Inflationary Effects of High Nominal Interest Rates
Author(s): Leon Podkaminer
Source: Journal of Post Keynesian Economics , Summer, 1998, Vol. 20, No. 4 (Summer,
1998), pp. 583-596
Published by: Taylor & Francis, Ltd.
Stable URL: https://www.jstor.org/stable/4538602
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LEON PODKAMINER
Inflationary effects of high
nominal interest rates
In the standard textbook view, rising interest rates should be followed
by lower prices. There are two ways to reach this conclusion: (a) higher
interest rates reduce money stock (suppressing demand for money)hence, on grounds of quantity-of-money theory-as well as the price
level; (2) higher interest rates imply that the economy is resting at an
upper part of the IS curve, meaning low effective aggregate demand and
hence, apparently, deflationary pressure. More recent standard macroeconomics textbooks work with the concept of the aggregate demand
function, through which price level and effective aggregate demand are
presumed linked. The aggregate demand function slopes downward
because of the presumed impact of interest rates on the price level (see,
for instance, Baumol and Blinder, 1988; Dornbusch and Fischer, 1984;
Mankiw, 1992; Stiglitz, 1993).
One obvious logical consequence of the presumed effect of interest
rates on price level is that rising interest rates should, ceteris paribus,
slow down inflation. This consequence seems to be of immense practical
importance. The IMF-sponsored stabilization programs for less-devel-
oped (and of late for the former centrally planned) economies usually
require, among other things, that monetary policy directly or indirectly
generate high interest rates. The minimum requirement is that interest
rates be positive in real terms (see Taylor, 1987, 1992, for discussion of
a typical IMF "conditionality"). Because the unfortunate proteges of the
IMF usually suffer from very high inflation, the nominal interest rates
engineered (or decreed) in these countries are often astronomical.'
Macroeconomic stabilization (not yet completed everywhere) of former
The author is Associate Professor at the Vienna Institute for Comparative Economic
Studies, Vienna. He expresses his thanks to an anonymous referee for valuable comments and acknowledges financial support from the Austrian National Bank.
1 The IMF-sponsored "shock therapy" applied in Poland at the beginning of 1990
stipulated a jump in the central bank's refinancing interest rate to 36 percent per
month, or about 4000 percent on the yearly basis (from 104 percent per year in December 1989). That was to reduce inflation, running at 18 percent per month in
Journal of Post Keynesian Economics I Summer 1998, Vol. 20, No. 4 583
c 1998 M.E. Sharpe, Inc.
0 1 60-3477 / 1998 $9.50 + 0.00.
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584 JOURNAL OF POST KEYNESIAN ECONOMICS
centrally planned economies is similar in that, in these countries, the
central banks have pursued policies resulting in very high real interest
rates (see Podkaminer, 1996).
The negative effects of restrictive monetary policy (and hence of high
real interest rates) on real activity tend to be acknowledged by mainstream macroeconomics. Contraction of aggregate demand-and
hence, often, of real output-is deemed an unavoidable cost of disinflation. As the experience of countries following the IMF guidelines
demonstrates, the costs of monetary restrictiveness may be high indeed.
(On the contrary, what is often observed is that the requisite effects of
restrictive policy on inflation do not materialize.)
Other unwelcome consequences of high (real) interest rates are also
discussed-though rarely in textbook expositions. A policy of high real
interest rates sustained over a sufficiently long period, even if it does
not result in a recession, often brings about a collapse of the banking
system. The latter outcome is convincingly discussed in Calvo (1992)
and McKinnon (1993). The recent banking crisis in Bulgaria is, arguably, due to very high (double-digit) real interest rates sustained for
almost two years (Podkaminer, 1996). The Chilean crisis of 1982-83
had similar roots. To the extent that restoration of financial order cannot
be achieved without a period of inflation restoring the proper balance
between banks' liabilities and assets (whose quality usually deteriorates
strongly during the period of high real interest rates), the policy is
counterproductive in terms of disinflation. Then, a high interest rate may
in fact be responsible for inflation, because it may well serve as a
reference point for inflationary expectations prevailing in the economy.
Price-setting firms and trade unions bargaining over wages may be
unaware of what macroeconomists believe is the link between interest
rates and the price level. The instinct seems to be to proxy future inflation
with current interest rates (see McKinnon, 1993).
Finally, high interest rates depress stocks of commodities throughout
the economy-particularly in retail trade. The costs of maintaining
December 1989, to less than I percent per month within six months. The December
1990/December 1989 inflation was to be less than 95 percent, while output was to
contract 1-2 percent. In fact, output contracted in 1990 by nearly 12 percent, while
inflation in 1990 reached about 250 percent. Only in January 1990 prices jumped by
80 percent. As industrial production fell by 25 percent, the necessity to reduce interest rates became obvious. Gradual reduction in interest rates, motivated by the concern over production, contributed, in time, to gradual disinflation. (Monthly inflation
came down to I percent only by mid-1997.)
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INFLATIONARY EFFECTS OF HIGH INTEREST RATES 585
"normal" stocks are magnified by interest costs. Even if production
capacities are grossly underutilized, the actual "market excess supply"
is either low or nonexistent. This gives the retail traders a quasi-monopolistic edge vis-a-vis the buyers. An occasional increase in demand tends
to be exploited by charging higher prices, rather than by placing additional orders with producers.2 An excess productive capacity does not
moderate price hikes, which should normally be expected under excess
supply in a competitive market.
That high interest rates can have direct inflationary effects through
higherproduction costs (i.e., costs of financing workingcapital)3 has not
been claimed, at least not explicitly, in the literature. Opinions of
Galbraith (1957) and Taylor (1983, 1992) are quite exceptional. Taylor
(1983, ch. 5) convincingly argued that a monetary contraction could, by
increasing interest rates, be stagflationary, that is, it could combine the
working-capital cost-push (due to nominal higher interest rates) with a
decline in investment demand (the so-called Cavallo effect). Clearly, in
Taylor's formulation, a rising interest rate may push up the price level.
What is not quite clear in that formulation is what to expect from prices
at a given, unchanged, level of the interest rate-if that level happens
to be high.
This paper advances the following proposition:
A sufficiently high, constant, nominal interest rate is alone capable
of generating steady inflation.
The next section examines a dynamic process of cost-price adjustments
when all working capital is financed by credit. The underlying model is
akin (but not identical) to the standard multi-good Sraffian model and,
of course, bears a resemblance to some aspects of Taylor's (1983)
approach. Upon application of relatively simple algebra, it is demonstrated that, even if nominal wages and the markups are constant, any
positive nominal interest rate has an inflationary effect. Properties of the
2 Another inflationary "abnormality" appearing under overly restrictive stabilization
policy derives from structural shifts in consumer demand and a structural supply inflexibility-both caused by the policy itself (see Podkaminer, 1995).
3 If high interest rates depress aggregate demand to the extent that output also contracts, unit cost of output is increased because of the rising burden of fixed costs
(depreciation of underutilized fixed assets and overhead expenses in the first place).
This is an indirect effect of high interest rates on costs, not discussed in this paper,
though it may be important to understanding inflationary acceleration observed
under overly restrictive monetary policy (see Podkaminer, 1993; Laski and
Podkaminer, 1995).
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586 JOURNAL OF POST KEYNESIAN ECONOMICS
input-output matrix alone determine the character of the ensuin
tion. There is a single indicator, specific to any input-output mat
turns out to be decisive. If the nominal interest rate is lower tha
indicator, inflation is dying out on its own (i.e., prices are rising
monotonically-but they converge to a limit), even if the interest rate is
kept constant all along. If the interest rate is higher than the matrixspecific indicator, inflation is steady-prices keep rising without converging to a finite limit. The focus then turns to deriving similar
conclusions outside the linear cost-price accounting framework. It turns
out that, under arbitrary sets of cost functions (in line with arbitrarily
postulated technological properties of production), high nominal interest rates may generate steady inflation. Again, a single technology-related indicator defines the upper limit of the nominal interest rates at
which prices must converge on their own.
The dynamic process of cost-price adjustments under linear
production technologies
The following assumptions have been adopted:
1. There are n different commodities, each produced by a separate
firm, or sector.
2. Production technologies are all linear. Labor is required directly
or indirectly in production of each commodity. ij is the direct labor
input in production of jth commodity, wj is the corresponding
nominal wage rate, and the product wjlj ( = W) is the direct unit
labor (wage) cost of commodityj. Let aj (ij = 1,2,. .. ,n) be the
quantity of commodityj needed to produce one unit of commodity i.
Matrix A = [a1j] is assumed to be viable and indecomposable (in
the terminology of Kurz and Salvadori, 1995).
3. Production takes one period of time. Inputs are purchased at the
beginning of the period. All purchases are financed by credit, paid
back (with interest) at the beginning of the next period. The
interest rate (nominal) is r.
4. Pricing of commodities is based on costs borne by firms. Price
pi(t + 1) of commodity i charged at the beginning of period t + 1
equals (1 + r)(1 + mi)[Wi + ,auijpj (t)] where m, is the markup.
5. All parameters (aij, m " Wi, r) are constant over time.
Assumptions 1, 2, and 5 are standard starting assumptions for the
elementary theory of "linear economic models" in the spirit of Sraffa,
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INFLATIONARY EFFECTS OF HIGH INTEREST RATES 587
Morishima, David Gale, and others (see Kurz and Salvadori, 1995, for
a comprehensive exposition). That theory also assumes that production,
in each sector, takes one period of time. But it does not pay much
attention to the way working capital is financed. The interest rate is not
singled out in the pricing formula. Instead it stipulates the pricing
formula aspi(t + 1) = (1 + m*)[Wi + y2aypj (t)], where m* is a markup
(usually assumed, in that theory, to be equalized across sectors) on direct
costs of labor and intermediate inputs. This formula may imply that all
working capital is financed out of a firm's own means (e.g., retained
earnings). Yet, formally, this pricing formula can also be used when a
part, or all, of working capital financed is borrowed. If the prevailing
interest rate on credit is r (and the spread between lending and deposit
rates is negligible), all firms, irrespective of their own financial endow-
ments, should be indifferent to the way working capital is financed. This
implies that the markup m* is related to the interest rate in the following
manner: (1 + m*) = (1 + r)(1 + m), or m* = (1 + r)(I + m)-1), where m
is "our markup"-that is, the markup on interest-augmented direct costs
of labor and intermediate inputs.
That sufficiently high nominal interest rates must have inflationary effects
can be seen immediately from the pricing formula in assumption 4. Even
in the most extreme case, with all Wj and mj equal zero, if I + r >
(maximaxj{ay pj (t)/pj(t))-', thenpj(t + I)pj(t) for eachj. Of course, with
positive direct unit labor costs and markups, all prices may be rising
even if the interest rate does not satisfy this condition. This can be seen
from the formula for the price differences p(t + })-p(t):
(1) pi(t + I)-p,(t) = (1 + r)(1 + mj)YJ,.a(pj(t}-p(tl))
Because r, all aij, and mi are nonnegative, it follows from equation (1)
that, if all p(t)-p(t-l) are positive (meaning inflation in period t), then
all p(t + 1)-p(t) are also positive-meaning inflation in period t + 1.
In matrix notation, equation (1) has the following form:
(2) Ap(t + 1) = (1 + r)MA Ap(t),
where Ap is the vector of price increments, andM
with elements (1 + mj).
Equation (2) is equivalent to:
(3) Ap(t) = (1 + r)tMtAtp(O).
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588 JOURNAL OF POST KEYNESIAN ECONOMICS
Let us assume Ap(0) is nonnegative (though not necessarily positive
in all coordinates), representing an initial inflationary impulse. According to equation (3), any such impulse has permanent inflationary consequences. The interesting question is whether or not the resulting
inflation will die out, that is, whether each coordinate of Ap(t) converges
to zero as t goes toward infinity. Because of the properties of matrix A
specified in assumption 2, all elements of At converge to zero. But all
(1 + r)t (1 + mr)' diverge (go to infinity). To derive the convergence
condition for Ap(t), one may invoke two well-known mathematical
facts :4
(a) Any square matrix A can be spectrally represented in terms of its
eigenvectors and eigenvalues. A' is then represented in terms of
eigenvectors of A and polynomials of order t of eigenvalues of A
(see Friedman, 1956, pp. 110-1 17, or Sandefur, 1990, p. 308).5
(b) The largest real eigenvalue X of an indecomposable, semipositive,
and viable matrix A is positive (and less than 1); the associated
eigenvector is positive (Perron-Frobenius theorems; see Kurz and
Salvadori, 1995, pp. 509-519).
It follows from (a) and (b) that for large values of t, each Api(t) is
approximately equal to [X(1 + r)(I + m,)]'ci, where c' is a positive constant.
This expression converges to zero only if A < (1 + r)-'(1 + mY)'. Ap,(t) equals
ci if X =(1 +r)-'(1 +m<)- andtends to infinityifX>(I + r)-'(1 +mY<. Hence,
all prices will stabilize only if the following condition is satisfied:
(4) X < (I + r)-1 maxi I 0 + mX) }
Alternatively, the adjustment process stabilizes only if
1 +r<?k-maxi{(1 +m,X)1-}.
If equation 4 holds, the unique limit (positive) price vector p exists and
is given by the following equation:
(5) p = [I- (1 + r)MA]-'W,
4 Mathematical conditions for the convergence of systems of linea
tions have been known to economists since at least the early 1 950s. Th
statement is in Nikaido (1968).
S The polynomial representation assumes no repeated eigenvalues. When A has repeated eigenvalues, the representation of A' is slightly more complex. The properties
of that representation for a large value of t are the same as of the polynomial one. In
our case, only the largest eigenvalue matters.
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INFLATIONARY EFFECTS OF HIGH INTEREST RATES 589
where I is the identity matrix. If equation 4 does not hold
limitless.6
If prices converge, the equilibrium price vector is linearly related to
the vector of unit labor costs-hence to the wage rates. According to
equation (5), whether or not the process converges does not depend on
the wage rates or unit labor costs. Prices can rise (possibly without any
limit) even if nominal wage rates stay constant. This may explain why
the conventional programs to stop very high inflation by freezing wages
under very high interest rates quite often fail. The cost-push inflation
does not need wage-price spirals to operate. Certainly, if wage rates
were indexed to prices, inflation would be higher and more "explosive."
Under wage indexing, the maximum interest rate consistent with price
stabilization r° would, paradoxically, have to be lower.
It is worth noting a certain similarity between equation 5 and the
post-Sraffian (and other linear economic models') analyses of equilib-
rium prices (see, e.g., Kurz and Salvadori, 1995, pp. 98-100). The
post-Sraffian analysis assumes uniform markups and wage rates and
ignores the interest on credit. Equation (5) generalizes formula (4.7)
from p. 98 in Kurz and Salvadori. Maximum positive (and uniform)
markup consistent with the equilibrium price system equals, in Kurz and
Salvadori, (1 - X)/X, where X is the largest real eigenvalue of A. Our
condition 4 for the case with uniform markup is: X < (1 + r)- (1 + m)-1.
Maximum uniform markup, given r, consistent with the price convergence equals, in our model, (1 - (1 + r)X)/(X((l + r)). Maximum interest
rate r°, given the markup m, consistent with price convergence equals
(1 - (1 + l) ,)/(( 1 + m)).
There is a fundamental difference between the purpose of "Sraffian"
(and most other linear economic models') analyses and that of our
reasoning. The Sraffian analysis is interested in some properties obtain-
ing under the equilibrium price system and, primarily, in the implied
relationship ("trade-off') between real wage rates and profit rates. It
studies economies where relative prices have already converged to the
values covering costs and (equalized) markups. As in any other general
equilibrium theory, it has to abstract from the inflation problem. This is
perhaps best seen from the fact that prices in the Sraffian system are
6 The equations pi(t) = [X(1 + r)(1 + mi)]tci imply that, for large values of t, the
rates Api(t)/p,(t-I) are proportional to the factors (i-gi))/( l-gi) where gi = ( l +
mi)(l + r). From this it follows that if(l + r) > k- (1 + mi)-1, then the rate at which
ith price rises approach the constant positive value-that is, in due time prices will
rise exponentially. (If condition [4] holds, that rate goes to zero.)
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590 JOURNAL OF POST KEYNESIAN ECONOMICS
"normalized": Their weighted sum is unity.7 The analysis does not ask
questions about the dynamic price (inflation) consequences of exogenously fixed markups (or, by implication, interest rates) exceeding the
limits of a technologically possible price equilibrium.8
Our model may be considered concerned with situations where the
stable price equilibrium has yet to be reached. Interest rates (and also
markups and wage rates) are not endogenized: No theory is here
advanced, or assumed, about mechanisms bringing these parameters
into positions necessarily consistent with a technologically possible
price equilibrium. Admittedly, our reasoning may be relevant for the
description of developments running their course when negative feedback from the demand side, or from economic policy, is weak, or
nonexistent.9 One consequence of the non-satisfaction of formula 4 is
that too high markups required by firms and/or too high an interest rate
prevailing in the economy may be incompatible with the technologically
possible stable price equilibrium. To the theory of linear economic
models, such a situation does not seem to be interesting or meaningful.
But, in practice, such a situation is only too easy to imagine and therefore
7 Observe that, if the markups were the same across sectors, then, under the assumptions made on matrix A, all relative prices would converge to fixed limits no matter
how large the interest rate and the markup are (and hence whether or not inflation is
limitless). Because Api(t) = [X(l + r)(l + m)]'ci, then Ap1(t)/Ap(t) equal, for large t,
c/Cj, for all i,j.
8 Early authors of multisector equilibrium growth models studied long-run properties of paths of output and income shares. Less effort was spent on the study of price
dynamics. That is understandable: A simultaneous analysis of prices and quantities in
a general equilibrium analysis is in most cases rather difficult, even in a static context. Importantly, static general equilibrium analysis does not explain the price level.
In multisector growth models, the results on the existence and stability of equilibrium
paths of output were derived with prices being "normalized" to unity, thereby ruling
out inflation. An "alternative dynamic system" studied by Morishima (1964, pp. 93130) seems unique in its concern with the paths of absolute and not merely relative
prices. One assumption under which that system is stable is that "an appropriately
small (positive) value is preassigned to the rate of interest rate" (p. 96). Morishima
did not derive analytical condition for "appropriate smallness of interest rate." The
nature of eventual instability was not explained. A boundless inflation was never
mentioned: Instability implied might refer (a) to prices converging to different finite
limits, depending on their initial values, or (b) to prices "circling" without ever settling down within a certain bounded area.
9 The feedback from the economic policy is likely to be "positive," meaning it is
likely to reinforce inflation. If, in response to rising prices, interest rates are increased, the cost-push inflation accelerates too. There is, in general, no guarantee that
the feedback from the demand side must be "negative"-that is, automatically restricting inflation.
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INFLATIONARY EFFECTS OF HIGH INTEREST RATES 591
worth studying. An economy with excessive interest rates does no
functioning. One possible escape route for such an economy is through
inflation. The other is contraction of output, or accumulation of bad
debts finally resulting in a financial crisis.
There are some practical lessons to be drawn from our reasoning.
According to formula 4, the maximum interest rate ro consistent with
price convergence is inversely related to X. But X itself is, for matrices
of the type assumed, less than 1 and is an increasing function of each of
the matrix elements (see Kurz and Salvadori, 1995, p. 517). The larger
the matrix elements, the larger X-hence, the smaller the maximum
interest rate ro. Recall that the matrix elements ai1 express technological
efficiency of production. The higher aij, the lower the efficiency. It
follows that maximum "harmless" interest rates in more efficient economies are higher than in the less efficient ones. More efficient economies can operate under high interest rates without pronounced
inflationary effects. In the less efficient, notably the underdevelope
economies, even much lower interest rates must generate protracted
inflations. Technological progress reflected in matrix elements aiq decreasing overtime may certainly offset the inflationary effects of interest
rates. That may explain why, in economies enjoying vigorous technological change, the inflationary effects of even quite high interest rates
may be negligible, or nonexistent. On the other hand, underdeveloped,
stagnant, and disturbed economies, where there is little or no technological improvement and where very high interest rates prevail, are likely
to suffer from permanent inflation.
Cost-price adjustments with arbitrary cost functions
The underlying production technology of model ofthe preceding section
stipulates fixed input-output coefficients for all commodities at any
output levels, thereby ruling out possible substitutability of inputs and
scale-of-production effects. Firms in a Leontief economy always purchase inputs in fixed proportions. Their unit production costs are therefore entirely determined by prices of inputs. Within a more general
production model, unit costs may be adjusted more flexibly, by changing
the composition of inputs (choosing relatively cheaper input substitutes)
or by varying the output level to exploit possible scale effects. Arguably,
inflationary effects of rising costs, in a model assuming arbitrary production functions for each commodity, may be less pronounced than in
the linear case. But, as will be demonstrated, the inflationary effects of
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592 JOURNAL OF POST KEYNESIAN ECONOMICS
sufficiently high nominal interest rates are present here as well, a
as long as the scale-of-production effects are not considered.
For this section the following assumptions are now adopted:
1. There are n different commodities, each produced by a separate'0
firm, or sector.
2. The production technology of the ith firm is summarized by a
(sector-specific) production function, which is rising with each
input and continuous.
3. Producers are input-price takers, adjusting input mix to input
prices in such a way as to minimize the total cost of producing
output whose level is assumed constant.
4. Wage rates are fixed, and so are employment levels (eventual
substitution among intermediate inputs does not affect the amount
of labor hired).
5. Production takes one period of time. Inputs are purchased at the
beginning of the period. All purchases (and payments of wages)
are financed by credit, paid back at the beginning of the next
period. The nominal interest rate is r.
6. The pricing of commodities is on the basis of costs incurred by
firms. Price pi(t + 1) of commodity i charged at the beginning of
period t + 1 is given by the following equation:
(6) pi(t + 1) = (1 + mi)(l + r)[W1 + Qyi,p(t))1yi],
where mi is the ith markup, r is the interest rate, Wi is the unit wage
cost, CQ(yi,p(t)) is the minimum level of nonwage costs of produc-
ing outputyi at prices p(t).
7. All parameters in equation 6 are constant over time; technologies
do not change so that the cost functions Ci do not evolve.
That a sufficiently high interest rate must have inflationary effects can
be seen at once from the pricing formula in assumption 6. Even if
markups and wage bills were zero, the unit costs of intermediate inputs
C/Iyi on the right-hand side of the equation are always positive and hence
at sufficiently large r, all pi(t + 1) would be higher thanpi(t). To derive
a more precise characterization of the inflationary potential of high
interest rates, let us formulate equation (6) as follows:
10 In fact, one can assume that each firm produces a bundle of goods. Assumption I
is adopted chiefly for the sake of greater notational simplicity.
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INFLATIONARY EFFECTS OF HIGH INTEREST RATES 593
(7) pi(t + 1)-p,(t) = (1 + m,)(1 + r) [C,(y,,p(t))C,(y,,p(t-1))]/y,
If p(t) > p(t-l), then for each i the cost Ci(t) is higher than
Consequently, irrespective of Wi, there is always a sufficiently l
such that p(t + 1) > p(t).
Because of the generally nonlinear nature of cost functions, it is m
difficult to say whether, and under what conditions, the dynamic ad
ment process described by equation 6 converges to a limit." On
however, invoke the theorem on contracting differentiable map
(see Kantorovich and Akilov, 1982, pp. 501-505) to derive a r
strong, but simple, condition for prices to converge. In our ca
following theorem holds:
Iffor every p and eachj, there exists a constant a (less than 1) such t
(8) (1 + r)E, (1 + mi) (6C,(y, p)/6pi) lyi < a
(where 6Ci(yi, p)/6p is a partial derivative of Ci with respect t
evaluated at p), then the process given by equation 6 converge
a unique and stable equilibrium p°, irrespective of the initial p
Nothing certain can be said about the existence or stability of
limit to the process ifequation 8 is not satisfied: In this case pr
may go to infinity, or keep "circling, " or may converge (dive
depending on the initialprices. One cannot rule out the possibi
that they may reach some equilibria, some of which may eve
happen to be stable.
Condition (8) has a simple economic interpretation. 6C,(yi,p)/6pj
ally equals the cost-minimizing quantity of commodity j used in
duction of y under prices p (see Diewert, 1991, p. 692). Let us d
that quantity by xi(yi,p). Thus, the maximum interest rate r° guaran
ing convergence of the cost-price adjustment process satisfies th
lowing condition:
(9) (1 + r°)maxjp{Si (1 + mi)xi(yi,p)/yi} < < 1
The ratio xi(yi, p)/yi is the cost-minimizing (variable) input-output coef
1 Systems of nonlinear differential equations studied by Solow and Samuelson
(1953) and Nikaido (1968) are mathematically akin to equation 6. The conditi
for convergence of such systems summarized by Nikaido refer to the behavior
tios of the dynamic variables (in our context, they would refer to the convergen
relative prices). As such, they cannot be invoked in this context.
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594 JOURNAL OF POST KEYNESIAN ECONOMICS
of producing yi with thejth input (given input prices p). Equivalentl
(10) 1 + r° < (maxjp{£i (1 + m,)x,(y,p)/y})-'.
In light of equation 10, the higher input-output coefficients and ma
the lower the maximum r°-precisely as in the linear case of th
section. When the markups happen to be uniform, one has
1 + r° < (1 + m)-1 (maxjp {Si xi(yi,p)/yi})- .
Assuming all xy(yi,p)/yi are independent ofy and p, one returns
linear case (with xij(yi,p)/yi = aij). Condition (10) takes on the fol
form here:
(11) 1 + r < (1 + m)-l(max {Zl,ai})-l.
For any r° satisfying equation 11, the cost-price adjustment pr
converges to a unique limit given by p = [I-(1 + r°)(1 + m)A]-lW
may be observed that condition (11) is generally more restrictive tha
r° < (1 + m)-l1-l derived earlier. This is because, for nonnegative matri
the maximum eigenvalue X < maxj {£,a.}. Therefore, condition (11
disqualify some r that are in fact still consistent with the convergen
A postscript
The preceding discussion has shown that, when pricing is based on costs
incurred by firms, a sufficiently high interest rate may result in prices
rising without limit. This proposition holds even if markups and wage
rates are reduced to zero. The cost pricing implies no role for final
demand. In particular, consumer preferences do not affect prices; nor
do they affect the quantities of commodities produced. A general
multicommodity dynamic model is still to be formulated that assumes
a greater role of demand conditions in the formation of prices and
quantities and yet indicates that too-high interest rates may generate
prices rising without limit.13
12 See Nikaido (1968, p. 108).
13 The literature on the stability of the price adjustment process in the general equilibrium models is very rich (for an advanced treatment of the subject, see Fisher, 1983).
Inflation as such is not tackled in the stability studies because they are concerned
with conditions for the convergence of relative prices. Boggio (1992) reviews various
issues relevant to the study of long-run stability of"production prices" when the (endogenized) demand conditions matter. From that perspective, the inflationary instabilities
due to endogenously imposed markups may be considered economically meaningless.
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INFLATIONARY EFFECTS OF HIGH INTEREST RATES 595
Attempts to stop high inflation typically involve policies resulting in
positive real interest rates. Nominal interest rates are, under such conditions, often quite astronomical. There are yet some technologically
determined limits for the nominal interest rates an economy can endure
without a risk of generating, or sustaining, inflation. Anti-inflationary
policy programs implying high nominal interest rates may well turn out
to be counterproductive.
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