§3. The Two Kinds of Choice

The possessor of the mine, however, is not compelled thus to copy in his real income the mine's fluctuations of physical or natural income. He may counteract any fluctuations in his whole net income which may be caused, in the first instance, by the choice of income C rather than B, or A. Or, if he prefers, he may further exaggerate those fluctuations. In fact he may make the time shape of his income follow any model he likes. He may do this as described under the first approximation, by either borrowing or lending in suitable amounts and at suitable times along his income stream; or, more generally, by buying and selling income streams or parts of income streams so as to fashion the time shape of his own final net enjoyable income to suit himself.

He may, for instance, so far as time shape is concerned, achieve an even flow of income such as he could get from the farm use of his land. But he will not on that account choose this farm use in preference to the mining use; for the mining use has the larger present value, and the undesirable time shape of its income stream, under our Edition: current; Page: [136] present hypothesis, can be very easily remedied. For instance, he may lend some of the proceeds of its earlier output and in later years be paid back with interest.

Of course, his loan at five per cent does not alter in the least the figure $9110, the discounted value at five per cent of all the ten items of income ($2000, $1800, $1600, $1400, $1200, $1000, $800, $600, $400, $200); it simply adds to the later of these ten figures and subtracts from the earlier ones. The present value of the additions is necessarily equal to the present value of the subtractions; for the additions are the repayments, while the subtractions are the loans, and the present value of any loan equals that of its repayment.

We may totally separate, therefore, in thought the two choices made by the land owner, namely, (1) the choice of C (mining) in preference to A and B on the ground of greater present value, and, (2) the choice of time shape. If, as just supposed for illustration, the second sort of choice is that of an even income stream, it will be at the rate of $455.50 a year perpetually. That is to say, the mine owner will lend at interest $1544.50 the first year (all but $455.50 out of his original mining income of $2000); in the second year he will lend $1344.50 (all but $455.50 out of his original $1800); and so on. When the ninth year is reached, he ceases to lend further, for the mine then yields only $400. Instead, he then ekes this out by $55.50 returned from the previous loans. Likewise, in the tenth year he ekes out the $200 from mining by $255.50 returned from loans. Thereafter he will get nothing further from mining; but his loans will have accumulated a sinking fund (of $9110) to take the place of the mine and from this fund he can annually derive a 5 per cent revenue of $455.50. Edition: current; Page: [137] Consequently, the net result of the double choice (mining use and even time shape) is to increase the perpetual income of $450 offered by farming to a perpetual income of $455.50. This new perpetual annuity has exactly the same time shape as that derived from the farming use, but is larger by $5.50 per annum.

Incidentally it may be observed that this mining income, thus evened out by financing into a uniform $455.50 per year, exceeds the uniform farming income of $450 in exactly the same ratio as the present value ($9110) of the mining income exceeds that ($9000) of the farming income.

The following table exhibits the operations in detail:

TABLE 3 Mining and Farming Use Compared
	Owner Receives from Mine	Of which He Lends	Leaving for Real Income	As Against Which the Farming Use Would Have Yielded
1st year	$2000	$1544.50	$455.50	$450
2nd year	1800	1344.50	455.50	450
3rd year	1600	1144.50	455.50	450
4th year	1400	944.50	455.50	450
5th year	1200	744.50	455.50	450
6th year	1000	544.50	455.50	450
7th year	800	344.50	455.50	450
8th year	600	144.50	455.50	450
9th year	400	-55.50	455.50	450
10th year	200	-255.50	455.50	450
11th year	000	-455.50	455.50	450
etc.	etc.	etc.	etc.	etc.

Or, instead of wanting a perpetual even flowing income, the land owner may prefer as his model the time shape of the forestry income. He will not, however, on that account, choose this forestry use in preference to the mining use. He will simply lend at interest from the items of mining Edition: current; Page: [138] income all of his $2000 the first year, leaving no income for that year; likewise, all of his $1800 the second; all but $310 the third; all but $413 the fourth and all but $516 the fifth, and every succeeding year until the ninth year. He will then turn around and use $116 from his loans just described to eke out his $400 and bring up his income in that year to $516. The tenth mining item, $200, will likewise be brought up to $516 after which he will depend entirely on his outside loans at five per cent, deriving therefrom exactly $516 every year.

The result will then be a series of income items exactly similar to the B, or forestry, series but each item magnified in the ratio of $9110 to $8820, the present values respectively of C and B.

The following table exhibits these operations:

TABLE 4 Mining and Forestry Use Compared
	Owner Receives from Mine	Of Which He Lends	Leaving for Real Income	As Against Which the Forestry Use Would Have Yielded
1st year	$2000	$2000	$000	$000
2nd year	1800	1800	000	000
3rd year	1600	1290	310	300
4th year	1400	987	413	400
5th year	1200	684	516	500
6th year	1000	484	516	500
7th year	800	284	516	500
8th year	600	84	516	500
9th year	400	-116	516	500
10th year	200	-316	516	500
11th year	000	-516	516	500
etc.	etc.	etc.	etc.	etc.

Since, therefore, any time shape may be transformed into any other time shape, nobody need be deterred from selecting an income because of its time shape, but every Edition: current; Page: [139] one may choose an income exclusively on the basis of maximum present value. It will then happen that his income, as finally transformed, will be larger than it would have been if he had chosen some other use which afforded that same time shape.

All this is true under the assumption used throughout this chapter, namely, that after the most valuable option has been chosen, you can borrow and lend or buy and sell ad libitum and without risk. If this assumption is not true, if a person were cut off from a free loan market, the choice among optional income streams might or might not fall upon that one having the maximum present value, depending on the other circumstances involved, particularly his preferences as regards time shape.

Of course our assumption is a violent one, made in this second approximation, as in the first, in order to simplify the theory of interest. But already it must be evident that the principle involved has important practical applications. To a very considerable extent a modern business man, with access to loan markets, can choose from among the various options open to him on the basis of present value, and trust to loans or other financing to rectify any inconvenience in time shape.

The lines AB and A'B' in Chart 15 picture alternative income streams, of which the descending one, AB, has the larger present value. The choice will fall on AB, and if the individual prefers the time shape of A'B', he will then lend some of the early receipts from the income stream AB and receive back some of the latter, converting his income AB of undesirable shape into the income stream A''B'' which has the desired shape. This final income A''B'' combines the virtues of both the original alternative incomes AB and of A'B'; it possesses the superior shape of A'B' and the superior present value of AB. As compared with A'B' it has the same shape but a greater size.

Edition: current; Page: [140]

In practice, of course, the two steps are usually made simultaneously, not successively. In fact, usually the borrowing or financing often precedes the choice of option, thus reversing the order of presentation here adopted for convenience of exposition. So it would be quite as true to say that the loan, with the choice of option it makes possible, is made to secure an increased income as it is to say that the loan is made to even up the distorted income given by the option chosen.

But were it not for the possibility here assumed of modifying the time shape of his income stream by borrowing and lending, or buying and selling, the land owner would not feel free to choose the one from among the optional income streams which possesed the highest present Edition: current; Page: [141] value. He might find it advantageous, or even necessary, to take one of the others, being scarcely able to live if his property offered only distant income. If his capital were all in the form of growing young forests, and he could not mortgage the future in some way, he would have to starve or give up some of his holdings. In actual life we find such people—people who are said to be "land poor." In fact, we are all somewhat hampered in the choice of options by difficulties and risks both in the choice of options and in the financing it requires.

But we see that, in such a fluid world of options as we are here assuming, the capitalist reaches his final income through the co-operation of two kinds of choice of incomes which, under our assumptions, may be considered and treated as entirely separate. To repeat, these two kinds of choice are: first, the choice from among many possible income streams of that particular income stream which has the highest present value, and, secondly, the choice among different possible modifications of this income stream by borrowing and lending or buying and selling. The first is a selection from among income streams of differing market values, and the second, a selection from among income streams of the same market value.