefore, the marginal net income is negative. Thus, after 60 ounces, an additional 10 ounces will lower the net income to 13; thus its marginal net income is minus 2 ounces.
Immediately, we have learned something more about Smith's eventual investment production decision. It is obvious that no one will knowingly invest additional money the marginal net income of which is negative. Smith will not invest 10 more ounces in order to see his net income dwindle by 2. Therefore, in our example, all points above 60 are eliminated from Smith's final decision. This leaves us with three possible points of decision: 40, 50, and 60 ounces. Now, we may compute the rate of marginal net income for each of these amounts. This is equal to the marginal net income at each outlay divided by the marginal outlay listed in Column 8. The marginal outlay is the additional amount of money which each given amount of outlay represents in Smith's decisions. Thus, Smith may either invest nothing or 40 ounces, the next step. His marginal outlay for an investment of 40 ounces, is 40 ounces. His marginal outlay at an outlay of 50 ounces is equal to 10 ounces, or the differential between 50 and 40--the two successive points of decisions. The marginal outlay at 60 is also 10 ounces. After that, there is no need to apply the concept, because these decisions have been ruled out. Column 9 lists the rate of marginal net income, and this gives the percentage of net income which each additional investment of units of money will earn. At 40, an addition of 40 ounces earns 7.6 ounces net; this is a percentage return of 19%. At 50, an addition of 10 ounces earns 6.4 more ounces of revenue-a marginal percentage return of 64%. At 60, the additional 10 ounces earns only one more ounce in revenue-a marginal rate of 10%. (47)
The alternatives that remain for Smith's consideration are condensed in Table 14 below taken from Tables 12 and 13:
Table 14 OUTLAY MARG. MARGINAL EXP. REVENUE EXP. NET INCOME EXP. MARG. OUTLAY INCOME 0 0 0 0 0 40 40 47.6 7.6 7.6 50 10 64 14 6.4 60 10 75 15 1 OUTLAY MARG. RATE OF NET RATE OF NET INCOME % MARG. INCOME % 0 0 0 40 19 19 50 28 64 60 25 10
To summarize how we obtained these columns: from technological knowledge, Smith could calculate the maximum physical product that could be obtained from each combination of factors, and this with the prices of factors, which we have taken as given, determine the maximum total product schedule for each possible alternative outlay of money investment. Horizontal spaces in the schedule were eliminated, i.e. where the marginal product is zero for each increase in outlay (it can never be negative). For each possible product, Smith estimates the selling price for which he could sell the product, and this times the quantity produced yields him the revenue schedule for each outlay. The net income is then easily calculated, and points where this absolute net money income is expected to be zero or negative are immediately eliminated from consideration. The rate of net income is the percentage that the net income bears to the money outlay at each point. Marginal Net Income, then, can be calculated: at each step this is the additional net income earned from the additional dollars invested. Marginal outlay can usually be taken at equal steps for each alternative, but this must change when the net income turns out to be zero or negative in certain cases, in which cases the marginal outlay considered by the actor must be greater in order to skip these points. Those points where marginal net income is negative are then eliminated from consideration, since it would be obvious folly to invest additional funds where only losses would be earned. The two key concepts now are the rate of net income (which is equal to net income divided by outlay) and the rate of marginal net income, which equals marginal net income divided by marginal outlay. These are listed in Columns 6 and 9 respectively.
Before continuing to discuss the decision between the remaining alternatives, we might well consider the question: is there a fixed relationship between the average rate of net income, which shows us the percentage return from the total investment, and the rate of marginal net income, which gives us the percentage return on each successive dose of monetary investment? The answer is definitively yes; in fact, at any point, the rate of net income is equal to the weighted average of the rates of marginal net income at that and preceding points, the weights being the size of the marginal outlay at each point. Thus, at an outlay of 50, the rate of net income is 28. This is equal to the average of the rates of marginal net income at that and preceding points, namely 64 and 19. However, it is not simply 64 plus 19 divided by 2 ((64+19)/2=41.5). This would be an unweighted average of the two numbers. Each number is multiplied by the marginal outlay at that point, and the sums are divided by the sums of the marginal outlays, which is total outlay at the final point. Thus, 19 times 40 plus 64 times 10 is divided by 40 plus 10 (((19*40)+(64*10))/((40+10))=1400/50=28). Or, at the money outlay of 60, the rate of net income equals 40 times 19, plus 64 times 10, plus 10 times 10, divided by 40 plus 10 plus 10 ((40*19)+(64*10)+(10*10))/((40+10+10))=1500/60=25).
Furthermore, at the first feasible marginal step, whatever it may be (in this case it is from 0 to 40 ounces), the rate of net income equals the rate of marginal net income, the net income equals the marginal net income, and the total outlay equals the marginal outlay. This is because the starting point is always zero--no investment--and the total of something after the first step is the same as the difference between the step and zero.
Thus, we see that the average rate of return is the weighted average of the preceding marginal rates of return, and that at the first step, the two rates of return are equal. This indicates another important truth: that the average rate at any point is equal to the marginal rate, if the distance between that point and zero is taken as the unit. Thus, if Smith is considering the investment of 60 ounces, his expected average rate of net income is equal to the marginal rate of net income, if the "margin" is taken as a unit of 60 ounces. Thus, the decision on an investment of sum of money is a "marginal" one in two senses: a) in the sense of the last small unit of money and its return, and b) in the sense of the return to a marginal unit taken as the size of the sum itself. Both sizes of marginal chunks are discrete steps, and both are taken into consideration by the actor. (48)
[Now we must return to the important concept of the rate of time preference and integrate our analysis of the rate of net income.] Any man, in deciding upon the allocating of any given sum of money between consumption and investment purposes, estimates the expected yield of net money income to be derived from his investment (modified where necessary by other psychic considerations) and compares it with his minimum required monetary return from that sum of money, taking into consideration his total stock, and his value scale. This minimum rate of return is his rate of time preference: any investment which he expects will yield him a lesser return will not be made. [Thus Smith and his investment decisions in the firm producing Product P. as shown in Table 14, are compared with his rate of time preference.] This rate of time preference is set by his relative valuations of present and future satisfaction; it is his "minimum supply price"--the lowest "price" at which he will part with his present money in order to invest in a prospect of a higher income at some time in the future. As an individual allocates more money to investment and less to consumption at any time, his marginal rate of time preference increases, until it finally becomes prohibitively high for any investment. This fact is set by man's necessity to consume in any given present, before making investments for the future. The entire schedule of a man's time preference rate, therefore, increases as the invested outlay increases, finally nearing verticality. [It can be calculated in marginal and averages form like net income.] If the rate of net income from the investment outlay is greater than the rate of time preference, he will make the investment; if not, he will abstain from the investment.
The investor Smith, in sum, does not simply try to maximize his expected net money income. He, like every actor in every situation and every choice, tries to maximize his psychic revenue and attain a psychic profit. He cannot only consider money income from the investment. He must weigh this against his psychic time preference rates. His maximization of psychic revenue, therefore, impels his investing so long as the rate of average and marginal net income exceeds his average and marginal rates of time preference. (49) [Investment decisions in a firm, then, will always be where the average and marginal rates of net income are greater than or equal to the average and marginal rates of the investor's time preference. More precisely, Smith's investment decision in the firm producing P, will be at the last marginal outlay where this occurs. In general, then, investment in a firm will be pushed to the last marginal outlay where expected average and marginal rates of net income are greater than or equal to the average and marginal rates of time preference for the investor. We may call this the Law of Investment Decision.]
There is an important modification in this analysis of Smith that must be made, before our investigations into his output and investment decisions can be completed. In this example, we have assumed that the investor Smith faces only one alternative: either invest in the given line of production or don't invest at all. In actual life, as we know, the investor has open to him a choice in the investment of money in many lines of production or many firms. [As explained earlier, the production and investment of a firm cannot be considered in isolation.! Smith must not only choose whether to invest or to consume (or add to cash balance), he must decide between several alternative lines of production. How then must our law be changed to indicate the determination of his total investment, and of the investment in each line of production? In the first place, it is clear that Smith is primarily interested in maximizing his psychic revenue from the total of the investments in his portfolio. His interest is not in firm A or B or C, but in his income from all of these investments as a whole. Therefore, he weighs his average and marginal rates of time preference against the gross revenue that can be achieved from all of his investments at the given outlay. Thus, at any total outlay, say 120 ounces, he determines what distribution of money among the alternative investments will yield him the maximum total gross revenue, and hence the maximum net income, and maximum rate of net income for the given outlay. At each point of outlay he decided on the distribution that will accord him the maximum gross revenue, and therefore he is able to deduce the maximum average and marginal rates of net income for each outlay. He invests his money up till the largest amount at which the maximum average and marginal rates of net income are larger than his average and marginal rate of time preference, respectively. At this amount, he distributes his outlay among the various enterprises in accordance with the "maximum revenue distribution" at that outlay.
In the final form of the Law of Investment Decision, then, there is not the previous direct and complete link between investment outlay of the individual producer and the output of the individual product-as there is when the individual producer invests in only one line of production. It is still true that the actor invests in production--in general up to the last point that his expected average and marginal rates of net income exceed his average and marginal rates of time preference. Since this is true for each man, it is clear that the production of all goods in the society at any period is completely determined by these factors. It is still true for each individual product that the amount invested is such that the average and marginal net income rates at that point are greater than the time preference rates at that point. In this sense, the law still holds. However, no longer does the investor push his investment in each particular firm to the last point before his time preference rates outstrip his income rates. He does not do so, because now he wishes to distribute his money outlays among several lines of production, in order to increase his revenue.
We must now return to our original question. How is the Smith, or in general, any investor's outlay in any given line of production, and therefore the output for that particular product, determined? To find the answer, we must look at a hypothetical illustration. Suppose now, that Smith has to consider, not only the product that we have explored in detail above, but also several other lines of production. Alongside the hypothetical money outlays, Smith lists, for each line of production, the expected net income from each outlay. Thus, let us say that he decided among firms producing products P, Q, and R, recalling that our illustration above consisted of product P Then we might have the following schedules:
Table 15 NET INCOME MONEY OUTLAY F Q R 10 -- 2 - 20 - 7 8 30 - 13 7.5 40 7.6 16 9 50 14 18 15 60 15 20 14
These net income schedules reveal what net income Smith expects to enjoy when investing a certain outlay in any given line of production. But these schedules permit combination into one maximum net income schedule, which will determine the investment distribution that will yield the largest net revenue for each given outlay. Thus, suppose Smith is considering an outlay of 50 ounces. He might invest them all in the firm producing P, in which case his net income will be 14 ounces. If he invests them all in the firm producing Q, his net income will be 18 ounces; in the firm producing R, his net income would be 15 ounces. Clearly, if he can only invest in one firm or in the other, then he will choose firm producing Q. But, since he can distribute his investments, he also considers the various investment combinations adding up to 50 ounces which involve two or more firms. Thus 40 in producing P and 10 in producing Q will yield 7.6 plus 2, a net income of 9.6. Mentally considering the various combinations, it becomes clear that prospectively the best is (30Q plus 20R) which yields a net income of 13 plus 8, or 21 net ounces. At each hypothetical outlay, the investor picks what appears to be that combination that will yield the highest net income. The following is Smith's maximum net income schedule with each money outlay, with the investment distribution in parentheses:
Table 16 MONEY OUTLAY MAXIMUM NET INCOME 10 2 (10 in Q) 20 8 (20 in R) 30 13 (30 in Q) 40 16 (40 in Q) 50 21 (30 in Q; 20 in R) 60 24 (40 in Q; 20 in R)
The best combination for any outlay is that one for which the sum of the net incomes from each line of production is the highest. An equivalent property of this condition is that the weighted average of the rates of net income from each line of production be the highest (where the weights are the money outlay in each line). Thus, take the problem of the best investment of 50 ounces. 50 ounces all in producing Q would yield 18 ounces income, or a 36% return. This is higher than an investment of 50 ounces producing P or R. But an investment of 30 ounces in B yields 13 ounces income, or 43%. An investment of 20 ounces in R yields a return of 8 ounces income, or 40%. A weighted average of these two yields by the respective outlays is: 30 times 43, plus 20 times 40, divided by 50. This equals 42%, the weighted average, which also equals the rate of maximum net income (amount of maximum net income divided by money outlay). Thus, the best distribution can be determined from schedules of rates of net income for each of the various outlays in the various lines of production. In this case, the distribution is not confined to producing just Q, even though producing Q is more profitable than either of the others at any given total investment.
From the maximum net income schedule, there can be deduced schedules of rates of maximum net income, marginal outlay, marginal maximum net income, rates of marginal maximum net income, etc. Thus:
Table 17 OUTLAY MAX. NET INCOME RATE OF MAX. MARG. OUTLAY NET INCOME % (1) (2) (2/1) (4) 10 2 20 10 20 8 40 10 30 13 43 10 40 16 40 10 50 21 42 10 60 24 40 10 OUTLAY MARG. MAX. RATE OF MARG. NET INCOME NET INCOME % (1) (5) (5/4) 10 2 20 20 6 60 30 5 50 40 3 30 50 5 50 60 3 30
Smith, or any investor, then proceeds analogously with the case of one product, investing money outlay (in the best distributions) up to the largest amount that his rate of marginal maximum net income is greater than [or equal tol his marginal rate of time preference, and his average rate of maximum net income is also greater than [or equal to] his average rate of time preference. Here again, average rate at any point is equivalent to the marginal rate (of maximum net income) at that point, with the size of the point itself considered as the unit.
We at last come to the end of the tortuous road of analysis of the determination of investor's decisions and of the amount of investment in any one productive firm. An investor will continue to invest rather than not so long as his expected average and marginal rates of return are greater than his average and marginal rates of time preference; and he will make his investment in that productive enterprise or combination of productive enterprises that will yield him the greatest possible net income, or rate of net income, for any hypothetical outlay. If we may eliminate the distinction between average and marginal by varying the size of the marginal chunk, then we may simply say that each unit of money outlay will be spent in the way that promises to yield the actor the greatest utility: in spending on consumer goods, if the rate of time preference for this amount is greater; or in spending on factors of production in that line or lines and in that firm or firm, where the rate of net return promises to be the greatest.
We have thus analyzed the principles according to which a man allocates his stock of money in accordance with expected greatest utility: the allocation of money units between investment in general and present consumption, and the decision between investment in various different firms and lines of production. The quest is for psychic profit, and the course of action that will yield the greatest utility--in the usual case, this line of investment will be the one that is expected to yield the greatest net return from the outlay. Exceptions are cases where other psychic factors, such as particular like for, or dislike for, the production process or the product itself, alters the decision from a pure consideration of monetary return. Otherwise, a man invests in those enterprises which he expects will yield the highest rates of return.
We have thus seen what determines the amount of stock of any good that will be produced in any particular period--it will be the amount that the producer had invested in a previous period in order to aim at such production. The amount of previous investment depends on the producer's anticipated net monetary return. It is clear that an increase in anticipated rate of net income in any line of production will tend to increase the investor's outlay in that product, and that on the other hand a decrease in the anticipated return will tend to diminish his investment in that process. If we interpret the concept of "increase in rate of net income," as meaning an increase in the entire rate of net income schedule, so that at each outlay of product, net income is expected to increase, it is obvious that the rate of net income schedule will intersect the investor's time preference rate schedule at a further point, so that an increase in the expected net income schedule will increase the amount of investment outlay in that product, and contrary for the decrease. Furthermore, an increase in expected return for producing P will tend to shift more of the investment outlay to this firm from competing firms Q, R, etc., and the contrary will occur with a decrease in expected revenue.
As a matter of fact, changes in anticipated rate of net income are most likely to take place throughout the entire range of the schedule. The factors that can change the rate of return are: a) expected future selling price, b) the prices of the factors, and c) the producers' production function-the physical efficiency in converting quantities of factors into quantities of product. It is evident that, with factor prices here assumed to be given, and known, the producer's anticipations of future income are governed by his anticipations of selling price and of his production function. It is clear that a rise in expected selling price for any good, will ceteris paribus, increase the amount of investment outlay in its production; and that an increase in physical productivity for any good will ceteris paribus, increase the amount of investment outlay. Conversely, decreases in expected selling price, and/or decreases in physical productivity will, ceteris paribus, diminish the investment in that product.
We have learned, therefore, that consumers' goods prices are determined by consumers demand schedule and by the stock produced and sold; that the sales of produced stock depend on anticipated future price; that the amount of stock produced depends on previous investment in production; that the previous investment in production depending on the net money income that the investor anticipated receiving, and the amount of investment will be up to the last amount at which the anticipated rate of return exceeds the rate of time preference; that the anticipated rate of return depends on: expected future selling price, and production technique (given factor prices). In the last analysis, then, consumers' goods prices depend on: consumers' demand schedules, and general time preferences, producers' anticipations of prices, and productive techniques.
Many questions remain to be answered. Among them is the discussion in Chapter IV on the final supply curve of the producers as compared to the stock on the market. (50) The "final supply curve" is the amount that will be called forth in supply in the future by certain prices. The discussion in Chapter IV implicitly assumed that the present ruling prices would be the ones that would be anticipated in the future. Thus, the figure below:
[FIGURE 15 OMITTED]
Implicitly assumes that the present prices of P1 is assumed to be the future price, and will call for the equivalent amount on the SF curve, which will tend to lower the final market price to P2. However, we may alter this restriction, and make the necessary mental allowances for any anticipated change in price. The main point of the diagram still obtains--that the present market price is not necessarily the "final" one toward which the market forces are tending. The question then remains: what principles determine the "final" equilibrium market prices? Even though this price is never attained in practice, it is important because it is the point (though always shifting) toward which prices tend to move. And a final selling price, given the productive technique, and given factor prices tend to set net entrepreneurial income. On what basis does entrepreneurial net income, the driving force in the money economy, tend to be determined? This problem, along with a discussion of time preference, must be taken up in subsequent chapters. (52)
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(1) Editor's footnote: Rothbard's reference to his earlier presentation of the "final supply curve" is absent from MES. Rothbard's discussion of supply and demand for an already produced stock of goods and his introductory analysis of entrepreneurship and production can be found in Rothbard (1962, 153-161, 249-257). See below (pp. 557-59) for Rothbard's further discussion of final supply curve.
(2) Editor's footnote: See Rothbard (1962, pp. 187-231).
(3) Editor's footnote: See Rothbard (1962, pp. 755-874).
(4) Editor's footnote: See Rothbard (1962, p. 219).
(5) "In every case the choice made is, at the moment when made, a present choice. We have no future desires though we may have a present forecast of a future desire. 'Future desires' means desires that will be present at some future time. Present desires are all those desires now being weighed in choice. Present desires may be either desires for present uses or for future uses (either in the same or in different goods). A present desire for future uses is but the anticipation of a future desire, though the two may be of unequal magnitude. It appears therefore that all time-choices are, in the last analysis, reducible to choices between present desires for psychic incomes occurring at different time-periods" Fetter (1915, p. 247). See also Fetter (1915, p. 239).
(6) Editor's footnote: See Rothbard (1962, p. 220).
(7) Fetter (1915, 240).
(8) Editor's footnote: See Rothbard (1962, pp. 367-451).
(9) Editor's footnote: See the editor's footnote below on p. 552.
(10) Editor's footnote: See Rothbard (1962, pp. 13-17).
(11) It is of course likely that Jones will weigh his decision on the basis of expected returns over a much longer period, say a decade, in which these returns may be considered to take place for a ten year period. We can adjust his calculations to cover any desired time period.
(12) See Boulding (1941, pp. 456-457) and Stigler (1946, p. 109ff).
(13) Here it must be noted that the constancy of price assumed in Case (a) did not necessarily follow for all possible decisions of Jones. Thus, if he decided not to produce the good at all, the price might well be affected, and be, say 12 ounces instead of the 10 ounces if he did go into production. But the constancy of price is only assumed for the relevant range of choice--in this case between the three different combinations. Case (a) only needed to assume that, between a product of 96 and 110 units, market supply would not be affected enough to change the price.
(14) Editor's footnote: See Rothbard (1962, pp. 126-130).
(15) On competitive price and monopoly price, see Fetter (1915, pp. 77-84, 381-385); Mises (1949, pp. 273-279, 354-376), Mises (1951 , pp. 385-392), Menger (1950 , pp. 207-225) and Wieser (1927 , pp. 204, 211-212).
(16) See Brown (1908, pp. 626-629).
(17) Editor's footnote: Rothbard slightly modifies his definitions of monopoly and competitive price below (pp. 538-39).
(18) For example, see Chamberlain (1942). Recently, however, Professor Chamberlin has repudiated the implications drawn by his followers that the "pure competition" situation is the ideal; indeed, he implies quite the reverse. Chamberlin (1950, pp. 85-92).
(19) Editor's footnote: This later section, whether or not it was intended to be included in the current chapter or a later one, was not found by the editor in the Rothbard archives. See Rothbard (1962, pp. 677-680) for his mature theory of monopoly gains on the free market. It is important to note that here he no longer uses the competitive versus monopoly price distinction.
(20) See Ely (1917, pp. 190-191). The famous Blackstone gave almost the same definition, and called monopoly a "License or privilege allowed by the king."
(21) The battle of the equal-liberty movement against monopoly has had a long history in England. In 1603, the British courts decided, with respect to one of Queen Elizabeth's numerous grants of privilege: "That it is a monopoly and against the common law. All trades... are profitable for the Commonwealth, and therefore the grant to have the sole making of them is against the common law and the benefit and liberty of the subject." In 1624, Parliament declared that "all monopolies are altogether contrary to the laws of this realm and are and shall be void." In the American states, the Declaration of Rights of the Maryland Constitution asserted: "monopolies are odious, contrary to the spirit of a free government and the principles of commerce" Ely (1917, pp. 191-192). See Walker (1911, pp. 483-484).
(22) Editor's footnote: In this footnote Rothbard refers the reader to later chapters on the hampered market on various monopoly grants. Rothbard originally wrote multiple chapters on the hampered market before the publisher required that he cut the length of the book down and remove controversial parts of the manuscript. Rothbard then had to write a summary chapter of his analysis (Rothbard, 1962, pp. 875-1041). Rothbard's multiple chapters on government intervention were eventually published as Rothbard (2009 ). See Rothbard (1970, pp. 1089-1144) for his analysis of various grants of monopolistic privilege. Rothbard also mentioned in this footnote that copyrights and patents would be discussed below, see Rothbard (1962, pp. 745-754) for his analysis on patents and copyrights.
(23) Editor's footnote: See Rothbard (1962, pp. 162-169, 176-185).
(24) That such was the original definition of monopoly in economics as well as law is demonstrated by the definition of the economist Arthur Latham Perry: "A monopoly, as the derivation of the word implies, is a restriction imposed by a government upon the sale of certain services" (Perry, 1892, p. 190). Still earlier, Adam Smith discussed monopoly in similar terms, and pointed out how monopolists may use the government privileges to restrict sales and raise selling prices; "Such enhancements of the market price may last as long as the regulations of police which give occasion to them" (Smith, 1937 , p. 62).
(25) Benham (1941, p. 233). On the rapid breakup of even a relatively successful cartel, see Fairchild et al. (1926, pp. 54-55). Also see Molinari (1904, pp. 192-195), Fay (1923, p. 41) and Fay (1912).
(26) Menger (1950, pp. 222-225).
(27) In many cases, fear of possible outside competition prevents any formation of a cartel, even when other conditions seem favorable. This is known as the influence of potential competition on would be cartelists.
(28) Editor's footnote: See footnote 22.
(29) Editor's footnote: See Rothbard (1962, pp. 79-94).
(30) Editor's footnote: See footnote 22.
(31) See Tucker (1926, pp. 248-257). For a defense of voluntary combinations from a juristic point of view, see Cooley (1878, pp. 270-271). Also see Flint (1902) and Croly (1909, pp. 359-365) for the economic defenses.
(32) Does our discussion imply, as Dorfman (1949, p. 247) has charged, that "whatever is, is right"? We cannot enter into a discussion of the relation of economics to ethics at this point, but we can state briefly that our answer, pertaining to the free market, is a qualified Yes. Specifically, our statement would be: Given the ends on the value scales of individuals, as revealed by their real actions, the maximum satisfaction of those ends for every person is achieved only on the free market. Whether individuals have the "proper" ends or not is another question entirely and cannot be decided by economics.
(33) See Stigler (1946, pp. 111-112) and Weiler (1952, p. 147ff).
(34) It is obvious that, for each of these combinations, more of both factors will produce at least as much as, and probably more than, the particular product. Thus, if (40X; 100Y) can produce 105 units of product, so can (45X; 105Y). This follows from the nature of scarce goods and scarce factors. The use of the latter combination to produce 105 units, however, would clearly be senseless. The latter, obviously more expensive combination, would either produce more and the surplus thrown away--which would be a ridiculous procedure; or else would produce just as much, in which case the factors would still be wasted and needless money expended. In describing constant outlay combinations, therefore, we assume that those combinations which are obviously more expensive for each product--using more of both factors--will be discarded at once. The only question then comes from the partial substitutability of one factor for another.
(35) The absurdity of the "technocratic fallacy" here becomes obvious. The technocratic charge is that business conducts "production for profit" instead of "production for use," and that the latter would prevail if engineers were granted dictatorial control over the productive system. It is clear from the discussion that technology cannot solve the production problem, and that therefore "production for (money) profit" is the only possible method of production beyond the very primitive level. Technology by itself could neither provide a guide to "maximizing production" nor to determining what should be produced. And it is also evident that business on the market takes account of the technological factor as much as is necessarily possible. It should also be clear that production for profit is necessarily production for "use." There is no reason to produce any good except to supply the demand for its use by consumers, whether the consumer is other persons or the producer himself (in the more primitive production situations). All production is for use.
(36) Editor's footnote: See below (pp. 535-37) for Rothbard's analysis when more than 2 factors are involved.
(37) On the vital importance of knowledge of "particular circumstances of time and place" see Hayek (1945, pp. 77-91).
(38) Editor's footnote: This analysis of factor pricing was planned to be in a later section, however it was never written because Rothbard changed his mind on the usefulness of using this approach. See Newman (2015) for more information.
(39) Editor's footnote: See Rothbard (1962, pp. 426-435).
(40) Editor's footnote: See Rothbard (1962, pp. 61-64, 68-70).
(41) Editor's footnote: See Rothbard (1962, pp. 367-451).
(42) Editor's footnote: See Rothbard (1962, pp. 367-451).
(43) Editor's footnote: See Rothbard (1962, p. 220).
(44) Editor's footnote: See Rothbard (1962, pp. 1-77).
(45) Editor's footnote: See Rothbard (1962, pp. 21-33).
(46) Editor's footnote: See Rothbard (1962, pp. 42-47).
(47) In Smith's particular case, marginal net income is only negative in the early and later stages. In some cases, there may well be points where the marginal net income is negative in between points where it is positive. In such cases, the point of negative marginal income is skipped over, and marginal outlay is assumed to be the difference between the two nearest points of positive marginal outlay. Thus, Jones' schedule of outlay and expected net income may be as follows:
Outlay Net Income Marginal Net Marginal Outlay Income 10 6 -- -- 20 10 4 10 30 8 40 14 4 20 50 19 5 10
(48) This statement will be surprising only to those who have been misled by the use of the differential calculus in economics. In calculus, the steps between points are treated as infinitely small, and therefore the marginal is thought to be the infinitesimal. In that case, "small" sized units will be recognized as approximations to some "ideal" marginal unit, but a "big" unit will not be thought of as marginal. Actually, the size of a marginal unit can be any amount, depending on the decision to be made. There is nothing ideal about infinitesimally small units, and they are not relevant to the real world of human action in any case, since action always deals with discrete steps.
(49) Editor's footnote: Strictly speaking, it must be greater than or equal to. An investor would still invest if the rate of return is equal to the rate of time preference, since his rate of time preference is the minimum he would need to earn in order to forgo the present money and invest. In the Evenly Rotating Economy, each investor only earns the interest rate, which is the societal rate of time preference.
(50) Editor's footnote: See footnote 1.
(51) Editor's footnote: Although not discussed in terms of "final supply curve," a similar diagram can be found in Rothbard (2008 , p. 27), which was not present in MES.
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|Author:||Rothbard, Murray N.|
|Publication:||The Quarterly Journal of Austrian Economics|
|Date:||Dec 22, 2015|
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