January 16, 2013
(Editing translation process)
Draft an algebraic approach to dynamic pricing analysis.1
(Utkast till en algebraisk metod för dynamisk prisanalys. 1)
Dag Hammarskjöld
As the first part of any analysis of the general price trend will naturally always be the finding that,
during a given time segment, the sum of all payments is equal to the total sales of goods and
services times the average price, to which turnover occurred. It is this truism that in (quantitative
theory) kvantitetsteorien expanded to a price declaration by the sum of all payments substituted
money supply times the money supply formulas of the type MV = PT. So far it is this construction
obviously of value, but it is remarkable, both in that it is a reasonably blunt analytical tool, and that
it does not exhaust the analytical possibilities that lie in the fact from which it is derived. So thereof
provides that the nothing of penningmängdsfluktuationernas economic background nor anything
about the trade turnover T's dependence on changes in the left side of the equation, although it is
evident that monetary fluctuations partly conditioned by altered drawdown, which must go back to
a shift of income expectations or payments for productive services and lead to a change in the scale
of production. On the other hand, it seems not impossible that if one avoids substituting the
monetary phenomena of the sum of all payments and instead try to work with a split, one on this
road could reach an analysis of price movements mechanism; payments for production purposes
during a series of periods to determine the product stream development, and the difference between
the payments and payments for products constitutes the profit or loss of production during
respectively. periods, which maintains the balance between short-term cash flows and is one of the
1
The prof. Lindahl, which kindly go through this essay in manuscript, I beg herewith to extend a heartfelt thank you. Of
the essay will be apparent that my debt of gratitude goes further; This outlined the method can be best characterized as a
combination and expansion of structures, which in conjunction with Wicksell used by Lindahl and JM Keynes in their
monetary theoretical works. As the interface for the literature confidant lie in the open day, I have not felt any detailed
account of the dependence is necessary. The doc. Myrdal's analysis of capital market equilibrium and its impact on price
developments in the essay "If monetary equilibrium theory" (Economic Journal, 1931, stitcher 5-6, p. 191) are present
investigation in a certain contrast ratio. For reasons to which I will return in a later context, this analysis must in my view
be described as abortive.
A special thanks I owe file. Laws. Einar Dahlgren, which in Proof examined the numerous formulas.
determinants for both the total disbursements and entrepreneurial disposition trends2. In the
following, an attempt shall be made to work out a method of analysis, which for now implied lines
initially eliminates the monetary factors, and direct links to the various paying the functions and
mutual respect, but unlike in the Lindahl-Myrdalska constructions and, like the quantity theory is
based on a posteriori registration of the actual purchasing power transfers occurred. Due to
problems scaffold complexity must be made in the drafting stages.
Initially assumed:
1. The processes take place in a closed society;
2. The payments are only of two types, namely payments for consumption purposes directly to
entrepreneurs, and payments from business owners directly to original factors of production
services in the respective periods;
3. The payments for consumption purposes only with the aid of already produced revenue of
productive services, respectively. with entrepreneurs productivity gains (temporary
differences between income and expenditure on consumer goods for production purposes
related to the current production of consumer goods);
4. The investment cost value corresponding to their antecipationsvärde, which means that
entrepreneurs not anticipate any production gains and then use those consumed tively, when
their outcomes;
5. The productive services, the results of non utmognat during the period in which they were
called in, utmogna the next period;
6. The fact that the utilized amount of productive services remain constant;
7. The price of productive services not change;
2
To prevent misinterpretation, it seems appropriate to predict post a note on the construction method in the following
analysis. In order to allow an extension to the statistical material production work with pure monetary income and savings
determinations. The production is further determined as the actual payments, which technically are attributable to resp.
parts of the production, though the cost determination in effect through depreciation - which is not done for technical
reasons, are affected by antecipationerna. Construction method is chosen to supply power to the simplest possible way
could be related to the payments. Antecipationerna included directly in the purchasing power of determination.
It now specified cost determination correlated profit concept is apparently not the accounting. A discussion of its relation
to this would be of interest, not least in the light of the very unjust criticism leveled against Keynes "wind falls". Here is
not the place for more than a few brief comments. When e-employment in an investment calculation for example. Myrdal
chart compares the anticipated revenue stream with production costs of the investment, the interest thereon, and the
remuneration of Kooper generating means, he does, in fact, a calculation of the difference between current revenues and
technical production costs, and thus of what is here described as production gains. If he then at winning the bleed does a
depreciation of value, this means only that he profits from the production draws its anticipated value. The accounting
income is then the difference between the anticipated and the bleed profits. No competition between this concept and the
win, with which this production work, there is apparently not. They take both positive and both must be addressed. It is a
matter of convenience in the manner in which they included in the analysis.
8. That productivity does not change and hence (7) "the efficiency-earnings" remain constant
and
9. The productivity nor increased by the fact that they used the services results utmogna only
after the end of the periods, during which they committed. In accordance therewith counted
nor by interest payments.
The two questions are answered in the school and how under these circumstances production profits
evolve and modify purchasing power relative scale, and how consumer prices change under the
influence of the lack of balance between the various cash flows, as reflected in particular in the
production profits. The gradual elimination of the specified premises to the answers later modified
to the greater reality fidelity.
Before the request goes to a answering these questions, it is necessary to add a few words about the
assumptions - but the real, utvecklingsmodifierande meaning which will be above premise-that
must be done on time snapshot of the different variables, which are included in the equations
derived from the immediately given identity relationship between payments, sales and prices, which
form the basis for the analysis. If over a period of a certain total payout for the production of
consumer goods and certain income from sales of goods consumption, obtained production profit
equal to the difference between revenues and payments. This production profits must be assumed to
precipitate at the end of the period, if antoges vest gradually over the period, it would represent the
self-purchasing power, which could be exploited consumption relatively and thus could affect
revenue, the problem would be insoluble. Production gain is assumed therefore enrolled at each.
periods ended and can thus, if the non anteciperats (condition 3), used relatively consumed only
during the next period. Consumer goods price represents, in fact, an average price for each.
periods, but it seems appropriate to tidsfixera also the period's end. Disbursements for productive
services have no time to fix, but if you like, assumed predetermined by contract at resp. periods
beginning.
The following algebraic terms come into play: Disbursements for productive services over a period
of n-number of periods is assumed to be n; of these is the period n the last, period n-1 the
penultimate etc. -Denoted E (6 and 7, a constant), the same period for consumption tively use
disposable production profits (which comes from the previous period) Dn-1; the portion of the period
for consumption tively use disposable purchasing power (E+Dn-1), which was not used until after
the end of Sn and the portion of the payments for productive services whose results utmognar only
after the end of In. The influence3 of the amount of consumer goods during the period is assumed to
be Qn and its price Pn. During the period n is obtained when production profits Dn = (E+Dn-1-Sn)–
(E+In-1-In). If (In-In-1) is represented by Nn, becomes Dn =Dn-1+Nn- Sn. Consumer goods prices Pn
obtained
Since production profits over a period n equals production profits in the previous period plus (Nn Sn), obtained apparently the outgoing production profits during the n:th period ΣnN - ΣnS. As each
N is the change in payments for services, whose results utmogna only after the end of a period, and
each S the change in the nominal savings during respectively. periods, there is thus a production
profits as soon cost value of the investment exceeds the nominal savings. Consumer goods prices
are as stated
one owns the Dn-1 =Σn-1N - Σn-1S. However, if the income for the period you have a whole
constitutes payment for productive services (Σn-1N =Σn-1S) and on Nn-1 is set = 0, the change in the
period influence the volume of goods in comparison with the previous period attributable
The formula shows that the decrease in the amount of consumer goods under the conditions
imposed are proportionate to the redistribution of income that the new investment brings. Would the
input income not in its entirety as compensation for the services used, this implies that the
consumption of commodity production change does not become proportional to the depth of income
redistribution. One obtains
where (E+Dn-1) represents the input income.
3
Ev. Försålda Jfr not 2 sid. 168.
Assuming Nn-1=0 is thus obtained for the output price in period n equation
showing that Pn varies in the opposite direction Sn and in the same direction Nn. Ratio respectively.
quantities are however quite complicated.
It is evident that E/Qn-1 means the price of consumer goods, as even equal production costs. The
equation thus determines the output rate as a function of those with which it is consistent if Nn=0
and Σn-1 N - Σn S=0. As the opening price during period n can be written
obtained as a condition of consistency between input and output price
Correspondence between Nn and Sn thus providing constant consumer price level, only when both
terms are = 0, respectively. When balance exists between the input nominal savings and investment
input (Dn-1=0). For constant price level is required, therefore, under defined conditions, a certain
relationship between saving the changes during the period and completed investment shifts, whose
height varies with the difference between the opening face-saving and opening investment.
How does the equilibrium condition, the assumption N=0 NULLIFIED?
The opening price during period n is obtained, of course, still
but this is now
The output rate E+Dn-1-Sn/Qn may further because Qn/Qn-1 in this case obtained E-Nn/E-Nn-1,
printed
The condition for (constant prices) priskonstans is thus
At Dn-1=0 gives the correspondence between Sn and Nn Thus in this case the consumer price level,
but gives only assumption Sn=Nn=0 is no longer the same results.
Instead (constant prices)
priskonstans obtained under the condition Nn-1=Nn=Sn. One can thus establish the following
theorem: Concordance between changes in nominal savings respectively. investment in a given
period provides constant consumer price level in the period, if either the input output gain is = 0 or
changes correspond to the investment shift, which existed in the previous period.
The first step to an extension of the results to the larger reality of faith is suitably repeal of the
assumption (5), that an investment in a period utmognar the next period. Regarding production
profits, this implies no major change. As payment for the production of consumer goods has
previously been entered on payments during the period plus the detailed investment cost value and
minus the outbound investment cost value. Now, if the constituent investments only partially
utmogna period, obtained instead as current production total disbursements during the period plus
the technical amortization of investments included minus the portion of the payments, the results of
which utmognar after the period end. The outbound investment cost value, however, is equal to the
depth of investment cost value less amortization plus the latter part of the payments, which means
that you can still put the cost of production equal to the total disbursements plus the depth minus the
outbound investment cost value. The situation is similar regarding the determination of the price
movement.
As the next step in approximationsförfarandet NULLIFIED premise (4), to be invested things, the
value consistent with their production costs. Entrepreneurs anticipate therefore productivity gains or
do, if you would rather put it this way, antecipationsvinster-which can be utilized consumed tively.
Suppose initially that the entrepreneurs in a state of pre-analyzed types over a period of some reason
anticipate a production profits Vn at period end. The op Relatively using purchasing power becomes
=E+Dn-1+Vn–(Sn+Kn), where Kn means vinstkapitaliseringen, therefore it against Vn outstanding
nominal savings. If Vn is not utilized consumed tively (Vn=Kn), exists for entrepreneurs no reason
for settlement from possibly bleed output gain of the pre-exploited purchasing power and, of course,
nor any basis that due to the anticipated produktionsresultatets utmognande such cost item introduce
some value depreciation. On the consumption tively use in the next period disposable production
gain is thus
Would be Vn to any part have been used relatively consumed (Vn>Kn), a settlement made, so that
the bleed output gain only the amount transferred as purchasing power, which is not already
antecipationsvis utilized. Production gains during period n is thus Σn N- Σn S+(Vn -Kn), but the part
of it that represent new purchasing power ΣnN–ΣnS+(Vn-Kn)–(Vn-Kn)=ΣnN-ΣnS. Regardless of
antecipationerna obtained also in this case, Dn=ΣnN+ΣnS. If antecipationerna include productivity
gains in recent periods worth of ΣxV, matched by a capitalization ΣxK, obtained during the period n
profit =Σn N-Σn S+(Vn-Kn)+(ΣxV-ΣxK) and purchasing power transmission to the next period
=Dn=ΣnN-ΣnS+(ΣxV- ΣxK). Any antecipationer and their exploitation for purposes kosumtions
lacking thus impact on profits and prices, then the anticipated profit outcomes. It is apparently
generally conclude that the output gain is equal to the absolute difference between the investment
plus the tartaric bleed present4 antecipationerna of profits during the current and following periods
and the total nominal savings (including both the non-consumption of monetary income for
productive services capitalization of - thus, failure to con tive advantage - an anticipated profit, or if
you prefer antecipationsvinst).
Introduced that result in the previously cited equations, which fix the condition of constant price
level, are obtained if the differentiation between S and K will be eliminated, so that the total
nominal savings (incl. vinstkapitaliseringen) is denoted by S, and the value of antecipationerna
production gains Dn, Dn+1, Dn+2 ..... D(n-1)+m at the time of the outcome of Dn written ΣmV and at the
time of the outcome of Dn-1 is designated Σm+1V, etc., equilibrium formula
4
Vinstantecipationens size can of course vary during the period, so that antecipationsökningarna be temporary purchasing
supplements and vice versa. There at the end, the production gain relevant addition is evidently equal to the net of these
minor changes, which in turn is equal to antecipationens absolute height at the time of production pigs dioxide bleed.
Added offset in vinstantecipationerna (ΣmV-Σm+1V)=Fn, the formula can be rewritten
It is clear that in this case the condition Nn-1=Nn=Sn not provide constant price level. If Nn is
assumed =Nn-1, the condition of constant price level rather than Sn=Fn+Nn, or that the nominal
savings to offset as much as investment payouts and vinstantecipationerna together. Added
Nn=Sn=0, then the condition
or to change the investment in the previous period relates to payments for productive services that
the change plus the offset in vinstantecipationerna to the consumption tively use disposable
purchasing power during the current period, etc.
Against the background of the previous production, it is easy to make the modifications that may be
necessary for waiver of premise (3), that payments for consumption purposes only with the aid of
already produced revenue of productive services - when (mao) assumes that even a revenue of this
species can be anticipated and potentially exploited consumed tively. Also in this case, of course,
that if the purchasing power of prior use, a statement must be made on the anticipated revenue,
when it will start, the words, the latent, possibly abused, possibly saved purchasing power is
entirely based on antecipationer of future revenues. With the time fixing the various quantities in
this analysis received, getting thus such as price and vinstdeterminanter alongside at the end of a
period this antecipationerna of profit during this and subsequent periods be antecipationerna of
revenues for productive services in the following periods. If these written Σm-1E’ and (Σm-1E’=ΣmE’)
is added =fn+1, obtained production profits
and price constant condition
or Nn=Nn-1 condition Sn=Fn+fn+1+Nn-1, etc. As f as opposed to F is not a significant variable in the
actual price discovery process and in general probably are in the vicinity of o, the grandeur of
practical analysis conveniently eliminated and reasoning therefore be maintaining the condition (3).
Prerequisite (2) includes in fact two different assumptions, namely that it only has two cash flows,
so that the total payments received
other, that the payments relate only to services during the period. The last mentioned assumption
uppgives preferably first; introducing thereby the possibility that entrepreneurs buy the originära
factors of production to their original owners.
If we initially assume that the purchase price corresponds antecipationsvärdet of productive means,
as transferred, both for the original owner, the purchase price is assumed therefore =Σm-1 e’ - and for
the buyer, ie Σmv=0 is the only change that one for unpaid payments during the period obtains the
formula E+Σm-1e’ and the total payments above formula with the addition of the same term Σm-1e’.
In the calculation of productivity gains and consumer goods prices will last term is obviously not
into the art market side, and on the revenue side are offset against the reduction of Σm-1 E’ with Σm1e’.
If the purchase price is less than antecipationsvärdet for the entrepreneur, he makes the
transaction a antecipationsvinst Σmv, which is one of the determinants of Fn. Exceeds the price
antecipationsvärdet for the original owner, this affects similarly the value of fn+1. The repeal of this
condition (2) leads therefore no change in the equations. As the services of the purchased appliance
utmogna, will of course payment in as a cost item. Prior Utilized gains on its use to go the usual
way of offsetting the bleed profits. It should in this context, in passing, noting that since the
probability suggest that purchases of productive facilities would not be ill able, unless the parties
considered it to make a profit on the transaction, this should tend to give both F and f positive
values, thus increasing the available purchasing power.
More complicated is the situation at the abolition of the first stage of the premise. Assumed
consumer goods producers make payments directly to the owners of factors of production for
ongoing services to the amount of e1 and capital goods producers to the sum u1 and further their
past, in the period utmognande payments be a1 and the part of e1 and u1 as utmognar after period
end, as i1, and assumed the additional quantities of the producers, to whom they make payments, as
e2, u2, a2, and i2, apparently obtained E=Σe and N=Σ(i-a). You get in this case productivity gains
not only in the production of consumer goods, but in all the previous production layers. The gains in
capital goods fall due course periods and utilized consumed relatively under them. It is therefore
necessary for the calculation of purchasing power size introduce their total value as an additional
positive item in addition to the pre-treated. The sum of the profits of capital goods are obtained if
(i1–a1) written n1 etc,
or, as may be un = 0,
Consumer goods producers outgoing profit thus becomes, if antecipationerna be left aside, equal to
Fragmentation of multiple payment streams thus changes the relationship between non-profit
production of consumer goods and the ratio of savings-investment. It is also clear that although only
a portion of the production gains that vest over a period are subject to the transfer, namely those that
accrue to the consumer goods producers - the only one, but methodically necessary intervention in
the various betalningsströmmarnas continuous process - this transfer algebraic terms are exactly the
same after the abandoning of condition (2) as in the earlier analysis. It should be noted, however,
then as well as the determination of the production gains, the investment term is defined in a way
that partially deviates from the traditional. When calculating system numerous payment flows,
mean investment payments for initial productive services, the results only after the end utmogna for
sale as consumer goods or capital goods (in both cases, of course, for goods substituted secondary
services)5. This is mainly relevant for price analysis, since the consumer goods supply is a function
5
In this way, the use of design as well ΣnN in substance the same as the total fixed capital formation. From the
complications that result if capital goods prices deviate from their cost value, this can be ignored. There is no reason to
also demonstrate the modifications in the formulas obtained in the case of productive use of any part of the purchasing
power, because they easily appear irrelevant to the outcome.
not previously by N but by n1, u1 and e1. Fully printed is thus obtained as a condition of
priskonstans in consumption layer:
or if the shift in consumer goods producers interim payments [(e1+u1)n -(e1+u1)n-1] is set =An,
The formula, which is not very useful for practical analysis, is of interest not least because, it shows
how little is left of the relationship between capital balance and constant consumer price level, if
you let go of the adoption of the two payment streams - even if one holds the assumption of
constant “efficiency-earnings” etc.
Conditions 6, 7, 8 and 9 have in common that they do not modify the method for producing pig
manganese determinering although they alter the size of a plurality of determination input terms. It
can therefore after elimination of condition (2) which definitely results6 establish the proposition
that in a closed society the production profits obtained in the production of consumer goods, as soon
as the nominal savings - including both savings of nominal income and the capitalization of
vinstantecipationer - is less than the sum of investments and antecipationer of future profits
including the one that is the subject of the determination, whereby the investment is the sum of
payments for productive services, whose results - whether this is intended for immediate
consumption or non-utmognar respectively. sold7 only after attaining the bleed.
How much larger is the aforementioned förutsättningars importance of price movement. To request
shall be transparent, anknytes analysis again to the starting position: all conditions except for
premise (9) assumed thus remain full productivity when services utmognande befitting a period =
6
For simplicity, is held on the foregoing manner, the condition (3).
So far consistently assumed that the sale utmognande production sold. Should this not be the case, the inventory
equivalent to investment both from price - and profit standpoint. Sales of previously utmognade but stored goods after
attaining the bleed will enter into the side of utmognandet of capital expenditures.
7
(I+p) of the immediate productivity and the contractual interest rate over a period = r. Added both
Σn-2N and Nn-1=0, is obtained
hill Nn-1 have a positive value, obtained instead
Would withal during period (n-1) investments have utmognat (Σn-2N>0), is apparently
Similarly received payments during respectively. Periods
In its simplest form, thus becomes the condition for priskonstans the repeal of condition (9) follows
(cf. p. 162):
If you own Dn-1=0 and p=r, gives Sn=Nn constant price level. Nn-1=Nn=Sn gives however only at
priskonstans Nn-1=0 (that Σn-1N=Σn-2N). The result is complicated of course, in degrees, of the
lifting conditions (2) and (5). Although nothing prevents that by a combination of the last foregoing
formula fully developed with the equations for priskonstans to which production requires led, works
out a formula that completely specifies the conditions for the consumer price level in a closed
society by restraining the conditions 6, 7 and 8, however, this seems hardly fruitful. Prerequisite (9)
reintroduced therefore on.
NULLIFIED only assumption (8), that productivity is constant, and assumed the period n wara wn
times greater than during the period (n-1) changes obviously, if Σn-1 N=0, the basic formula for
priskonstans to
Also eliminates the premise (7), that the price of productive services not change, and assumed this
instead offset in direct proportion to productivity, is the aforementioned prerequisite condition for
priskonstans:
Neither Sn=Nn vid Dn-1=0 or Nn-1=Nn=Sn thus gives in this case the constant price level. However,
included as the last formulas seen productivity displacement under the above conditions in such a
way that, if the condition of constant consumption price level at constant productivity is filled,
productivity, price change causes a displacement which is inversely proportional to the change in
productivity.
Replacing the assumption Σn-1 N=0 with wn-1=1, appears productivity change in a different way.
Since the technical installment of opening investment = Σn-1N and investments during the period =
Σn N - software upon (5) assumed the force - obtained left side of the formula
and during the next period
Productivity change appearance in the left side of the formula for priskonstans, such as it is
obtained after withdrawal of condition (2), becomes more complicated. Acceptance of productivity
change to be uniformly distributed over the entire production, receives left side during period n the
following form (u1 divided according to whether the payments relate to goods, the price of which
includes payment for the period utilized productive services or not, in un1 and (u1 –un1); investments
are written as functions of the payments, which constitute them, so as to obtain in
(e1+un1)+i’’(u1
–un1)]:
= i’
is useless to continue the algebraic analysis along these lines. It is clear enough to show and how
productivity changes to be incorporated in the full equation for priskonstans, and that the above
principle, the price movement in the fulfillment of the condition for priskonstans is inversely
proportional to productivity change, only under certain highly simplified conditions.
Since E in right side of the formula for priskonstans at repealing condition (2) turns into (e1+u1), it
will be at an incorporation of the full equation of changes in the price of productive services
necessary to work with the same wordy writing style as the introduction of technological changes.
Then change influence with knowledge of pricing conditions in general can easily be assessed more
generally, it is unnecessary to set out more detailed analysis in algebraic form.
As this trial a methodology is intended to be limited to situations in a closed society, there remains
only to consider the importance of condition (6). How is thus the simple formula for priskonstans,
the amount utilized productive services are moved? The offset is assumed to correspond to a
payout, which at the same price of productive services is =Bn. It then receives
providing fixed price level of Sn=Nn in Dn-1=0 but not on Nn-1=Nn=Sn. Apparently gives nor
Sn=Nn=Bn priskonstans. Even at this point obtains the equation of condition (2) repeals, a
meaningless convoluted shape, since you have to account for the point in the process, on which the
new productive forces find use.
Denoted the relative offset in the price of productive services with hn, and assumed productivity
offsets break a period of constant productivity (wn-1=1), obtained at the same time waiver of
conditions 6, 7, 8 and 9 the following conditions priskonstans:
For the price level of consumer goods in a closed society must be constant over the period n, is
required, then, that both this equation and the equation on p. 167 apply. Although a combination of
the two equations is possible, it shall not be attempted here, since they are already in this condition
are quite opaque.
Certainly, the method of highly refined. This presentation is intended to work out its basic features
and show the way in which the various phenomena in the economic development of the author's
view, the simplest be included in the formulas. Method of fertility can be discussed, but that it made
possible the safe determination of the price of theoretical importance of relationship-saving
investments, seemingly speaking in its favor8. It should perhaps also be noted that both of the
factors that directly determine the entrepreneurial dispositions, namely production gains and
vinstantecipationerna, and the associated disparity between the prisdeterminerande payment flows
in explicit form part of the equation. In this respect, the method is fundamentally different from the
structures, which work only with the relationship between antecipationer at a given moment.
Supplements: Myrdal's formulas for capital balance. The contribution to the expansion of the
wicksellianska (Monetary Theory) penningteorien, Associate Professor Myrdal left in his essay (If
monetary equilibrium theory)9, he has also combinations with algebraic formulas illuminated
reasoning has considered the question of the relation-saving investments, price level. The purpose
of the algebraic the deduction would only have been to make explicit the conditions under which a
conformity between existing realkapitalens value and costs of reproduction means that the line also
exists between savings and investment. Myrdal says thus10: In order to more definitively confirm
our study results in this part, we would need to evince that the two equilibrium equations - the one
that focuses on investments, return on investment, and that are focused on the situation in the capital
market - quite generally are consistent body but somewhat later is underlined in the abstract and not
always realistic nature of the conditions shown to underlie consistency. He attaches as well the
deduction and the results practical significance. In recent issue of the formulas the practice of the
statistical evidence is discussed, he quotes eg. : >> We have thus shown that the equilibrium
conditions (compliance-saving investments) - admittedly over a couple of theoretical
approximations - can be derived from the first (the one that focuses on investeringsräntabiliteten)
and therefore consistent with this. Especially as the practical application of the first equilibrium
formula face enormous methodological difficulties, it is obviously of the utmost importance, that in
practical work is also the second equilibrium formula will be used alongside the first.11 >> Latter
opinion supports closest to the idea that Myrdal considers the conditions that must be introduced,
for both, by him given equilibrium formulas school (meeting) with each other - or with another of
8
It should be noted that this determination is not affected by the difficulty to withdraw the conditions 6-9, since the well
eliminated the assumptions 2-5. Meth intend to in a future study to show how the formulas can be rewritten in the bank
statistical terms and in this form used in the statistical analysis.
9
Ekonomisk tidskrift 1931, häft 5-6, sid. 191.
10
Sid. 231.
11
Sid.264.
Myrdal's formulation - to capital formula to (derived) from the return formula, in practice not be
more important, than to the formulas in the statistical analysis could be used alternatively.
Myrdal's summary of what he calls the first two equilibrium conditions may be subject to discussion
session. For Wicksell, the normal rate of interest have appeared, among other things that a normal
equilibrium price, which could be determined graphically as the intersection of the curves of supply
and demand for loan capital in a given pricing moments. The demand curve should be from
Wicksell's general theoretical points of him as soon as have been conceived as a line, which against
any interest rate on the price axis corresponding to a point on the quantity axis at which the
marginal investment return was equal to the relevant interest rate. With this approach eliminated the
question of the relationship between the interest rate that causes the balance on the capital market,
and investeringsräntabiliteten; latter factor is not one of the first co-ordinated basis for determining
the normal rate, and even less can be deduced from the capital requirement return condition.
Räntabilitetens importance of fixation is limited to determining efterfrågekurvans (Demand curves)
shape; typically're also return condition marginal seen satisfied, wherever the intersection of the two
curves is, therefore, the interest rate than the capital market point of view is normal. Myrdal
perceive however Wicksell in a different way. He relates Although capital determination for a given
pricing moments but focuses on return condition in a form that is not marginal and f island nor tied
to the next investment but can be said to mean that the value of existing real capital must meet the
costs of reproduction12. This condition determines the non efterfrågekurvans(Demand curves) form
in the pricing thereof provides that moment, but that it does not change between this and the
previous pricing torque respectively. not changed in a way that causes the investment scope of the
current interest rate is moved. The condition in question are therefore not related to the margin
theoretically supposed equilibrium fixation, for which, because of its association with the
development in time is irrelevant, but should, it seems, be attributed to the second part of the
Wicksell problem complex, which has the same importance for the explanation of actual changes in
investment scale from time to time as the marginal return on the determination of efterfrågekurvans
(Demand curves) form at any given time. For the following discussion of the Myrdalska formulas
will also casually stated that he had not managed to put the terms in connection with Capital
determination of the equilibrium interest rate, so much less demonstrate, that this determination can
be derived from the return condition of the form given by him.
12
The extension to the existing real capital is a deliberate modification of Wicksell thought, which, however, would be
impossible, if followed newly designated routes.
The point in Myrdals preparation in this context immediately attracts the attention, however, is not
now the case, but the meaning and the analytical value of the formulas, to which the second
equilibrium condition derived from the first. The reader is assumed familiar with the detailed
meaning of the Myrdal using algebraic symbols.13
Is the first equilibrium condition is satisfied, there is as Myrdal consistency of the existing capital
(C1) and reproduction costs (R1), ie C1=R1 . Termed the anticipated capital expenditure payments of
R2and the anticipated free the waiting (S + D), the second equilibrium condition attributed R2 =S+D.
It should be emphasized that all the terms in this formula denote the sum of the individual, the
pricing situation in question discounted sums of antecipationer on capital expenditures, savings,
etc., as required in the determination of the equilibrium interest rate for common pricing theoretical
lines, and thus are fundamentally different meaning than in present paper discussed the formula
(ΣN–ΣS=0), which relates to the specific sequence at different times. To derive the formula
R2=S+D from the formula C1=R1 before Myrdal equations
where the last two equations in the nature of approximations, the validity of which must be
postulated, for the deduction to be implemented. Of the system of equations follows immediately,
that conformity exists between the new value of the investments and the waiting, then C2=S+D.
Thus it is clear that over the Myrdal imposed conditions, the new investments anticipated value is
consistent with the anticipated capital expenditure payments, taking R2=S+D. The key point of
Myrdal's evidence is therefore the determination of the relationship between C2 and R2 are related to
the relationship between C1 and R1 Myrdal says: "If the old and new real capital are of the same
type, then becomes (at C1=R1) also C2=R2". The kit appears as self-evident and its inclusion in the
chain of evidence that a song be bold - obviously changed nature of the investments - but possible
approximation. As soon be shown, however, leaves room for a fallacy, that breaks all the evidence.
If the provisionally accepted, it seems that the deduction complete.
13
Except in the following defined terms are used Myrdal well known (cf. anf. Piece. Sid.231) designation E for income, S
for savings (both terms as defined by Lindahl lines), Ku for entrepreneurs' gross income from the sale of consumer goods,
Ke consumer cost to the consumer and D depreciation minus the appreciation of the existing capital stock.
13 -33185. Ekonomisk Tidskrift 1932. Häft 5-6.
However Myrdal presented deduktionssättet may lack capital balance, that R2><S+D,,
mathematically obtained by a displacement of the relationship between C1 and R1, respectively. by
either of equations Ku=Ke and E=Ku+C2-D non satisfied. Suppose at first, to have C1<R1. With the
same deduktionssätt as before would one obtain C2<R2 and R2>S+D. The result is puzzling, since
the last formula indicates an inflationary trend but the initial change C1<R1 a deflationary tendency.
The fault lies obviously in the fact that man from C1<R1 close to C2<R2. This end is true, assuming
that the new investments are of the same species as the old, but it is wrong, when in the formula
R2>C2=S+D sounds and that formula be meaningful must let –R2 mean they actually planned
disbursements for investment purposes. If there is a negative return differential of the previous
investments (C1<R1), as anticipated, of course, not new investments of the same species as they age.
Nothing prevents, that entrepreneurs make investment losses, but they anticipate investment losses
and yet retain the investment plans, however, can not be imagined. A deduction, which requires the
adoption of this meaning, is prohibitive. One can therefore conclude that with the content which
must be added terms in the equations E=Ku+C2-D and R2=S+D, the magnitude C2 must be ≥R2,
independently of how the relationship between C1 and R1 is manifested. This means, however, that
the connection between the two equilibrium conditions in the formulation administered by Myrdal
completely broken, and further that not in the specified conditions of Myrdal head can have any
positive displacement of the capital account, such as Myrdal perceive and algebraic fix this. If you
have general C2>R2,, the R2 obtained >S+D, only if Ku assumed <Ke or lack of congruence in resp.
antecipationer payment lamellar entrepreneurs entails a net deduction from inkomstantecipationerna
=-A. In the latter
What is the nature of the imbalance in the capital market that obtained with the introduction of A or
revocation of adoption Ku=Ke? Apparently, it can only be in anticipation moment. An accounting
registration always gives Ku=Ke and also excludes the existence of a difference A. During the actual
market run, so as Myrdal capital market is always in balance, the second equilibrium condition can
head to have any meaning only if it is referenced antecipationerna. But if this is the case, one may
ask, how equilibrium condition can be relevant for the explanation of consumer price developments,
such as it is clear from the relationship vending power-consumption payments current, then the
fixation of the formula for the equilibrium interest rate in a given pricing instantly provides a gentle
also by the findings of bouts between different times. If you own R2>S+D, because Ku is <Ke, does
this mean in the real price discovery process only, the actual consumer goods prices tend to be
above the anticipated. The question, how consumer goods prices determineras in relation to
production costs through time allocation of consumption tive payments and production results
utmognande, thus, as far as the author. can be seen, not in explicit form Myrdalska included in the
analysis. For those of the author. in this matter and not in equilibrium fixation at a given moment to
see the real capital problem, therefore appears Myrdal's discussion on this point as flawed, insofar
as it refers to as a contribution to penningteoriens (Monetary Theory) utbyggande for practical
analytical purposes. Myrdal pointed out above ways to treat the relationship between relations C1|R1
and C2|R2 is attributable to certain shortcomings of earlier hinted kind also in the analysis of
räntabilitetsfaktorns importance for development. A discussion of this point, which is of less
interest in this context, seems suitably ought to wait until the Myrdal mentioned German version of
his investigation published.