Praxeological Time Preference and Interest:
Ludwig von Mises's Contribution to Interest Theory
J. Patrick Gunning
[28 May 1998]
Professor of
Economics and Finance / College of Commerce and Economics / Sultan
Qaboos University || P.O.Box 20, Al-khod, SQU 123, Sultanate of
Oman || Fax (968) 514043 || Phone (968) 515822 || Home (968)
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Gunning |
Outline
Praxeological time preference, as applied to economics, refers to
the idea that individuals acting in the consumer role distinguish
between actions on the basis of whether they expect the effects to
be felt sooner or later. This concept, which was developed by Ludwig
von Mises, has been confused by neo-Austrians with the idea of positive
time preference. Positive time preference refers to the idea that
some set of goods, money, or utility is always preferred
in the present to the same set in the future. Neo-Austrians have
mistakenly asserted that Mises subscribed to the latter idea.
The main application of these concepts is in explaining market
rates of interest. Whereas Mises deduced the positive rate of
interest from praxeological time preference, neo-Austrians have
deduced it from the assumption of a positive time preference.
This paper has three aims. First, it shows that Mises did not
subscribe to the positive time preference view. Part one defines
praxeological time preference as it was presented by Mises and it
describes positive time preference as expressed in a recent paper by
Peter Lewin that was critical of Mises. Part two assesses Lewin's
interpretation of Mises. The second aim is to show how the notion of
positive time preference as a foundation for a positive interest
rate has evolved in the neo-Austrian literature. This is done in
part three. The third aim, which comprises part four, is to expand
on Mises's argument by presenting the basic assumptions that are
necessary to deduce a positive rate of interest under the conditions
of the pure market economy. A brief conclusion is presented in part
five.
1. Praxeological vs. Positive Time Preference
To illustrate the distinction between positive time preference and
praxeological time preference, consider Lewin's discussion. He is
concerned with the former concept, although he uses several terms to
refer to it. First he defines time preference as follows.
...$100 today is not valued the same as
$100 a year from now. They are economically different goods. In
terms of the consumer's subjective preference ranking the marginal
utility of $100 today is greater than the marginal utility today
of $100 a year from now. This is time preference whose
expression is Interest.(Lewin 1997: 144)
Next after citing a passage (discussed below) which he associates
with Mises's definition of time preference, he writes that Mises "purports
to prove praxeologically the necessity of positive time
preference."(Lewin 147: emphasis added) Finally, he
defines the theorem of time preference as the theorem "that
time preference for the present must exist."(148) For
Lewin the three of these seem equivalent. Time preference means the
theorem of time preference, which maintains that there is positive
time preference, which implies time preference for the present. To
avoid the confusion that might arise from using these different
terms, in the following discussion I use the term positive time
preference to represent the theorem that Lewin claims Mises
held. I take it that the theorem is illustrated by the passage
quoted above.
As distinct from this, I use the term praxeological time
preference to refer to the simple notion that individual
preference takes account of time. This is the notion that no normal
human being would (1) postpone all of his want satisfaction to the
indefinite future nor (2) if he could, take all of his potential
want satisfaction in the present. His preferences take account of
the time at which he expects his wants to be satisfied. The next
step in the paper is to more fully describe this idea, as Mises
presented it.
The fundamental assumption that Mises made was that the choices of
acting man "regarding the removal of future uneasiness are
directed by the categories of sooner and later."(Mises
1966: 483) "Time preference is a categorial requisite of human
action."(ibid.: 484)
Mises demonstrated praxeological time preference in two ways. In
the first, he adopted the role of the consumer-saver. He wrote: "He
who consumes a nonperishable good instead of postponing consumption
for an indefinite later moment thereby reveals a higher valuation of
present satisfaction as compared with later satisfaction."(ibid.:
484). In the second, he adopted the role of the capitalist-investor
of money. "Those contesting the universal validity of time
preference fail to explain why a man does not always
invest a sum of 100 dollars available today, although these 100
dollars would increase to 104 dollars within a year's time.(ibid.:
486, emphasis added) The fact that a "capitalist"
sometimes chooses not to invest some of his money
demonstrates time preference. Note that Mises did not present this
as a proof of time preference, only as a demonstration.
Thus, Mises's argument went something like this. No one would
postpone all of his consumption to the indefinite future. Therefore
every individual must exhibit time preference, meaning that "[h]is
choices regarding the removal of future uneasiness are directed by
the categories of sooner and later."(Mises
1966: 483) Moreover, a person must prefer to receive satisfaction in
the near future to satisfaction in the distant future. If he was
indifferent as to when he received satisfaction, we would have no
reason to suppose that he would consume in the near future and, if
his time preference does not change, in the distant future either.
Indifference, which Mises interpreted to mean "in the absence
of time preference,' implies that an individual would be willing to
postpone all his satisfaction to the indefinite future.(1)
2. On Lewin's Interpretation of Mises
It seems unlikely that Mises would have been misinterpreted if he
had presented his argument more clearly. In fact, Mises does make
statements that make it appear like he might have held the stronger
theorem of positive time preference. Lewin concludes that Mises
believed that he had proved "praxeologically the necessity of
positive time preference" on the basis of the following
quotation:
Time preference is a categorial
requisite of human action. No mode of action can be thought of in
which satisfaction within a nearer period of the future is not --
other things being equal -- preferred to that in a later period. The
very act of gratifying a desire implies that gratification at the
present instant is preferred to that at a later instant. He who
consumes a nonperishable good instead of postponing consumption for
an indefinite later moment thereby reveals a higher valuation of
present satisfaction as compared with later satisfaction. If he were
not to prefer satisfaction in the nearer period of the future to
that in a remoter period, he would never consume and so satisfy
wants. He would always accumulate, he would never consume and enjoy.
He would not consume today, but he would not consume tomorrow
either, as the morrow would confront him with the same alternative.
Not only the first step toward
want-satisfaction but also any further step is guided by time
preference. Once the desire a to which the scale of values
assigns the rank 1 is satisfied, one must choose between the desire
b to which the rank 2 is assigned and c that
desire of tomorrow to which -- in the absence of time
preference -- the rank 1 would have been assigned. If b
is preferred to c, the choice clearly involves time
preference. Purposive striving after want-satisfaction must be
guided by a preference for satisfaction in the nearer future over
that in a remoter future.(Mises 1966: 484; Lewin 146-7)
I examine each paragraph in turn.
In the first paragraph, the second sentence makes the apparently
very strong and contestable assertion: "No mode of action can
be thought of in which satisfaction within a nearer period of the
future is not -- other things being equal -- preferred to that in a
later period." Lifted from its context, this appears to be the
theorem of positive time preference. However, since nothing else in
the paragraph supports this interpretation, one ought to examine the
sentence carefully. Upon closer examination, the sentence in
question contains the phrase "within a nearer period."
In other words, Mises seems to be referring to some nearer
period. The idea Mises wants to present seems to be best captured by
the third sentence. This sentence does not imply positive time
preference in the usual sense. And it seems fully consistent with
the second sentence. The only point that Mises seems to be making
here is that to assume that an individual is indifferent to the time
at which satisfaction will be felt is tantamount to assuming that he
is not an actor. Thus the study of action implies the study of time
preference.
Now turn to the second paragraph. It ends with the apparently
strong statement that action is guided by a preference for near
future satisfaction over remoter satisfaction. Consider, in
addition, the following two sentences at the end of the introductory
paragraph of the section from which Lewin took his quote: "...Satisfaction
of a want in the nearer future is, other things equal, preferred to
that in the farther distant future. Present goods are more valuable
than future goods."(483) However, the introductory sentences of
this paragraph are: "...[A]cting man does not appraise time
periods merely with regard to their dimension. His choices regarding
the removal of future uneasiness are directed by the categories
sooner or later." Moreover, consider the way that the section
ends.
The last part of the section discusses what Mises takes to be the
customary way of expressing time preference. He begins by writing
that "[i]t is customary to express the essence of the
time-preference theory by saying that there prevails a preference
for present over future goods." But he ends by discussing the
case of the miser.
The case of the miser does not
contradict the universal validity of time preference. The miser,
too, in spending some of his means for a scanty livelihood, prefers
some amount of satisfaction in the nearer future to that in the
remoter future.(ibid.: 490)
One may object that this customary means of expression obscures
the issue. However, one would be hard-pressed to maintain that Mises
subscribed to the idea of positive time preference.
3. The Evolution of Misinterpretation
Lewin's claim that Mises held the positive theory of time
preference comes at the end of a series of similar claims in the
literature of Austrian economics. All of the claims were concerned
with the problem of explaining interest. The aim of this section is
to describe this literature as it pertains to the point in question.
The confusion seems to have started with an apparently innocuous
statement by Israel Kirzner about Mises's theory.(2)
Israel Kirzner
After saying that Mises never published his own special study of
the theory of interest, Israel Kirzner says (among many other
things):
Interest is not the specific income
derived from using capital goods; nor is it 'the price paid for the
services of capital.' Instead, interest expresses the universal ("categorial")
phenomenon of time preference and will therefore inevitably emerge
also in a pure exchange economy without production."(Kirzner
1976: 53, referring to Mises 1966: 524, 526)
So far as I know Mises did not mention a pure exchange economy. On
the pages to which Kirzner refers, he discussed interest in the
evenly rotating economy; but Kirzner cannot legitimately be
referring to this, since Mises defined the evenly rotating economy
as containing capital goods and simulated production.(3)
In any case, Kirzner was correct to say that interest would emerge
in a pure exchange economy due to praxeological time preference, as
will be shown below.(4)
Laurence Moss
Now read Laurence Moss's description of the same issue:
According to Ludwig von Mises, this
preference for earlier rather than later enjoyments in inherent in
all acts of individual choice and is termed "time preference."
It has been claimed [by Kirzner] that Misesian time preference
guarantees the emergence of a positive rate of interest in a pure
exchange economy, that is, where there is no production and the
economic future is known with certainty.(Moss 1976: 157)(5)
Moss transforms Kirzner's reference to "universal
('categorial')" time preference into a "preference for
earlier rather than later enjoyments." This may have been the
beginning of the misinterpretation. Moss does not refer to Mises's
evenly rotating economy or to any other textual evidence for his
interpretation of Mises.
Roger Garrison
Kirzner's characterization of Mises on interest in the pure
exchange economy was repeated in a critique of Moss by Roger
Garrison (1979: 149). Garrison correctly points out that Moss's
definition of time preference in terms of neoclassical "time
allocation" is an inaccurate representation of Misesian time
preference, which is based on action. But he follows the pattern of
not providing textual support for the view that Mises held that
there would be interest in a pure exchange economy.
Writing six years later about a capital-using economy, Garrison
presents Mises's theory of time preference as follows:
...[M]arket participants are not
indifferent about time considerations; they do have time
preferences. Whether it is taken as a logical imperative or a broad
generalization, there is a systematic preference for "sooner"
rather than "later"; the future is systematically
discounted. As a consequence, the sum of the equilibrium values of
(present) inputs falls short of the anticipated value of (future)
output by the extent of the time discount.(Garrision 1985: 169)
The problem with this characterization is Garrison's statement
that there is a systematic preference for "sooner" rather
than "later." It would be more correct to say that
praxeological time preference is a systematic preference for (1)
sometime rather than never and for (2) some later rather than all
sooner.
Most disconcerting in Garrison's essay is a footnote in which he
says that "Mises...makes the case that (positive) time
preference is a logical imperative."(ibid.: 185, note
10, referring to Mises 1966: 483-8) I could find no evidence of this
in the cited pages.
Kirzner Again
A sympathetic interpreter of the above papers might argue that
these writers did not really mean to imply positive time preference,
as defined above. There merely faced the same difficulty as Mises of
describing praxeological time preferences. However, the same cannot
be said for Kirzner's most recent discussion of time preference and
interest. Kirzner characterizes the "interest problem" as
that of explaining why the price of a machine is not bid up to the
point where it exactly equals the expected periodic rentals of the
machine. In other words, he asks about the source of interest
income.(Kirzner 1993: 167-8) He answers by pointing to the rate of
interest in the market economy. So the next step is to ask why there
is a rate of interest. To deal with this issue, he refers to the "Austrian
theory of interest," which he attributes to Frank Fetter and
Mises. He equates the Austrian theory with the pure time preference
theory. He says that this theory "solves the interest problem
by appeal to the widespread (possibly universal) positive time
preference." "If, in fact, people do prefer (other aspects
of the situation aside) to achieve their goals sooner rather than
later, then the dilemma posed by the machine and its
rentals...dissolves."(171-172)
Whereas Kirzner earlier (1976) had not mentioned "positive"
time preference, it here plays a central role in his explanation. He
would be at least partly following Mises if he wrote that the
dilemma would dissolve if it was true that people would never
postpone achieving all their goals indefinitely. However, to make
the condition that people must prefer to achieve their goals sooner
rather than later does not reflect Mises's views. Mises did not
claim that people prefer to achieve all of their goals
sooner rather than later, except in the sense that they would never
postpone achieving them indefinitely.
Percy and Bettina Bien Greaves
In the original 1940 German version of Human Action,
Mises included a section in which he used his time preference theory
to assess Bohm Bawerk's theory of interest. Since he left this out
of his English version, Percy Greaves decided to add it to a
glossary he prepared for Mises's treatise.(Greaves 1974: 150-7)
Bettina Bien Greaves translated the excerpt and Percy Greaves edited
it. The critical passage is translated as follows:
...In acting, one must always, without
any exception, value a satisfaction at an earlier point in time more
than the same kind and amount of satisfaction at a later time. It
this were not so, then it would never be possible to decide in favor
of a present satisfaction. Whoever uses or consumes anything,
whoever by acting to relieve to a greater or lesser extent a felt
uneasiness is always expressing a preference for an earlier over a
later satisfaction. Whoever eats and consumes anything is making a
choice between a satisfaction in the immediate future and one in a
more distant future. If he were to decide differently, if he were
not to prefer the earlier to the later satisfaction, he would never
be able to consume at all. He could not even eat and consume
tomorrow, because when tomorrow became today, and the day after
tomorrow became tomorrow, the decision to consume would still call
for valuing an earlier satisfaction more than a later satisfaction.
Otherwise, consumption would have to be delayed still
further.(Greaves, 1974, 156-157)
I believe that this statement makes it absolutely clear what Mises
meant when he said that present goods are preferred over future
goods. He was referring to what I have called praxeological time
preference in this paper. However, in the translation, the section
in which this statement appears is entitled "All Consumers
Prefer Present Goods."(ibid.: 156) This
characterization gives a mistaken impression.
Beyond this, in a preview of the translation, Mr. and Mrs. Greaves
write: "For the same reason that 'a bird in the hand is worth
two in the bush,' present goods are worth more than the identical
items in an uncertain future."(ibid.: 150) This is
not what Mises meant. Uncertainty is a separate
characteristic which Mises did not mention at all in this context.
Murray Rothbard
Murray Rothbard discussed time preference in his textbook. His
discussion concerned Mises's critique of Schumpeter's claim that
interest would not exist in the evenly rotating economy. Mises based
his conclusion that there would indeed be interest on the assumption
that there could be no capital goods in the evenly rotating economy
unless capital goods had a price, which he defined as "originary
interest."(Mises 1966: 530-1) Furthermore he argued that the
evenly rotating economy would contain no consumer saving since we
assume when we make the construction that actors are fully aware of
the fact that the future does not differ from the present. But
Rothbard's reasoning is different. He provides two reasons for the
rate of interest in the evenly rotating economy. The first is that
the rate of interest is positive because individual time preferences
"are all positive."(Rothbard 1962: 385-6).(6)
This answer directly contradicts Mises's statement about consumer
saving, although Rothbard did not acknowledge this. The second,
following Mises, is "capital consumption would ensue" if
there was no rate of interest.(ibid.)
We are not concerned here with interest rates in the evenly
rotating economy. The only point to be noted is Rothbard's claim
that individual time preferences are all positive. His claim appears
to be related to his argument that "we can (if we know them)
compare [the individual time preference schedules of two men] based
purely on their demonstrated time preference.(ibid.: 328)
In other words, it may be meaningful to say that "Robinson's
time-preference schedule is higher than Smith's."(ibid.:
328-9) Mises, of course, did not attach a sign to time preference,
and he did not write anything about demonstrated preference.(7)
4. Rates of Interest in the Market Economy(8)
Why are there rates of interest? The answer is simple enough,
given the existence of error-avoiding entrepreneurship. It
is (1) that individuals have time preference and (2) that there is
at least one of the following (a) differences among individuals in
their time preference or (b) specialization with respect to the
satisfaction of wants through time. Either of the latter conditions
combined with condition (1) is sufficient to lead to intertemporal
markets and, therefore, interest rates. Individuals in a market
economy establish interest rates for the same reason that they
establish relative prices -- in order to exchange. The only
difference is that the exchange is inter-temporal. Just as there can
be no negative price among goods, there can be no negative interest
rate.(9)
To comprehend the complexity of market interest rates, we assign
all of the action aimed at satisfying wants to entrepreneurship. We
say that it is the task of entrepreneurship to identify and put into
practice the means that are available to satisfy consumer wants.
Recognizing that consumers wants have a time dimension,
entrepreneurship is careful, given its aim of earning profit, not to
devote all of the non-specialized factors of production to the
satisfaction of the most immediate wants. Because of time
preference, if it did this, the profitability of shifting some means
toward the satisfaction of future wants would be infinite. At the
same time, the potentially infinite profit from producing at least
some present goods assures that entrepreneurship does not cause all
satisfaction of wants to be postponed indefinitely. Whether people
have a "positive" preference for present goods over future
goods of like kind and quality is irrelevant. Given the presence of
entrepreneurship, all that is necessary for a positive rate of
interest to exist is that they are not indifferent as between the
present and future -- i.e., that they prefer some goods now and some
later.(10)
Consider what would happen if there was a shift of social time
preference toward the consumption of later goods rather than sooner
goods. This means that consumer-savers, having estimated the future
prices and availability of goods, have decided that at the current
interest rates on their savings, the additional future goods they
expect to buy with the savings are worth more than the present goods
they must give up. Entrepreneurship would receive and send signals
to the effect that saving had increased and that spending on current
consumers goods had decreased. In addition, it would send and
receive signals that consumer-savers planned to consume a larger
amount of future goods than otherwise. The higher savings, other
things equal, would cause the interest rates on loans to be lower
than otherwise. Combined with the anticipated higher demand for
future goods, this would encourage producing entrepreneurs to embark
on production projects that would make the future goods available.
If the producing entrepreneurs do not embark on such projects, the
consumer-savers would find that the future prices are much higher
than they expected. Like the producing entrepreneurs, they will have
made entrepreneurial errors.
The Assumption That Entrepreneurship Avoids Systematic Errors
To deduce that there will be rates of interest in the market
economy, we must add an assumption about entrepreneurship.
Assumptions about time preference and specialization are
insufficient. We must add that entrepreneurship avoids systematic
errors -- that it tends to appraise, make decisions, and bear
uncertainty in ways that are more likely than not to satisfy
consumer-saver wants, in light of production possibilities. We can
see why this assumption is necessary by considering the possibility
of a zero interest rate.
Could the supply of loanable funds ever exceed the demand for
loanable funds at a positive rate of interest? The answer is clearly
yes. If producing entrepreneurs did not want to borrow all of the
saved money at a positive rate of interest, the interest rate would
fall to zero. However, to the extent that producer borrowing fell
short of consumer saving, consumers' entrepreneurial expectations
that future goods would be available to buy at expected prices would
be incorrect. Future prices would turn out to be higher than
expected. Moreover, producing entrepreneurs will have made errors in
not anticipating the higher future prices. Thus, for the interest
rate to fall to zero, both consumer-saver-lender entrepreneurs and
producer-borrower entrepreneurs would have to make errors.(11)
Roundaboutness
It is easy to see why the marginal revenue product of methods of
production that take different lengths of time (i.e., the revenue
product associated with different periods that Bohm Bawerk called "roundaboutness")
is irrelevant to the question of whether there is a positive rate of
interest. So long as the conditions described above hold, there will
be rates of interest regardless of this element. Of course,
entrepreneurship may have occasion to alter its appraisals of the
physical factors of production on the basis of when the revenue
generated by their use is expected to be received. Such changes will
get reflected in entrepreneurship's decisions to make products
available for consumption at different times and, in turn, the rates
of interest. However, while changes that lead to different
entrepreneurial perceptions of physical productivity can cause
entrepreneurship to change the rates of interest, they have nothing
to do with the deduction that rates of interest in the market
economy must be positive. Thus Kirzner was correct to say that
interest would emerge in a pure exchange economy without production.
But this deduction does not depend on the assumption of positive
time preference in the sense that this term was used above.
To summarize, the deduction of a positive rate of interest in a
market economy is based on the assumptions (1) that individuals have
time preference, (2) that there are (a) differences among
individuals in their time preference or (b) specialization with
respect to the satisfaction of wants through time, and (3) that
individuals acting entrepreneurially do not make systematic errors
in their efforts to use their means to achieve their ends.
5. Conclusion
Mises did not hold the view that a particular set of goods, money
or utility is necessarily preferred in the present to the same set
in the future. He merely claimed that individuals cannot be
indifferent to when they receive their satisfaction; since if they
were, they would not evaluate their satisfaction according to the
praxeological categories of sooner and later. The view, or more
correctly the praxeological axiom, to which he subscribed was that
in choosing between alternative courses of action, actors take
account of the time at which they expect the alternatives to have
their effects. Actors, by definition, would never postpone all of
their satisfaction until the indefinite future. And they would never
completely neglect the future in their actions. We have called this
idea praxeological time preference. On the basis of this
assumption, combined with assumptions that individuals' time
preferences differ, that there is specialization in the satisfaction
of wants, and that individuals acting entrepreneurially do not make
systematic errors; the paper deduced a positive rate of interest.
Notes
1. "[T]here
cannot be any question of equal valuation of nearer and remoter
periods of the same length. Such an equal valuation would mean that
people do not care whether success is attained sooner or later. It
would be tantamount to the complete elimination of the time element
from the process of valuation."(483) From the viewpoint of
praxeology, "[w]e must conceive that a man who does not prefer
satisfaction within a nearer period of the future to that in a
remoter period would never achieve consumption and enjoyment at all."(486)
2. Outside of
this literature, Frank Knight (1941: 412) appears to have also
misinterpreted Mises on this issue.
3. See Mises
1966: 247; 531.
4. However, I
do not agree that Mises did not publish his own special study of the
theory. I think that such a study is in the pages of Human
Action.
5. Also see
ibid., 164n.
6. He
elaborates his theory of interest in the evenly rotating economy
based on positive time preference by using demand and supply
diagrams at ibid.: 323-332.
7. Rothbard's
concept of demonstrated preference in relation to Mises is discussed
in Gunning 1998.
8. The
following discussion of interest rates is based on the assumption of
neutral money. In other words, we are abstracting from the
influences of changes in the quantity of money and in the demands
for cash balances. To include these influences would take us off the
main subject of the paper.
9. In this
respect, Rothbard (1962: 323-32) is correct to derive rates of
interest from differences in time preference, although he could also
have derived them from a combination of uniform praxeological time
preference and specialization in the satisfaction of wants.
10. Provided,
of course, either that time preference differs as among individuals
or that there is specialization in the means of satisfying wants
over time.
11. Could
the market rate of interest ever be negative. Mises wrote that under
deflationary expectations, the gross rate of interest on a contract
could indeed be negative (ibid.: 542). But this seems impossible, as
pointed out by Walter Block (1978: 124n). It is possible that
Mises's argument can be salvaged, however. During the Great
Depression, many creditors agreed, in effect, to accept repayments
on loans that were only a fraction of the amount promised rather
than force the debtor into bankruptcy. One might characterize this
as indicating that they accepted a negative rate of interest If this
is what Mises meant, he had a strange way of writing it. (Thanks to
Paul McCaffree for helping me see this point.)
References
Block, Walter (1978). "The Negative Interest Rate: Toward a
Taxonomic Critique." Journal of Libertarian Studies.
2, no. 2, 121-124.
Garrison, Roger (1979). "In Defense of the Misesian Theory of
Interest." Journal of Libertarian Studies, 3, no. 2,
215-26.
Garrison, Roger W. (1985) "A Subjectivist Theory of a Capital
Using Economy," in O'Driscoll, Gerald P. and Mario J. Rizzo
(1985). The Economics of Time and Ignorance. Basil
Blackwell, New York.
Greaves, Percy L. Jr. (1974). Mises Made Easier: a Glossary
for Ludwig von Mises's Human Action. Dobbs Ferry, New York:
Free Market Books.
Gunning, J. Patrick (1998b). "Austrian Welfare Economics?: A
Misesian Response." (manuscript)
Kirzner, Israel (1976). "Ludwig von Mises and the Theory of
Capital and Interest." in Lawrence S. Moss (ed.), The
Economics of Ludwig von Mises. Sheed and Ward, Inc., Kansas
City.
Kirzner, Israel (1993) "The Pure Time-Preference Theory of
Interest: An Attempt at Clarification." in Jeffrey M. Herbener
(ed.), The Meaning of Ludwig von Mises. Kluwer Academic
Publishers, Norwell, Massachusetts.
Knight, F. H. (1941) "Professor Mises and the Theory of
Capital." Economica. (November).
Lewin, Peter (1997) "Rothbard and Mises on Interest: An
Exercise in Theoretical Purity." Journal of the History of
Economic Thought. 19, no. 1, 141-159.
Moss, Laurence S. (1978) "The Emergence of Interest in a Pure
Exchange Economy: Notes on a Theorem Attributed to Ludwig von Mises."
in Louis M. Spadaro, New Directions in Austrian Economics.
Sheed Andrews and McMeel, Inc., Kansas City.
Rothbard, Murray N. (1962). Man, Economy, and State.
Menlo Park, California: Institute for Human Studies.
Von Mises, Ludwig (1940) "A critique of Bohm Bawerk's
Reasoning in Support of His Time Preference Theory." in
Greaves, Percy L. Jr. (1974). Mises Made Easier: a Glossary for
Ludwig von Mises's Human Action. Free Market Books, Dobbs
Ferry, New York.
von Mises, Ludwig (1966). Human Action: A Treatise on
Economics. Henry Regnery Company, Chicago.