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RENT UNDER THE ASSUMPTION OF 
EXHAUSTIBILITY 

SUMMARY 

The abstract character of the conception of land as the basis of rent, 
466. — Modification of the rent theory according to the possibility of 
preventing exhaustion, 469. — Effect of the assumption of exhaustion 
upon the economic intensity of utilization, 471. — Influence of the rate 
of interest on intensity of utilization, 474. — Influence of prices on 
intensity of utilization, 477. — Determination of the extensive margin, 
480. — The so-called royalty from mines forms a part of economic rent; 
Ricardo's discussion, 481. — Relation of royalties and rents to prices, 
485. — Incidence of taxation under the modified assumptions, 486. — 
Conclusion, 488. 

In the infancy of economic science rent was distin- 
guished from other forms of income as the periodic 
return from the use of land. And because land itself 
was regarded as one of the great agents in production, 
the existence of a peculiar type of income attributable 
to it appeared particularly suitable. 

This complete correlation between rent as an income 
and land as its source was not destined to continue. 
In the England of the classical school rent was usually 
a form of income which seemed to leave the basis of 
income unimpaired. Year after year the landowner 
might receive a substantial return without decreasing 
the capital value of his investment. It is not strange 
that the imperishability of the basis of rent came to be 
considered an essential characteristic of rent as a form 
of income. It became necessary, therefore, to define 
anew the basis of rent so that it might conform to this 
preconceived essential characteristic of rent itself. 
Accordingly Ricardo modified the economic concept of 
land as the source of a rent payment, and introduced the 

166 



THE ASSUMPTION OF EXHAUSTIBILITY 467 

assumption that rent is a payment for " the original and 
indestructible qualities of the soil." Later writers have 
interpreted Ricardo's criterion of land more rigorously 
than did Ricardo; and after passing through a process 
of gradual refinement, the Ricardian assumption has 
been reduced to its extreme form in Professor Commons' 
conclusion that the property of extension is the essential 
quality which distinguishes land from other kinds of 
goods and constitutes the basis of rent. 1 Thus the 
concept of land as the basis of rent has been gradually 
reduced to an abstraction. 

A practical man might well ask why it is necessary to 
develop an elaborate and peculiar doctrine to explain 
the value of the services of natural agents when by very 
assumption a large part of natural agents are excluded 
from the scope of the explanation. Why must rent be 
a payment for an original and indestructible property 
in order to be rent ? The question is a part of the long 
continued dispute as to the desirability of distinguishing 
land from capital, and rent from other forms of income. 
It is not necessary, however, in this connection, to 
wander so far afield. This question may be disregarded 
if it can be shown that indestructibility is not a charac- 
teristic which separates rent from other forms of income. 
The ground will then be clear for a reconsideration of 
the rent theory under the assumption of exhaustibility. 

In one sense there is no basis of rent which is im- 
perishable. For there is no conceivable basis which 
might not lose its utility, and therefore, its ability to 
yield a rent. A change in social demand may cause 
even the property of extension to lose the ability to 
yield a rent. However, it may be alleged with justice 
that the word indestructible has been employed by 

1 Professor Marshall seems inclined to a similar view, altho he has not come out 
unreservedly in its favor. Principles of Economics, 5th ed., bk. iv, chap, ii, sec. i. 



468 QUARTERLY JOURNAL OF ECONOMICS 

Ricardo and his followers in quite another sense: in 
the sense that the use for which rent is paid does not 
cause the impairment of the basis of rent. In this 
sense the basis of rent may be indestructible. The 
clearest illustration is urban land. In the case of agri- 
cultural land also it is frequently possible to isolate the 
income attributable to the indestructible properties. 
When the elements which are exhausted are economi- 
cally replaceable, the expense of replacement determines 
the value of the exhausted elements; and the remainder 
of the total surplus may be considered the rent of the 
inexhaustible properties. In many cases, however, it 
is not possible to isolate the returns assignable to the 
indestructible properties. In the case of mines, for in- 
tance, it is impossible to separate the value of the 
exhausted properties from the value of the inexhaustible 
properties. It is easy to determine how much the 
capital value of a coal mine is reduced by the process 
of use. But this capital value is nothing more than 
the present value of the surplus income from the mine 
during a period of time, — that is, the present value of 
the total rent which it will yield, — and this rent con- 
sists of two indistinguishable elements: the return for 
the coal used up and the return for the site value of 
that coal. A similar impossibility exists in the use of 
agricultural land when it is more profitable to exploit 
the soil than to conserve it : for instance, under frontier 
conditions. 

It seems clear, then, that under the Ricardian assump- 
tion rent may be referred to a small part only of the 
total category of natural objects. Moreover it is fre- 
quently impossible to distinguish rent from the income 
of the destructible elements. These facts appear to 
justify an attempt to alter the Ricardian statement of 
rent in such a way as to avoid the necessity of assum- 



THE ASSUMPTION OF EXHAUSTIBILITY 469 

ing that rent is paid only for the " indestructible quali- 
ties of the soil." 

Exhaustion consists either in a change of place or in 
a change of form. Coal may be removed from a mine 
and continue undestroyed. In this case the exhaustion 
is merely relative to a given locality. So far as the 
theory of rent is concerned, it is the exhaustion with 
reference to a particular locality that is of primary im- 
portance whether the valuable elements are absolutely 
consumed or merely removed to another location. 

This exhaustion with reference to location may be 
prevented by restoring other elements of the same kind 
in place of those removed in the process of utilization. 
Whether or not this is true depends to a large extent 
upon economic conditions. For instance, it is physi- 
cally possible to restore a forest, but such a restoration 
may not pay. It is even physically possible to restore 
mineral that has been removed from a mine, but it is 
hardly conceivable that it would ever be economical. 
Even in the case of agriculture, the experience of the 
world has abundantly proven that restoration is fre- 
quently unprofitable. In this sense exhaustion may 
be characteristic, under certain conditions, of nearly 
all natural objects. 

The relation of the assumption of exhaustion to the 
theory of rent largely depends upon the possibility of 
preventing exhaustion so far as a given locality is con- 
cerned. It is necessary, therefore, to consider several 
cases which may be presented schematically as follows : 

1. Prevention of exhaustion is economical. 

(a) May be effected without additional expense. 

(b) Requires additional expense. 

2. Prevention of exhaustion is not economical. 
When prevention requires no extra expense, the Ri- 

cardian theory is not invalidated by the assumption of 



470 QUARTERLY JOURNAL OF ECONOMICS 

exhaustion. The entire return attributable to land is 
a surplus which accrues so long as the conditions of 
demand and supply remain unchanged. Exhaustion 
occurs; but the process of restoration is merely inci- 
dental to the process of most profitable utilization. 
Likewise, the assumption that exhaustion is preventable, 
provided it is profitable to incur an extra expense for 
that purpose, does not seriously impair the Ricardian 
theory of rent. The extra expense either may be con- 
sidered a part of the expense incident to the process 
of production or may be charged against the land and 
deducted from its net return. In both cases the rent, 
after all deductions are made, will be the same. The 
difference is merely one of accounting. 

In those cases where the prevention of exhaustion is 
either impossible or unprofitable, a considerable read- 
justment of the rent doctrine is necessary if the assump- 
tion of inexhaustibility is to be avoided. 

Under the assumption of inexhaustibility land re- 
sembles labor in the sense that it perishes through 
non-use rather than through use. If it is capable of 
furnishing a valuable service year after year, the failure 
to utilize it in any year is the source of loss, just as labor 
suffers loss from unemployment. When, however, it 
is assumed that the benefits that may be derived from 
the natural object are exhaustible and non-replaceable, 
the point of view is altered. The owner of a valuable 
coal deposit, for instance, desires to derive the maximum 
benefit from the limited supply which he owns. If for 
any reason less benefit can be derived by immediate 
removal and sale of the coal than by waiting until some 
future time, it may be profitable to postpone utilization. 

The simplest condition that might produce this result 
is an expected alteration in the price of coal. If the 
price is rising and the prospect is that the rise will 



THE ASSUMPTION OF EXHAUSTIBILITY 471 

continue, the owner of the mine will find it to his 
interest to take out but little coal in the present. This 
is true because the resources at his disposal are limited. 
Obviously this motive would not exist if the basis of 
income were perpetual. Likewise a lowering of the 
prices of those factors which enter into the expenses of 
production will make profitable a postponement of re- 
moval. On the other hand, a decrease of prices of the 
product or an increase of the prices of the factors of 
expense, in so far as such changes are continuous or 
anticipated, will create motives for rapid utilization. 

Outside of mere price change, however, the owner of 
the mine will be moved by still more fundamental con- 
siderations. One of these considerations is diminishing 
productivity. 1 According to the Ricardian theory of 
rent the landowner will find it to his interest to add 
units of labor and capital to a given surface of land up 
to the point where the last unit applied just equals the 
product which might be derived from its employment 
on marginal land. In familiar phraseology, labor and 
capital are added up to the intensive margin of culti- 
vation. According to the theory, such a ratio between 
the factors of production will yield the maximum rental 
to the landowner, under the given conditions. The 
exhaustibility of the natural resource, however, dictates 
a different course. The owner of the mine may well 
hesitate to proceed beyond the point of maximum aver- 
age returns per unit of expense. 2 At this rate of removal 
the average net return per ton of coal is a maximum, 
since the average expense of removal per ton is a mini- 

1 This phrase is used to designate the decrease in product which results from the 
increase in the expenditure for the other factors of production applied to a given 
surface of land. 

2 In a strict productivity theory of distribution it would be necessary to continue 
the comparison of the units of labor and capital instead of substituting units of expense, 
since the latter assume the determination of the value of labor and capital. In the 
consideration of the policy of a single entrepreneur, however, it need not be seriously 
inaccurate to employ the more convenient and more easily illustrated idea of expense. 



472 



QUARTERLY JOURNAL OF ECONOMICS 



mum. The attempt to appropriate the coal more 
rapidly results in a diminishing product per unit of 
expense and, therefore, a diminishing average net return 
per ton of coal. Were the mine owner influenced by 
no other consideration, his interest would demand that 
no more coal be removed at any time than can be re- 
moved at a minimum average expense per ton. If he 
is willing to wait for the return from his coal, he can 
postpone for future removal all coal over and above 
that amount which can be removed at a minimum 
average expense per ton. 

The point may be illustrated by the accompanying 
table, which shows the results of removing various 
quantities of coal from a mine during a definite period 
of time — one year. It is assumed for convenience that 
each ton of coal is worth $1.00; so that the same 
figures represent both the quantity and the value of 
the product. 

TABLE I 

Variations in the Net Return in the Removal of Varying Quantities 
of Coal in a Given Period of Time 



Quantity 

of coal 

removed 

(tons) 


Value 

of coal 

removed 

(dollars) 


Expense 

of removal 

per 100 

tona 


Total 

net 

return 


Average 

net 
returns 

per 
100 tons 


Increase 
in expense 
due to the 
removal of 
eaoh add'l 

100 tons 


Net return of 

each additional 

100 tons after 

the point of 

maximum net 

returns per 

100 tons 


100 


100 


$120 


-$20 


-$20 






200 


200 


100 


00 


00 






300 


300 


80 


60 


20 






400 


400 


50 


200 


50 






500 


500 


52 


240 




$60 


$40 


600 


600 


55 


270 






70 


30 


700 


700 


59 


287 






83 


17 


800 


800 


64 


288 






99 


1 


900 


900 


68 


288 






100 





1000 


1000 


73 


270 










1100 


1100 


79 


231 











THE ASSUMPTION OF EXHAUSTIBILITY 473 

The figures in the table show that the minimum 
average expense per ton is achieved by taking out 400 
tons of coal during the year. If more than this amount 
is removed, each ton will yield a smaller net return than 
if its removal is postponed until it may be effected at 
the minimum expense. Were the mine an inexhaust- 
ible basis of income, there would be no necessity for 
solicitude on account of the fact that each ton yields 
less than a possible maximum. The interest of the 
owner would dictate the extraction of eight hundred 
tons of coal. At this point the value of an additional 
one hundred tons just equals the expense of its removal. 

It is necessary to turn aside for a moment to con- 
sider certain confusions which are involved in the con- 
cepts of diminishing productivity and diminishing 
returns as applied to mines. 

Some writers have denied that a mine is subject to 
the law of diminishing productivity. Altho admitting 
that the extension of mining to other fields as well as 
to lower depths may be subject to diminishing return, 
Professor Marshall appears to deny the diminishing 
productivity which results from an attempt to accel- 
erate the process of extraction by an increased appli- 
cation of the other factors of production to a given 
surface. He compares a mine to a reservoir. " The 
more nearly a reservoir is exhausted," he says, " the 
greater is the labor of pumping from it : but if one man 
could pump it out in ten days, ten men could pump 
it out in one day, and when empty, it would yield no 
more." 1 It is not denied that the physical possibility 
suggested by Marshall may occur in some cases. The 
probability, however, of an indefinite acceleration of the 
rate of removal without incurring an increased expense 

1 Principles of Economics, bk. iv, chap. iii t section 7. J. S. Mill expressed a similar 
opinion, but more guardedly, with respect to collieries and other such surface deposits, 
but not with respect to ordinary mines. Principles, bk. iii, chap, v, section 3. 



474 QUARTERLY JOURNAL OF ECONOMICS 

per unit of result appears to be very unlikely in ordi- 
nary circumstances. Even in the case of surface de- 
posits, such as those of the Mesabi Range, the attempt 
to remove the entire surface supply in a very short 
period would entail a much larger investment in fixed 
capital than would be necessary over a longer period. 
In the case of mines where the sinking of shafts is neces- 
sary, an increase of the rate of utilization must often 
mean the sinking of an increased number of shafts and 
the provision of a more elaborate equipment than would 
be required for a lengthier period of extraction. It 
appears fairly safe to assume that, as a general rule to 
which there may be certain exceptions, the law of 
diminishing productivity is applicable to mining as well 
as to agriculture. 

It must be clearly understood that the term diminish- 
ing productivity as employed above has been used in 
the sense in which Ricardo used it; that is, with regard 
to successive applications of labor and capital to a 
given surface of land. The conclusion that the owner 
of a mine may stop short of the point where the last 
unit of expenditure just equals its product constitutes 
an exception to the modern productivity theory only 
when the quantity of land is measured by surface. 
After the quantity of coal to be removed has been de- 
termined, the ordinary statement of the productivity 
theory is applicable. In the removal of that coal ex- 
penditures will be profitable so long as an additional 
outlay facilitates the process of removal to a sufficient 
extent to justify the expenditure. 

The influence of the rate of interest has thus far been 
disregarded. It is obvious, however, that the ten- 
dency for the owner of the mine to postpone for future 
removal all coal which would otherwise have to be 
removed at an increased average expense per ton is 



THE ASSUMPTION OF EXHAUSTIBILITY 



475 



counteracted by the fact that the present value of the 
return from future removal is lessened by the discount 
on the future. The net return from each ton removed 
in the present, even at an increased expense, may be 
greater than the present value of the same coal removed 
at minimum expense in the future. The basis of com- 
parison, of course, beyond the point of maximum aver- 
age net returns must be the net return from the removal 
of an additional quantity of coal (columns six and 
seven of table one), not the average net return. 

TABLE II 

Present Values of the Net Returns Derived from the Removal of Various 

Quantities of Coal at Different Future Periods with Interest at 

Ten Per Cent 



Present Value of 



No. 

Tons 



2d 
Year 



3d 
Year 



4th 

Year 



5th 
Year 



6th 
Year 



7th 
Year 



8th 
Year 



The maximum 
average net re- 
turn per 100 tona 

Net return of each 
additional 100 
tons 



400 



500 
600 
700 
800 
900 



$50 



$45.45 



$41.66 +,$38.46 + $35.71 +;$33.33 +$31.25 + 



$29.41 - 



36.36+ 33.33 + 30.76+! 28.57 + 

27.27+ 25.00 I 23.07+ 21.42 + 

15.45+ 14.16+ 13.07+ 12.14 + 

.90+ .83+ .76+ .71 + 





26.66 + 
20.00 
11.33 + 

.66 + 




25.00 
18.75 
10.62 + 
.62 + 




23.52 + 
17.64 + 
10.00 
.58 + 




Table II illustrates the theoretical method of deter- 
mining the rate of utilization as a resultant of the two 
antagonistic factors: diminishing productivity and the 
discount on the returns from future removal (assumed 
to be ten per cent). If the total quantity of coal to be 
removed under the assumed conditions is only twelve 
hundred tons, there is no reason for the mine owner to 
remove more than four hundred tons a year; for the 
present value of the net return of the last four hundred 
tons removed in the third year is $41.66, whereas the 
removal of an additional one hundred tons in the first 
year will yield a net return of only forty dollars. If 



476 QUARTERLY JOURNAL OF ECONOMICS 

the entire quantity of coal is 3,700 tons, the owner of 
the mine will find it desirable to remove six hundred 
tons in the present ; for the sixth hundred tons could not 
be removed at any time in the future so as to yield a 
greater net return than thirty dollars. If postponed 
until the eighth year, the present value of the net re- 
turn is only $29.41. 

In the theory thus far presented, certain conditions 
have been left out of account for the sake of simplicity. 
In the first place, it is assumed, with Ricardo, that the 
landlord has the option of leasing the land to others or 
of using it himself. This assumes, of course, that 
the landlord will so adjust the contract in case of a 
lease that the mine will yield the maximum rent which 
might be derived from his own utilization. The limi- 
tations of this assumption need not be further con- 
sidered here. 

In the second place, the ideal rate of utilization illus- 
trated above implies operation on a large scale in the 
first year, with a decline in the magnitude of operation 
in successive years. It will be necessary to employ a 
larger amount of fixed capital in the first year than in 
successive years. A part of this fixed capital provided 
for the larger scale of operation in the first year will be 
wasted. It will, therefore, pay for the entrepreneur 
to adjust his rate of removal so that the rate of utiliza- 
tion will be more nearly uniform. This rate will be 
somewhere between the two extremes represented by the 
maximum rate of utilization in the first year and the 
minimum utilization of the last year. A third modifi- 
cation is made necessary by the fact that in the above 
consideration of the economic rate of utilization sub- 
stantially constant returns were assumed. No allow- 
ance was made for the possibility that the removal of 
coal in the first year may change entirely the condi- 



THE ASSUMPTION OF BXHAUSTIBILITY 477 

tions of removal in the second year. The removal of 
the 400 tons may have exposed coal which is not only 
of a better quality but also capable of being removed at 
less expense per ton than the coal removed during the 
first year. On the other hand, the deposit made 
accessible by the removal of the 400 tons may be of 
an inferior quality and so situated that the average 
expense of removal per ton will be greater than for 
removal in the first year. This may be true because 
of greater depth or special difficulties encountered, such 
as water or gas or the thinness of the vein of coal. In 
short, mining is subject either to the law of increasing 
returns or to the law of diminishing returns or to both 
tendencies alternately according to conditions. 1 

The assumption of decreasing returns would not affect 
the above conclusions. The owner of the mine would 
have no motive to accelerate the rate of removal of his 
coal simply to get access to the less profitable coal 
at lower depths. Under the assumption of increas- 
ing returns, however, a more rapid removal in the 
present might be justified by the fact that the larger 
net returns from the mine are in the future and are 
subject to the discount. With this modification the 
principles of utilization as above outlined will continue 
applicable. 

The influence of differences in the price of the product 
has thus far been disregarded. In an earlier part of 
this paper the effect of changing prices was discussed. 
The influence of higher or lower price levels must now 
be considered. 

It should be noted that, were there no discount on 
the future, a higher price level would not necessarily 
change the economic rate of utilization. It might still 

1 Ricardo believed the law of diminishing return is normally characteristic of mining. 
Principles of Political Economy, chap. iii. On the possibility of increasing returns, cf . 
Taussig, Principles of Economics, vol. ii, p. 95. 



478 



QUARTERLY JOURNAL OF ECONOMICS 



be economical to extract the coal at the point of maxi- 
mum average net returns per unit of coal, as determined 
by the physical conditions of appropriation and the 
expense of the other factors. 



TABLE III 

Variations in the Net Return of Varying Quantities of Coal in a 
Given Period of Time (Price of Coal $2.00 Per Ton) 













Increase 




Quantity 
of coal 

removed 
(tons) 


Value 
of coal 
removed 


Average 
expense 
of remov- 
al per 100 
tons 


Total 

net 

return 


Average 

net 
returns 
per 100 

tons 


in expense 
due to re- 
moval of 
each add'l 

100 tons 
beyond the 

point of 
maximum 

av. net 

returns 


Net return of 
each additional 
100 tons beyond 

the point of 
maximum av. 

net returns 


100 


$200 


$120 


$80 


$80 






200 


400 


100 


200 


100 






300 


600 


80 


360 


120 






400 


800 


50 


600 


150 






500 


1000 


52 


740 


148 


60 


140 


600 


1200 


55 


870 


145 


71 


130 


700 


1400 


59 


987 


141 


83 


117 


800 


1600 


64 


1088 


136 


99 


101 


900 


1800 


68 


1188 


132 


100 


100 


1000 


2000 


73 


1270 


127 


118 


82 


1100 


2200 


79 


1331 


121 


139 


61 


1200 


2400 


87 


1356 


113 


175 


25 


1300 


2600 


96 


1352 


104 


204 


-4 


1400 


2800 


106 


1316 


94 


236 


-38 



This point is illustrated in Table III, which is similar 
to Table I, except that the price of coal is doubled. The 
difference between the average net returns per hundred 
tons remains the same. The effect of the rise of price 
is merely to add one hundred dollars to the net return 
per hundred tons in every case no matter what the 
quantity removed. The point of maximum net returns 
is not changed. 



THE ASSUMPTION OF EXHAUSTIBILITY 



479 



Altho a higher level of prices does not necessarily 
compel a change in the rate of utilization when there is 
no discount on the future, such a discount will affect 
the relative merits of present and future removal, and, 
therefore, the rate of utilization. For under the higher 
prices the magnitude of the net return per hundred 
tons, both in present and in future, is increased by the 
same amount. Because of the increase in the amount 
of the net return the discount of the net return for a 
future use will result in a larger deduction in arriving 
at present value than before the rise of price. Conse- 
quently the future use will be relatively less desirable 
than its competing present use. 



TABLE IV 

Present Values of the Net Returns derived from the Removal of Various 

Quantities of Coal at Different Periods with Interest at Ten Per Cent 

(Price of Coal $2.00 Per Ton) 



Present Value of 


No. 
Tons 


1st 
Yr. 


2d 
Year 


3d 
Year 


4th 

Year 


5th 
Year 


6th 
Year 


7th 
Year 


8th 
Year 


The maximum 
average net re- 


400 

500 

600 

700 

800 

900 

1000 

1100 

1200 


$150 

140 

130 

117 

101 

100 

82 

61 

25 


$136.36 + 

127.27 + 
118.18 + 
106.36 + 


$125.00 

116.66 + 
108.33 + 


$115.38 + 

107.69 + 
100.00 


$107.14 + 
100.00 


$100.00 ; 


$93.75 

87.50 
81.25 
73.12 + 
63.12 + 
62.50 
51.25 
38.12 + 
15.62 + 


$88.23 + 


turns per 100 tons 
Present value of 


! 93.33 + 
86.66 + 
78.00 
67.33 + 
66.66 + 
54.66 + 
40.66 + 
16.66 + 


82.35 + 


the net return 


! 92.85 + 
83.57 + 
72.14 + 
71.42 + 
58.57 + 
43.52 + 
17.85 + 


76.46 + 


from each addi- 


' 97.50 + 
84.16 + 
83.33 + 
68.33 + 
50.83 + 
20.83 + 


90.00 
77.69 + 
76.92 + 
63.07 + 
46.92 + 
19.23 + 


68.82 + 


tional 100 tons.. 


: 91.81 + 

: 90.90 + 

74.54 + 

55.45 + 

22.72 + 


59.41 + 

58.82 + 
48.23 + 

35.88 + 
14.70 + 



This point is illustrated in Table IV, in which all the 
conditions are the same as in Table II except that the 
price of the product is doubled. At the original price 
of one dollar per ton the difference in the net return of 
the fifth one hundred tons in the present, as compared 
with the present value of the net return per hundred 
tons when four hundred tons is removed one year from 
the present, amounts to $5.45 in favor of the latter. 



480 QUARTERLY JOURNAL OF ECONOMICS 

When the price of coal is doubled, this difference dis- 
appears and the balance is in favor of the fifth hundred 
tons removed in the present. For the net return in 
the latter case amounts to $140, while the present value 
of the net return per hundred tons derived from the 
removal of four hundred tons in the second year is 
only $136.36. If the mine owner has 3,700 tons of 
coal subject to the assumed conditions of Table IV, 
he will derive maximum returns from the entire quan- 
tity by adjusting his margin of utilization as indicated 
by the dotted line in Table IV, which shows a more 
rapid rate of removal than under the lower price. (See 
Table II.) 

Altho the influence of an increase of price is in 
the same direction as under the Ricardian theory, the 
intensive margin cannot fall so far that the product 
and expense on the margin just coincide, as under the 
Ricardian theory. For, however long the period of 
utilization may be and however large the discount on 
the future may become, the net return from the removal 
of coal at the point of time most remote in the future 
can never be reduced to zero. Hence, in theory, the 
competition of this surplus over expense which is mar- 
ginal in time must always be great enough to prevent 
the coincidence of product and expense on the intensive 
margin of present utilization. 

If we turn from the consideration of the conditions 
which determine the intensive margin of utilization to 
those which determine the extensive margin, the altera- 
tion in assumption with regard to exhaustibility does 
not greatly change the Ricardian formula. It is likely 
that an extension of the margin will occur whenever 
such an extension is sufficient to repay the expense of 
removal. Altho there will be a surplus on the in- 
tensive margin, there will be no surplus on the extensive 



THE ASSUMPTION OF EXHAUSTIBILITY 481 

margin. It has been suggested that while the exten- 
sive margin yields no rent, it may yield a royalty : that 
is, a return to cover the value of the mineral extracted. 1 
It will be apparent from the above analysis that this 
cannot be true theoretically. The value of the coal is 
due to the fact that it yields a net return above the 
expense of extracting it: that is, the value is a result 
of the rent. In order that the coal in situ may have a 
value, the conditions of utilization must be such that 
the coal may be extracted and sold in the present at an 
expense sufficiently low to yield a surplus. For, 
except when the mine is subject to increasing returns 
as lower depths are reached, or unless prices are ex- 
pected to change, it is impossible that future uses may 
yield a surplus unless conditions are such as to yield 
a surplus in the present. Hence the coal in the mine 
on the margin which yields no rent, except in the cases 
above-noted, has no value which could be made the 
basis of a charge for depreciation. In the case of ex- 
haustible natural objects above the margin of utiliza- 
tion the Ricardian doctrine of rent is characterized by 
much confusion. Ricardo first sought to rule out all 
payments for minerals and timber from the category of 
rent. In the chapter " On Rent " he criticizes Adam 
Smith very severely for the assertion that the demand 
for timber and its consequent high price in the more 
southern countries of Europe, caused a rent to be paid 
for forests in Norway, which could before afford no 

1 Notably, Professor Sorley in an article on mine royalties, published in the Journal 
of the Royal Statistical Society for'March, 1889; Marshall, A., Principles of Economics, 
5th ed., p. 439, note; and Flui, A. W., Economic Principles, pp. 108-109. In his 
recently published Principles of Economics, Professor Taussig questions the assump- 
tion that marginal mines would bear a royalty charge even tho yielding no rent surplus. 
Professor Taussig does not attempt to prove his point. Professor Sorley bases hia 
position upon the argument that a landowner of a mineral deposit which is marginal 
must have some inducement to compensate for the necessity of incurring the bad 
repute of his neighbors on account of the fact that a mine is an unpopular institution. 
This is a question of fact which need not be discussed here. 



482 QUARTERLY JOURNAL OF ECONOMICS 

rent. " Is it not, however, evident," says Ricardo, 
" that the person who paid what he thus calls rent, 
paid it in consideration of the valuable commodity 
which was then standing on the land, and that he actu- 
ally repaid himself with a profit, by the sale of the 
timber ? ... in the case stated by Adam Smith, the 
compensation was paid for the liberty of removing and 
selling the timber, and not for the liberty of growing it. 
He speaks also of the rent of coal mines, and of stone 
quarries, to which the same observation applies — 
that the compensation given for the mine or quarry is 
paid for the value of the coal or stone which can be 
removed from them, and has no connection with the 
original and indestructible powers of the land." l 

Strangely enough, in the next chapter Ricardo de- 
velops a new doctrine. He appears to disregard 
entirely his previous positive denial that the return to 
mines or forests is to be classed as rent. His treatment 
of the subject is a mere extension of his previous dis- 
cussion of agricultural rent without modification. 
" Mines," he says, " as well as land, generally pay a 
rent to their owner, and this rent, as well as the rent 
of land, is the effect, and never the cause of the high 
value of their produce. . . . The metal produced 
from the poorest mine that is worked must at least 
have an exchangeable value, not only sufficient to pro- 
cure all the clothes, food, and other necessaries con- 
sumed by those employed in working it, and bringing 
the produce to market, but also to afford the common 
and ordinary profits to him who advances the stock 
necessary to carry on the undertaking. The return 
for capital paying no rent would regulate the rent of 
all the other more productive mines. This mine is 
supposed to yield the usual profits of stock. All that 

1 Principles, cbap. ii, section 24. 



THE ASSUMPTION OF EXHAUSTIBILITY 483 

the other mines produce more than this will necessarily 
be paid to the owners for rent." 1 Nowhere in his 
book does Ricardo make an attempt to explain the 
apparent contradiction. In fact, the law of mine rent 
as stated in chapter three is several times reasserted and 
illustrated, especially the point that the entire net 
return from a mine is rent. 2 

Later writers have tried to harmonize the two antag- 
onistic principles developed by Ricardo, by combining 
them. It has become customary to recognize that the 
return imputed to a mineral deposit consists of two 
parts: a rent and a royalty. This plausible doctrine 
has been maintained by so many writers that it is de- 
sirable to devote considerable attention to it. 

The essential fallacy of this explanation of mine rent 
lies in the fact that the so-called royalty is nothing 
more than a depreciation charge which results from 
capitalizing a terminable series of incomes. A little 
attention to Bohm-Bawerk's illustration of the nature 
of the income from durable goods would have shown 
clearly that the current distinction between rent and 
royalty is not sound. Bohm-Bawerk has shown that 
when the succession of incomes is regarded as inter- 
minable, the present value of the most remote in time 
is nothing. The income in the present is all regarded 
as interest. When, however, the successive prospective 
incomes are terminable, the present income is divided 
into two parts: that is, from the entire net income in 
the present is subtracted the present value of that por- 
tion of the income whose accrual is most remote in time. 
The remainder is interest; the subtrahend is a depre- 
ciation fund, or charge. 3 It is this depreciation fund 

1 Principles, chap, iii, section 32. 

1 Notably in the discussion of the rent of woodland, chap, xii; in the chapter en- 
titled " Taxes on Gold " ; and in chap. xxiv. 

• The Positive Theory of Capital (Smart Translation), bk. vi, chaps, vii and viii. 



484 QUARTERLY JOURNAL OF ECONOMICS 

which has been called a royalty. In short, the royalty 
is the product of the process of capitalization. The 
business man, unconcerned with socially valid distinc- 
tions between rent and interest but desirous of keeping 
intact his fund of capital, charges to depreciation the 
amount by which the total value of the mine or farm 
has been reduced by utilization. 1 

To consider that the amount which is left in the pres- 
ent after the subtraction of the amount of depreciation 
is determined by the law of rent is to confuse the 
process of capitalization of a rent surplus with the 
conditions which determine rent itself. This amount 
which is regarded as the economic rent of the mine, as 
distinguished from the so-called royalty, is obviously a 
quantity which varies with every change in the rate of 
interest and with the degree of remoteness of exhausti- 
bility. The true rent, indeed, in the present is not 
simply this amount; rather it is the whole surplus as 
determined by the difference between the gross product 
in the present and the expenses of production. 2 It 
may be said that there can be no objection to calling 
this depreciation fund a royalty. This is true. The 
objection lies in applying the term rent to the residuum 
after the subtraction of the so-called royalty from the 
total net return. For the actual amount of this so- 
called rent is not determined in amount by the condi- 
tions which give rise to a surplus over the expense of 
utilizing natural agents. It is determined mainly by 

1 Mr. J. A. Finlay, a New York mining expert employed by the State of Michigan 
to appraise the mines of the state for purposes of taxation, has recently used this method 
of capitalization in the valuation of Michigan mines. An account of the appraisal ia 
published by Mr. Finlay in the Engineering and Mining Journal for September 9, 1911, 
p. 488. 

« In the article on mine royalties already referred to, Professor Sorley recognises 
the identity of rent and royalty so far as mines above the margin are concerned. 
As already pointed out, he attempts to show the existence of the royalty in the case 
of marginal mines. Professor Sorley does not attempt to explain the nature of this 
royalty. 



THE ASSUMPTION OF EXHAUSTIBILITY 485 

the process of capitalizing such a surplus. Only in- 
directly is the surplus responsible for the size of this 
pseudo-rent, as the whole may limit the size of its parts. 
Inasmuch as the removal of all coal in the present, 
beyond the point of maximum net returns per unit of 
coal, is subject to the competition of future uses; it 
might be considered that the value of all coal extracted 
beyond this point is subject to an opportunity cost 
measured by the present value of the net return which 
would be derived from the coal if extraction were post- 
poned until the future. Even this opportunity cost 
does not represent a value of coal in addition to the 
rent surplus; for the entire surplus in the present is 
none the less a real surplus merely because a smaller 
return in the future could be derived from the same 
coal by postponement of utilization. 

The relation of mine rents to price has naturally been 
the subject of much confusion. Generally speaking, 
modern writers who have given attention to this sub- 
ject have taken the position that royalties " enter into 
price " although the so-called rent of the mine does not. 
This position is maintained on the ground that the 
royalty is a capital fund which must be remunerated in 
order to induce the owner of the mine to employ it 
productively. 

It is now generally recognized that the old idea that 
rent does not " enter into price " does not imply that 
rent may not be a determinant of relative prices. The 
question, then, of the relation of royalties and of rents 
amounts to this: are they forms of income which are 
disposable ? If they were partly or entirely taken by 
taxation, would the supply of land be decreased ? 

In this sense a royalty may " enter into price " under 
certain conditions, and under other conditions it may 
not enter into price; but in no case is its relation to 



486 QUARTERLY JOURNAL OF ECONOMICS 

price attributable to the fact that the royalty is capital 
which must be replaced. The entire pseudo-rent and 
nearly all the royalty might be taken without causing 
the mine to fall below the margin of utilization. For, 
since the royalty itself is a part of the total surplus, 
the owner would be foolish to abandon his mine so long 
as any surplus is obtainable. What will happen is 
that the residuum of the old royalty will be recapitalized 
and divided into a new royalty, and a new rent. The 
actual amount of each will be determined by the condi- 
tions of capitalization. 

It does not follow, however, that a tax on the mine 
will in no way affect the supply of the product placed 
on the market in the present. Such a tax may disturb 
the relation between present and future. It has been 
shown that the tendency is for the rate of utilization 
to be so adjusted that the present value of the marginal 
uses in present and in future are just in balance. Much, 
therefore, will depend on the manner in which the tax 
is applied. 

An annual tax on the value of the mine, provided the 
tax is expected to be permanent, will increase the ten- 
dency for the mine owner to remove the coal in the 
present rather than in the future. For, since the mine 
must pay the tax as long as it is operated, the tax may 
be evaded by increasing the rapidity of exhaustion. 
This will be true even if all of the so-called rent and a 
part of the royalty is taken by the tax. Far from pre- 
venting the mine from being utilized, it will actually 
increase the amount of coal placed on the market; 
and if demand is constant, will probably lower price. 

On the other hand a tax upon the annual surplus 
from the operation of the mine, even if it is so heavy 
as to take more than the pseudo-rent, will not create 
an inducement for the mine owner to alter the adjust- 



THE ASSUMPTION OF EXHAUSTIBILITY 487 

ment of utilization between present and future. If 
the rate of extraction is already adjusted upon the most 
profitable basis, nothing will be gained by postponing 
until the future, coal that will yield a greater net re- 
turn in the present. For the tax can be avoided only 
to the extent that the surplus return is reduced, and 
the loss in surplus must always be greater than the 
saving in the tax. The effect of such a tax is to take 
a certain share of each dollar of surplus whenever it 
appears, whether in the present or future. The tax 
can only be evaded by losing that part of the dollar 
which remains. This is true on the assumption that 
the tax is regarded as permanent. Of course, in any 
case, if the tax is regarded as merely temporary, the 
tendency will be to transfer as much as possible of the 
process of production to the future. 

In the case of a tonnage tax consisting of a fixed 
amount per ton, the balance of motive between present 
and future will probably be affected in such a way as 
to encourage a slower rate of utilization, and the post- 
ponement of a greater amount of coal for future extrac- 
tion. If, previous to the levying of the tax, the marginal 
net return from coal to be extracted in the present is 
in equal balance with the present value of the marginal 
net return from future uses, the tax will reduce the 
net return of a given quantity of coal which is on the 
margin of utilization in the future less than it will 
reduce the net return in the present. This is true 
simply because the future tax is discounted. For in- 
stance, suppose that the marginal present use yields a 
net return per ton of one dollar while a competitive 
future use twenty years from the present will yield a 
net return of two dollars per ton, the present worth 
of which is one dollar (assuming a discount at five per 
cent). A tax of ten cents per ton will leave the net 



488 QUARTERLY JOURNAL OF ECONOMICS 

returns of present and future ninety cents and one 
dollar ninety cents respectively. The present value 
of the future coal, however, is ninety-five cents instead 
of ninety cents, indicating the probability that a lower 
rate of utilization will be adopted. 

The consideration of the incidence of taxes on mines 
makes clear the fact that the royalty is not a necessary 
part of supply price. The entire rent and part of the 
royalty may be taken without affecting supply provided 
it is done in such a manner that the relation between 
the net returns from present and future production are 
not disturbed. 

It will now be apparent that of the two solutions 
which Ricardo applied to the problem, the idea that 
the rent of a mine or forest comprises the entire sur- 
plus above the expenses of production is the more 
nearly correct explanation. At the same time, Ricardo 
was not justified in extending his theory of rent to 
exhaustible natural agents without modification, espe- 
cially when the rent-bearer is exhaustible and non- 
restorable. For the location of the internal margin of 
utilization is determined by the competition of present 
and future uses rather than by the coincidence between 
product and expense. Consequently the rate of in- 
terest exercises an important influence in determining 
the location of the internal margin. On the other hand, 
the price level of the product has substantially the same 
influence upon the rate of utilization as under the Ricar- 
dian assumptions. Moreover, there is no alteration in 
the method of determining the extensive margin; altho, 
when the comparison is between surfaces, the intensive 
margin does not coincide with the extensive margin. 

These modifications do not necessarily nullify the 
conventional statement that rent is the difference 
between the product of a given amount of labor and 



THE ASSUMPTION OF EXHAUSTIBILITY 489 

capital applied to good land in the most profitable way 
and the product of an equal amount of labor and capital 
applied to marginal land. It is only necessary to give a 
special interpretation, as above, to the phrase " in the 
most profitable way." However, the traditional division 
of the net return from exhaustible natural resources 
into a rent and a royalty is justified only as a method 
of capitalization. The real economic rent of such 
resources comprises the entire net return from the rent- 
bearer, including the so-called royalty. 

Lewis Cecil Gray. 

University op Saskatchewan.