PROFITABLE DESTABILIZING SPECULATION AS INTERTEMPORAL PRICE. DISCRIMINATION by David H. Feldman and Edward Tower*. In "The Case for ...
PROFITABLE DESTABILIZING SPECULATION AS INTERTEMPORAL PRICE DISCRIMINATION byDavid H. Feldman and Edward Tower* In "The Case forFlexible Exchange Rates" Milton Friedman [4, p. 175] developed the proposition that destabilizing speculation is necessarily
unprofitable.
On
the same
page
through,he qualified his proposition by not ing that a full analysis of the problem would require a satisfactory definition of exactly what constituted both speculation and desta bilizing behavior. He recognized that it is difficultto separatewhat he analyzed, namely in the sense of purchasing "pure speculation" now for resale later under conditions of un from other sorts of transactions. certainty, for example, the "speculator" who Consider, to set price. This could his power recognizes come together to be a group of sellers who form a cartel. In this paper we explore how can earn profit by intertem such a speculator porally
destabilizing
worsen
the welfare
the price. Moreover,
note that destabilization may
we
improve or
of nonspeculators.
The literatureon destabilizing speculation
has passed through a number of stages. Early to refute Friedman's attempts proposition rested on very particular counter-examples. Baumol around [1] built a counter-example
unrealized paper profits and Kemp one
based
speculative
on a excess
backward bending demand function.
[2] built non
In the
late 60s Farrell [2] showed that in the pres
ence of a fluctuating excess demand function an increase in the variance of price could if the ex accompany profitable speculation cess demand in each time period function is in as of other prices independent periods, long as it is nonlinear covers and the speculation more than two time periods.1 He did not, on state conditions however, nonspeculative
demand under which profit fromprice desta bilization
actually
would
occur.2
Newberry's analysis [8] of stochastic limit
pricing3 is closer to ours in that the profita bility of a destabilized price is explored in the context
of a speculator-producer
with market
power. Newberry shows that price destabili zation may be both profitable and welfare improving to nonspeculators (relative to a fixed pricemonopoly outcome) iftheprice is randomized
between
values
above
and below
the limitprice and if themonopoly price is sufficientlygreater than marginal cost.4 He argues that the absolute value of the price elasticity of demand must be falling suffi ciently rapidly at the limitprice in order for price destabilization of this sort to be profit able.
This condition, is overly strong. however, a We reve nonmonotonic identify marginal nue curve as the source of the profitability of to a pro price destabilization intertemporal
= ducer-speculator. Since MR P(I I/77), where 77is the absolute value of the price elasticity
of demand,
nonmonotonic
MR
can
arise only when this elasticity falls with in
et al. (3) creased price. However, Formby have shown that the conditions under which revenue is upward marginal sloping are not
as stringentas formerly thought. Positively revenue can be generated by sloping marginal con of well behaved simple transformations vex demand functions.5
I. Inelastic Supply In order to focus on the intuition behind the problem we first consider the simplest necessary
possible
diagram
between
F and D'.6
tomake
the point.
In figure 1 SBS' is themarginal cost of pro is the demand curve, duction and DAEFD' which isflat in rangesDA and EF, has unitary elasticity between A and E and is vertical The
corresponding
mar
* Colgate University, and Duke University, respectively. Our thanks toAnthony Brewer and Kent Kimbrough for helpful insightson earlier drafts and to an anonymous refereewho helped shape this version. Remaining errors are the property of the authors. Parts of this paper were written while Feldman and Tower were visiting at Duke and Simon Fraser Universities, respectively. 60 Sage Publications Inc. is collaborating with JSTOR to digitize, preserve, and extend access to The American Economist www.jstor.org
®
from the supply curve of figure 1.OALL'
s
revenue
the total
curve
is
that corresponds
to
figure 1 's demand curve. By destabilizing the the
price
total
revenue
attainable
production level between A'
for any
and R will lie
Thus the marginal along the segment AT'. revenue curve ismade convex. The cartel will
B. 0 S .I
ID
choose to produce at R and destabilize the price as long as the slope of AT' exceeds the slope ofOC, or in otherwords as long as the modified marginal revenue exceeds marginal
|A 'E
Quantity
ij'
! ! IMC2/V\! \ \!B' I 1/ // \c? MC4
ginal
Com
at A, with an obvious the market loss to consumers (an efficiency cost
as well), and monopoly profits to be divided
between
was discrimination price in the preceding analysis be
cause of the upward discontinuous jump in revenue
the marginal
curve.
This
issue
is
the total cost curve, C, to reflect cost. The total revenue curve, rising marginal
petitive equilibrium is at E. Suppose that the suppliers forma cartel but feel constrained to maintain a fixed price. They will choose to supply welfare
II. The General Case
have
1and 2
is DAA'REFD'.
be profitable.9,10
demonstrated more generally infigure 3.We
*Z
curve
may
Intertemporal made profitable 0 \Quantity
revenue
speculation
\/
\jytf Jy
FIGURES
Such intertemporal price discrimina or raises sup tion, speculation, destabilizing demanders' and eco welfare pliers' profits, nomic efficiency above the levels in the mo
nopolistic uniform price case. This then is found a new sense in which destabilizing
! MC3I
\ MC,,' |
cost.
the suppliers.
Now suppose that the cartel no longerfeels
to supply at a given price all of constrained the time. Suppose also that the cartel has a on intertemporal monopoly storage or, alter
natively, that the good is perishable once
consumers reve the marginal buy it.7 Using nue curve DAA'REFD' the cartel could pro
duce OR units in every period, selling at A a fractionRD'/A'D' of the time and dumping the surplus at the price Pc (above marginal cost) the remaining fractionA'R/A'D' of the time.8The condition under which this inter temporal price discriminationmaximizes car tel profits is shown in figure 2. The kinked curve OC'C is the total cost curve derived
drawn
R, is drawn with inflectionpoints (Ii and I2) so that it isconsistentwith a marginal revenue curve that isboth nonmonotonic and upward sloping
over
part
of the
relevant
range
of
quantities. IfR intersectseach ray from the origin only once, and each time from above, curve has the normal downward the demand slope. The
standard
outcome
monopoly
is pro
duction at D where the vertical distance be teen R and C
In the case of the
ismaximized.
price discriminating cartel the total revenue attainable for any production level between B and E can be made to lie along the segment B'E' by sellingat B' and at E' forappropriate fractions of the market period. The total rev enue curve is again made convex by destabil
izing pricing behavior. To maximize profits the cartel will choose to produce where the vertical distance between themodified total revenue
curve
OB'E'Z
and
the
total
cost
curve ismaximized. This is shown as point A infigure 3. To exhaust itsproduct the cartel must sell at B' a fractionAE/BE of the time 61
Price
Z'B'
A
.
Pc
the marginal
Using
output increases under the cartel's If, however,
_
____.IGV^
or E'Z.
cost curve
derived fromfigure 3's total cost curve (MC2)
S'
price discrimination. single price
optimum
lies to the rightof point S in figures 3 and 4 then price discrimination increases cartel profitsbut reduces the level of output.11
E-F
III. A FurtherGeneralization
S-j-'B
Johnson [6] has analyzed speculation in a general equilibrium framework using an
J-J-J-^Quantity
can also box diagram. We Edgeworth-Bowley do a general equilibrium which sim analysis
C
ply requires us to reinterpretfigure 3. Just
L'
-*" y^ ^ -*"^ S
think of dollars
i I
^X
on the vertical
axis as a second
commodity. Then if the home country im ports dollars and exports Q, R becomes the
if the "do foreign offer curve.12 Furthermore, actor consumes mestic" dollars then C only a domestic becomes trade indifference curve, since all points along it involve zero produc cost curve, when er's surplus, the supplier's
i
shiftedvertically, lays out the entire indiffer
ence map. ()/?-fe-DTQu0ntlty
FIGURES 3 and 4
the cartel
equates
revenue
marginal
periods (the slope ofR at B' and E'). interemporal
arbitrage
of marginal
in both
It is this revenue
that permits profit from destabilizing the price. As with other forms of price discrimi it is not hard to show that consumers' surplus, and economic efficiency, may rise or
nation
fallwith the advent of price discrimination. It is interestingto note that this formof price discrimination does not rest on exploiting preference differences between individuals but rather involves treating identical con sumers
differently
over
time.
and
clearly
shows
the range of situa
tions for which price discrimination is the
outcome. The marginal profit maximizing revenue curve Z'BTiI2Z to the corresponds
total revenue curve in figure 3. The modified
marginal
revenue
curve
is Z'B'A'E'Z.
Price
discrimination will not occur ifmarginal cost intersects
62
marginal
revenue
supplier the domestic
in
the
ranges
in true general
equilib
cum speculator would per private sector to trade con
tinually at the price-quantity point given by the tangency of his trade indifferencecurve to the modified
total revenue
curve. Thus,
in
general equilibrium we see that the optimal solution
for the domestic
country
is to com
bine the use of fluctuating inventorieswith
either state trading or else a fluctuating mum import tariff.
opti
NOTES 1. Farrell's suming
to as independence assumption requires do not store the good that non-speculators
in question. Given
fluctuating
Figure 4 illustratesthe issue usingmarginal
curves
course,
and our mit
and at E' a fractionBA/BE of the time.Thus
Of
rium such vertical parallelism need not hold,
the independence assumption,
non-speculative
excess
demand,
and
no
transactions costs he shows that linearity of the nonspeculative demand function is both necessary and sufficientforFriedman's proposition to hold. 2. Hart [5] dispenses with Farrell's independence as sumption. He finds conditions under which spec ulation is profitable, given that speculation is dis turbing a stationary state equilibrium. Intertem poral price relationships are important toHart but in his model non-speculators make decisions fol lowing ad hoc rules and expectations formation is
notmodelled. It isnot possible to draw conclusions about welfare inHart's frameworkbecause demand price reflectsmarginal utility conditioned on ex pectations which may not be fulfilled. 3. The limit price is the price at which?if itwere expected to persist?oil consumers would be will ing to undertake costly projects to switch to other forms
of energy.
4. His result is not dependent upon assumed behavior toward risk. 5. Consider the demand function q = 600/?"M + 4 500/?~3 which isa summation of constant elasticity functions. This example is presented in Formby, Layson and Smith [3]. 6. Production of mineral water, crude oil or electric power may exhibit this sort of marginal cost step function.
7. Perhaps the good is gasoline and there are econ omies of scale in building storage facilities. Since over marginal sells at a markup cost, the to a non-cartel of storage storer is higher than to a cartel storer.
the cartel cost
8. To maximize profit the cartelwill choose to sell at a rateOA' per period (at price OD) for the largest fraction (#0 of the period possible, subject to the constraint that itbe able to sell the restof itsoutput in the remaining fraction of the period {2). Hence to sell at price OD for as long as possible within each market period requires disposing of the re mainder of itsper period output (at price Pc) at the quickest rate possible consistent with themarket demand
curve,
or at OD'
per period.
Given
4>\OA'
= 1we obtain = + 02 OD' = OR and 0, + 2 fa and fa = A'R/A'D'. RD'/A'D' 9. A logical extension of this argument would involve modeling cartel behavior under conditions of un certainty.This would require some notion of how individual suppliers within the cartel form expec tations about demand conditions. This would more closely identifythe above argument with some of the literatureon destabilizing speculation that has developed
mol
since
Friedman's
[1] and Hart
early work.
See
Bau
[5] and the references cited
therein.
10. Figure 1 can be used to tell a wholly differentstory of destabilizing speculation yet one which yields the same
conclusion
with
respect
to intertemporal
price discrimination. Suppose that supply is com petitive. Furthermore, suppose that suppliers have
become accustomed to selling each period at Pc. Suppose also that a single speculator initiates a forwardmarket and that all sign forward contracts to sell theirwhole output to this speculator at Pc. Assume that the good isperishable so that the total quantity produced in each market period must be sold in that period. Once the speculator has cor nered themarket he will be able to secure a profit of DAGPc in those fractions of themarket period when he sells high while disposing of his excess inventories at cost the restof the time. 11. IfMC intersectsMR such thatwe have two equal profit levels of output then output could rise or fall with the advent of a destabilized price.With price destabilization themodified MR curve has no up ward sloping position. As long asMC is an increas ing function of quantity therewill be a single profit maximizing output choice. 12. For an analysis of what circumstances might give rise to inflectionpoints in the offercurve see Tower (1975). References 1. Baumol, W. J. (1957). Speculation, Profitability, and Stability. Review ofEconomics and Statistics 39 (Aug.): 263-71. 2. Farrell,M. J. (1966) Profitable Speculation. Econ omica 33 (May): 183-93. 3. Formby, J. P., Layson, S. and Smith,W. J. (1982). The Law of Demand, Positive Sloping Marginal Revenue and Multiple Profit Equilibria. Economic Inquiry 20 (April): 303-11. 4. Friedman, M. (1953). Essays inPositive Econom ics,Chicago, 111.: University of Chicago Press. 5. Hart, O. D. (1977). The Profitability of Specula tion. Quarterly Journal of Economics 41 (Nov.): 579-97.
6. Johnson, H. G. (1976) Destabilizing Speculation: A General Equilibrium Approach. Journal ofPolit ical Economy 84 (Feb.): 101-108. 7. Kemp, M. (1963). Speculation, Profitability, and Price Stability.Review ofEconomics and Statistics 45 (May): 185-9. 8. Newberry, D. M. G. (1978). Stochastic Limit Pric ing.Bell Journal ofEconomics 9 (Spring): 260-69. 9. Tower, E. (1975). On theFunctional Relationship Betweeen Tariffs and Welfare. Journal of Interna tionalEconomics 5 (May): 189-199.
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