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Dumping at less than marginal cost
Journal of lntemational Economics 12 (1982) 169-182. North-Holland Publishing Company
DUMPING
AT LESS THAN MAtRGINAL COST Stephen W. DAVIES
Universiry of East Anglia, Norwich NR4 7TJ, UK
Anthony J. McGUINNESS Ulziversityof Sheflield, Shefield, UK F:eCe,ivedOctober 1980. revised version received March 1981
The traditional analysis of dumping in an export market I:reatsthe term merely as a synonym for price discrimination1in an international context. Cruciallly,it does not predict that goods will be sold overseas at price less than marginal cost. This paper explores the poss%bilitythat dumping can occL;r in the more obvious *lay’ sense of sielling at less than marginal cost. It suggests three reasons why this may occur: in circumstances of uncertainty: pursuance of managerial goals; and strategic entry deterrence. In the lirst of these the traditional prediction of reduced surplus for domestic consumers is no longer assured.
1. Introduction The traditional analysis of ‘dumping’ in the export context has always defined that tern? to mean selling a homogenecaus product in both overseas and domestic markets, with a higher price in the latter. In effect it is a synonym for price discrimination by a domestic monopolist in an international context. The analysis rests crucially on the assumption of a Ushaped cost curve and, although it allows the possibility that goods may be ‘dumped’ on foreign markets at a price lower than average costs, it presumes that the net export price is always equal to marginal cost. Two predictions emerge from the model: assuming that discrimination is feasible and profitable, it leads the domestic monopolist to expand his total output whilst raising his domestic price. So, for domestic consumers, dumping le,ads to a welfare loss. This analysis is described more fully in section 2. Our interest in this paper is to explore the possibility that discrimination might lead to dumping in the more obvious ‘lay’ sense that goods arc sold on the export market at less than marginal cost.’ At the same time we shall ‘We suggest that this interpretation of the term is more in keeping with the popular view of dumping (as represented in press reports and allegations of ‘unfaime.ss’ by produlcers and/or unions In afflict& industries).
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1982 North-Holland
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’
SW! Dmies and A.J. McGuinne~v, Dwpiny
at less than marginal cost
assume a horizontal (or L-shaped) cost curve in order to encompass those real world circumstances where the nature of technology makes U-shaped costs unlikely. In section 3 we suggest three reasons why goods may be sdd at less than marginal cost on the world market: in circumstances of uncertainty, pursuance of managerial goals, and strategic entry deterrence. We also explore the welfare consequences for domestic consumers. 2. The conventional analysis The traditional analysis mentioned above is described by Caves and Jones [ 1973, pp. 212-215). It may be summarised briefly as follows. Cuihsider a profit-maximising monopoly seller in the domestic market facing an upward sloping marginal cost (A4C) curve, demand curve p =4(x) and marginal revenue curve MR(x) in fig. 1. In the absence of an export market. optimality implies the choice of the x0, p. combination.
F
d
x2
xo
x1
x3
D
Fig. 1
However, suppose there exists a large world market for the product concerned and that, net of transport costs and/or tariffs, he is abIe to export at price pt. (Thus, the world market is large enough for the domestic: monopolist to be able to sell any quantity within the relevant range without depressing pt.) Assuming that effective price discrimination is physically and legally possible, the monopolist will choose to distribute his output between the two
S.W. Davies and A.J. AlcGuinness, Dumping ut fess than marginal cost
171
markets so as to equate marginal revenue (MR) in both to MC. Since marginal revenue in the export market is pt, this does require, of course, that pl> MR(X,). As drawn, this condition is fulfilled and the monopolist will expand output up to the point where p,= MC. Total output is therefore OX, and, if marginal revenues in the two markets are to be identical, dolmestic output is now OX, and X,X, is exported. Domestic consumers now pay a higher price and have experienced a loss in surplus. 6;rt we should qualify this statement by pointing to the special case where the average cost curve lies everywhere above the domestic demand curve. In those circumstances, and if average costs are Falling sufficiently to be less than pd at X,, it stray be that the export option has enabled the achievement of sufficiently low unit costs for domestic production to be now profitable. In this case, then, consumers will receive sonze surplus [as opposed to none without trade -see Basevi ( 197011. Three features of this model are of relevance for present purposes. First, the ‘net’ export price must exceed MC at non-trade optimal output if exports are to oc:cur at all. Second, the p, line must intersect MC at some point if the level of exports is to be determinate. (In turn, these two points dictate an upward-sloping MC curve.) Third, exports are not sold at a loss in the sense that the marginal unit incurs a cost in excess of price. In that sense, then, exports are not dumped. On the other hand, the net export price may be less than average costs: this is true where AC> MC at output OX,: in other words, scale economies are not fully exploited at OX,. Given the assumption of rising MC, this does not imply an L-shaped average cost curve, but, only that minimum AC is attained at some scale in excess of OX,.* 3. Ilumping at price below marginal cost In this section we consider our two questions. Can dumping still occur without rising MC and where the net export price is below marginal costs? We conduct the analysis in terms of fig. 2, ir which costs are assumed to be L-shaped. More specifically, we assume a fixed cost element, F, and constant marginal costs, c. We also ilssume pt to be below marginal costs, i.e. p,
*Our exposition of this traditional model follows standard textbook practice in assuming rising MC. A determinate solution with consstcmtcosts could be achieved by relaxing the assumption that world price is insensitive to the scale of the domestic monopolists exports. Equally, as suggested by a referee, one might assume that domestic factor prices are bid up as the monopolist’s scale increases, Rut. either way, the central prediction would remain: exports are not dumped at price less than MC.
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S.W Davies and A.J. McGuinness,
Dumping at less than marginal
cost
D
MR
Fig. 2
rates. Ex-ante, he sets output on the basis of a subjective probability distribution describing different p, outcomes; the density function is denoted by fjp,) and is continuous with the following restrictions: (i) b >p, z=-a, i.e. the monopolist behaves that pr will fall within finite upper and lower bounds; (ii) E(p,) CC, i.e. his expcctatiou of p, is less than marginal costs (thus, In this case, the p, line in fig. 2 may be interpreted as E(p,)); and (iii) 1: f(p,)dp,>O, i.e. he attaches a positive probability to pt>c. Thus, he believes there is some chance, 110matter how small, that exporting will be profitable. To keep things simple, we assume risk-neutrality and a strict one period analysis - all output must be sold. Therefore ex ante the monopolist selects optimal X, say X*, so as to equate expected marginal revenue to costs. Expost, with X* now given, he will equate marginal revenue in the two markets - if possible. This will be possible if MR(X*)p,, he will find it most profitable to direct his entire output to the home market. In shoit, then, for given X*, marginal revenue is MR(X*) if MR(X*)rp, or pt if MR(X*)
S.W Davies and A.J. McGuinness, Dumping at less than marginal cost
II :‘3
marginal costs: MRiX*)
b
M W(A *)
W
The second-order condition for a maximum is satisfied given strict concavity of revenue, R =X4(X), with respect to X, which we shall assume throughout. We also assume non-negative profits at the optimum (i.e. fixed costs are covered). It is also easily shown ,that the optimum is an interior one in the sense that b > MR(X*)>U.~ We can now move fairly easily to two results, (A) The
dumping possibility encourages the monopolist to expand beyond the no-trade optimum output level (X0 in fig. 2), i.e. X* > X0.
output
Proof. The no-trade optimum is defined by MR(X,)=c. But, given the dumping option, this output yields an expected marginal revenue [from (1)-l:
cj f(p,kbt + j ptf(ptkbt a
(2)
C
=c~f(p,)dp,-cjf(p,)dp,+jp,fL (I E
-PI
(3)
C
=c+;ip,-c)ftiJdpt. P
(4)
From assumption (iii), the second term in (4) is positive and so expected marginal revenue at X0 exceeds c. Since c is expected marginal revenue at. X*, concavity of the revenue function therefore confirms that X* > X0. This is, of course, the same result as in the traditional important, it leads directly to our seconld rea:ult.
analysis, but, more
(B) There will be circumstances when dw rprng will occur ut net export price less than marginal costs. (More correctly, the subjective probability of this is 1zon-zero.) I?Td*ooJ
The probability
that export price is less than costs (i.e. p, CC) but
‘To see this, define MR(X1)=b and MR(X,)=a. From (l), at X,, expected marginal revenue is 6 (If(p,)dp, +O= bx [from assumption (iii)]. At X2, expected marginal revenue is a ! p, J(p,)dp, = E(pJ X+ > X,. JIE.
G
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S.U! Davies and A.J. McGuinness, Dumping at less than marginal cost
more than MR(X*), i.e. that dumping will occur at J+*rc, is: j
(5)
f @,)dp,-
MR(X*)
Since we have already found that X* >X,, and thus MR(X*)< MR(X,) =c, this probability is positive given a continuous probability distribution. The intuition of these results is fairly obvious. The monopolist is persuaded to produce an output level greater than X0 by the possibility that pr may exceed marginal costs. Ex-post, with all costs already sunk, output is disposed of as profitably as possible between the two markets. In some cases (where pI is ‘not too far’ below c) this will involve ‘selling at a loss’ on the export market. In other cases, of course* (where p,>c) actual profits will be higher than those achieved without the dumping option.4 Let us now turn to the implications for domestic consumers. Domestic price is 4(X*) where no dumping occurs [i.e. where: MR(X*)> pJ and 4(X,) otherwise [i.e. where MR(X*)
W = 4(X*)
“p”fhbbt a
+ i
(6)
4(X&%&h
MR(X*)
where MR(X,J = pI for MR(X*) c pt. Consider this expression for the family of demand curves which satisfy I$(X)=~,+~,MR(X)
for all X,
(7)
where kO and kl are constants. It is easily confirmed that both the linear demand curve and the constant elasticity demand curve satisfy (7). Substituting (7) into (6), noting that +(X,J= k, + k,p,, we have MR(X)*
W)=ko +k, Mw*)
J a
fO+)dpt+ i z-+fh)dptI . Mi(XW)
1
Since the term in brackets is expected marginal revenue, from (I), it follows that E(p)=k,-tk,c.
(3
4Similar results emerge if we substitute an uncertain domestic demand curve for uncertainty concerning p,. A further cause of uncertainty might involve the yield achieved from given inputs. This is of direct relevance to allegations of dumping agricultural produce. In that case an analysis of hoti dumping at less than marginal cost can occur is sufliciently obvious intuitively to require no further elaboration here.
S.W Davies and A1.J. MeGuinness, Dumping at less than marginal cost
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Given that the no-trade optimal output also satisfies MR(Xo)=c, it follows that the expected price is identical to p. in fig. 2 [since p. =kO +krc from (7)J So E(P)= PO.
(10)
Thus, in contrast to the analysis of section 2, the dumping option has led to no increase in the (expected) price faced by domestic consumers. We should qualify this by noting our (slightly) restrictive assumption concerning the form of the demand function (7). [It should also be clear that, in this instance, the assumption of constant costs is crucial. If, on the other hand, we re-consider the case of rising marginal costs, then MC(X*)>MC(X,) since X* > X, and thus E(p)= k, + k, MC(X*) > p. = k. + k,MC(X,,).] At any event, a simple comparison of E(p) with p. tells us little about the relative magnitudes of consunret surplus. In general, an expression for the expected consumer surplus associated with X* will depend not only on the form of the domestic demand curve, but also on the second and higher order moments of the probability distribution. This prevents us from providing any general conclusion on the domestic welfare implications of dumping. However, the linear demand curve is a special case with interesting (and perhaps intuitively surprising) results. Let us now suppose therefore that p=&X)=a-px.
(W
It is an easy matter to show that at price p, consumer surplus is (ct-~)~/2fl. Thus, the no-trade certainty surplus associated with price p. is CS = a2/W - @/B)po + (MOP&
(12)
On the other hand, expected consumer surplus associated with X* where domestic price varies depending on the actual pt outcome is E(CS) =( 1/‘2j)E(a2-2ap +p”) =(a2/2/?) -(a/fl)E(p) +(1/2/3)E(p2)(13) Substituting (12) into (13), it follows that E(CS)=CS--a/fl{E@)-PO} +(~/~B){E(P~)-P&
(14)
and from (10)
-CS+(l/2/?)var(p).
(1%
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Dumpisg at less than
marginal cost
this special case, then, aithough the dumping option leaves domestic consumers facing the same price on average, it will generate a larger expected consumer surplus given any variability in domestic price, this being assured by the uncertainty concerning pr. As stated above, once we move beyond the linear demand curve, the comparison between E(CS) and CS will involve higher moments of the probability distribution which may be negative or positive and thus no general conclusions are possible. It should also be clear that the above result is limited to horizontal cost curves: as already seen, with rising MC, E(p)>po and there is no certainty that E(CS)> CS.’ In
3.2. Dumping
by the sales maximising f;rm
Consider now the case where the domestic monopolist acts so as to maximise sales revenue rather than profits. Perhaps this is due to a divorce of control from ownership, but let us suppose that owners inr:ist on profits of at least x0 being earned. Fig. 3 is a fairiy standard representation of the circumstances under which the constraint is effective. We assume that the sales revenue maximising output exceeds output level X, (thus the total revenue function, not shown, is still rising at this point) but that managers are unable to expand scale further because to do so would violate the profit constraint. n
xo
‘d
xs
x1
x
i_rg. 3
5Needless to say, the possibility of risk-averre consumers and/or s recognition that the utility of foreigners may also be of interest, further qualify our result.
S.W Davies and
A.J. McGuinness, Dumping at less than marga’nal cost
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But let us now introduce the world demand curve of fig. 2, where p, is now certain but, as shown there, below c. Under certain circumstances the dumping option will allow managers to increase total sales and output beyond X, before encountering the profit constraint. These circumstances may be shown graphically as follows. The slope of the profits function is, of course, MR-MC and thus the level of profits at which the marginal revenue curve cuts the pt line is given by the point at which the profit function has slope pt- MC. Since ptc MC by assumption, this must occur to the right of X0 in fig. 3. So long as this point lies to the left of X,, then dumping is desirable from the manager’s point of ;iew. In the diagram this is shown as occurring at output X,. Clearly, the firm is now able to supply Xd to the domestic market whilst selling on the export market until the line AA’ intercepts the no line at X1. Exports are XdXl, domestic price is 4(X,) which exceeds the no-trade price 4(X,). Quite simply, the effect of the dumping option has been to shift the profits function to the right at scales of output in excess of Xd, leaving shareholders no worse OR, but yielding managers greater utility. Thus, again we have dumping at ;price below MC, but this time with an unequivocal loss in consumer surplus. Signilicantly, we do not need to invoke the assumption of rising MC as in the traditional model.6 From fig. 3 it is clear that such dumping is more likely, (a) the closer is pt to c and (b) the lower is the profit constraint. The magnitude of dumping is determined, in addition, by the curvature of the profits function - being greater the less elastic is domestic demand. 3.3. Dumping as an entry deterrent Thus far, implicit in the analysis is the assumption that domestic entry is blockaded, i.e. the domestic monopolist is able to price domestically without attracting new firms into his industry. Bf we now relax this assumption another motive for loss-making dumping emerges, namely that of discouraging new domestic entry. The argument is again easily explained using a simple profits function diagram, fig. 4. Exactly as in fig. 3, ODEB shows profits, absent both dumping and the threat of domestic entry. The dumping option involves an upward shift in the AB portion of the curve to AA’, exactly as above. But let us now suppose a pool of potential entrants into the domestic industry. Suppose they are deterred from entering only if the incumbent sets price no 6Having said this, a qualitatively similar result emerges with rising MC. We now re-define if costs are rising at all scales beyond X0. pc< MC(X,) and point A has slope pt - MC(&)<0 The AA’ line is now no longer linear but is, rather, concave but always to the right of the original profits function. This means that interception with the rrr,line lies to the left of A’, but, necessarily, at an output level >X,. Thus the output expansion is less pronounced than for horizontal costs, but dumping will still occur at a loss and domestic price will still rise.
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S.W Davies and A.J. MeGuinness, Dumping ac less ban marginal cost
n
Fig. 4
higher than the limit leueI, pL, and thus output no less than XL, where pL =&XL).’ At all Iower outputs entry will occur and thus the ODE portion of the curve is now unattainable. (Let us leave open, for the moment, the question as to what profit levels are attainable by the incumbent should entry occur.) As drawn, the diagram shows XL to the right of Xd [defined, as above, by pI= M&X,)]. This means t!lat a more profitable means of achieving limit output is now pocsible: thz incumbent may supply X, to the domestic market (at a pric.: in excess of PL) and XdXL to the export market. So long as Xd X,) is clearly more likely (a) the nearer is X, to B (the ‘competitive’ output) and (b) the nearer is X, to X0. The former is determined by the height of entry barriers and the latter by c-p,, as above. Clearly, this result does not require rising MC and if the incumbent does ‘The determinants of P, and X-Lare of no particular interest here, bait following traditional limit price theory we might suppose, say, the Sylos postulate, under which X, will be determkd by the magnitude of scale economies (or fixed costs in this model) and an” absolute cost barriers which may obtain. ‘This is a threat which is clearly more plausible for undifferentiated products, or at least those with insignificant capital sales expenditure.
S.W
Davies und
A.J. MeGuinness, Dumping at less than marginal cost
179
decide to deter entry (i.e. set limit output), it leads to a higher domestic price and loss of consumer surplus. Whether or not entry deterrence is the most profitable option will depend on the shape of the profit function to the left of E, given entry. But what we have established (assuming the threat of switching from export to home market is credible) is that dumping may make entry deterrence more profitable, and thus more likely. At this point we should acknowledge a close affinity between this simple analysis and that of recent work in Industrial Economics concerning the deliberate creation of excess capacity as an entry deterrent [see Spence (1977)]. In the Appendix we explore this affinity a little further. 4. Summary The standard textbook analysis described in. section 2 suggests that a domestic monopolist will only dump on an export market (a) if marginal costs are rising at all scales beyond the no-trade profit maximising output and (b) if the net export price exceeds marginal cost at that output. Moreover, it interprets the term ‘dumping’ to mean merely price discrimination, one consequence of which is that goods are never dumped at below marginal costs. By modifying this model to allow, in turn, for uncertainty, managerial objectives and strategic entry deterrence, we have suggested a range of motives for dumping. In the circumstances described in section 3, we have shown how dumping may still occur given an L-shaped costs curve and at a price below marginal costs. In two of our three modifications (sales maximising or entry deterring firms) one result of dumping is that domestic consumers are charged a higher price, as in the conventional analysis (this holds for rising or constant costs.) In the third modification (uncertainty concerning the export price), consumers’ surplus is less clear-cut. Interestingly, however, given constant marginal costs, dumping leads to no change in expected domestic price, at least for a given family of demand curves, including the linear. Moreover, for the linear demand curve only, this leads to an increase in domestic consumers’ expected surplus. We conclude from these results that the traditional economic analysis of dumping, because it has been defined so restrictively, may be totally inappropriate as an aid to understanding a practice which may be quite commonplace in the real world (and increasingly so if public pronouncements by aggrieved parties are to be believed). Appendix:Dumping and excess capacity as entry deterrents In this appendix we briefly explore how the dumping option impinges on the use of deliberate excess capacity as an entry deterrent.
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S.W Davies und A..!.
McGuinness, Dumping ut less than marginal cost
Much of the contempo:ary academic interest in excess capacity as an entry deterrent can be traced to Spence (1977) who models this possibility in a purely domestic framework. The basic idea is that incumbent firms ‘choose capacity in a strategic way designed to discourage entry’ (p. 534). In the preentry period some of this capacity may be left idle in order to raise price, whilst maintaining a credible threat to expand output and reduce price when entry is threatened, thereby reducing prospective profits of new entrants (operating on a residual demand curve) to zero. In much the same way in our third case, subsection 3.3, we have suggested that where dumped output, oversea*;, can be easily switched back to the domestic market, this may provide a means by which an incumbent may deter entry, without actually supplyirrg the entire limit output to the home market. In what follows we shall assume that both threats are credible, although quite clearly in some circumstances this may not be so for either one or both threats. Most of the interesting points of comparison between the two strategies can be explained using the following simple cost function which can be introduced into our main text analysis with little extra complication. Suppose the incumbent’s total costs are TC=F+c,Y+c,K,
(A4
with F and X defined as earlier; K is capacity, C~is the marginal cost of
expanding capacity and c, is the marginal cost of expanding output. (This is e!;sentialiy Spence’s model 1 (pp. 543-547).-j K is assumed to place an upper limit on X, i.e. K 2 X. With no threat of entry, capacity will always be fully used, K = .Y, and our profits function in fig. 4 and fig. 5 now has a slope of MB(X)=-c,-c,. Introducing the threat of entry, potential entrants are assumed to believe that the incumbnt will produce at full capacity, K =X; should they enter. As such, limit cupucity (K,) in thts model has the same value as limit output, XL (under the Sylos postulate), in the conventional limit model. But, having installed that capacity, and so deterred entry, the incumbent may decide to restrict output to less than XL (and leave some capacity idle). It is not diCf”rcuitto see the circumstances under which this will occur. If marginal revenue at XL is less than the mar&al cost of ourput c,, it will be profitable to restrict output back to the point where MR(X)=c,, the costs of capacity now being fixed. Turning to fig. 5(a), this is assumed to be the case and optimal output, given capacity K,, is X, corresponding to the point on the unconstrained proiit function having slope MR(X,)-c,-c,= -c,. This is shown as point F. [Note, however, that since this involves X,-X, excess capacity, profits are lower by c,(X,-X,) than those shown at point F.] Returning to our analysis of dumping, fig. 5(b) repeats fig. 4. [But note that now c =c,+c,,
and so the slope of the profits function is MR(X)-c,-c,
S.W Davies and A.J. McGuinness,
Dumping at less than marginal
cost
181
‘d
Fig. 5 (a) Excess capacity strategy:
MR(X,)=c,, MRW,.hc,, slope
at F = - c,.
(b) Dumping:
MR(X.,l= P,, MR(Xd< ~rq slope at A=p,-c,
-c,.
and the assumption that the export price is less than marginal cost is expressed as pt < c, + c,.] Dumping was shown to be profitable Jvhere Xd
A lies to the left of F (the situation
depicted in the figure), i.e. pI >c,>MR(X,). Here, without the dumping option.. it wouid be profitable to hold excess capacity, but given that the option is open, it is even more profitable to dump. In this case capacity is used to the full, dumping leads to an even greater restriction of domestic supply (and higher domestic price) than would be so given excess capacity. (And. of course, :profits are higher.) (2) c,>p, 3 MR(XL) (i.e. F to the left of A and both to the left of E). Here, while dumping is more profitable than supplying the entire limit output to the domestic market, it is even more profitable to leave idle capacity. So the dumping option is not taken. up (unless a policy of switching sales from the overseas to the domestic market is considered more credible than that of bringing into play previously idle capacity, should entry be threatened). (3) p,>MR(X,)>c, (A to the left of E, but F to the right of E). Here, while excess capacity is not profitable, dumping is. As in case 1, the dumping option will lead to a restriction of domestic output and an increase in price. (I)
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S. W;Davies and A.3. MeGuinness, Dumping at less than marginal cost
Quite clearly, the likelihood of these (and other cases) will depend on the magnitudes of c,, c, and pt as well as MR(X,). For example, remembering that p, cc =c,+cx (by assumption), case 2 is more likely when marginal costs are predominantly output-related, rather than capacity-related, whilst case 3 is rather the reverse. Finally, we note that, in a second variant of Spence’s model (pp. 538-541), marginal output costs are assumed to depend on the level of capacity. This gives rise to a fairly conventional analysis, in terms of upward sloping shortrun marginal costs curves, in which it can be shown that the dumping option may lessen the extent of excess capacity held, whilst leading to an increase in domestic price (case 1 above). This is quite closely related to Blattner’s (1973) earlier, but rather confusing, analysis of this question. Acknowledgements
Thanks for helpful comments are due to Roy Houghton, Bruce Lyons, Mike Waterson and an anonymous referee, none of whom is responsible for remaining errors. The referee has drawn our attention to an unpublished paper by Wilfred Ethier entitled ‘Dumping’ which apparently overlaps only slightly with our own. At the time of writing we were not aware of that paper.
References Basevi, G., 1970, Domestic demand and ability to export, Journal of Political Economy ‘18,330337. Blattner, N., f973, Domestic competition and foreign trade: The case of the excess capacity barrier to entry, Zeitschrift fur Nationalokonomie 33,403-412. Caves, R. and Jones, R., 1973, World trade and payments (Little, Brown, Boston). Spence, A.M., 1977, Entry, capacity, investment and oligopolistic pricing, Bell Journal of Economics 8.534-544.
DUMPING
AT LESS THAN MAtRGINAL COST Stephen W. DAVIES
Universiry of East Anglia, Norwich NR4 7TJ, UK
Anthony J. McGUINNESS Ulziversityof Sheflield, Shefield, UK F:eCe,ivedOctober 1980. revised version received March 1981
The traditional analysis of dumping in an export market I:reatsthe term merely as a synonym for price discrimination1in an international context. Cruciallly,it does not predict that goods will be sold overseas at price less than marginal cost. This paper explores the poss%bilitythat dumping can occL;r in the more obvious *lay’ sense of sielling at less than marginal cost. It suggests three reasons why this may occur: in circumstances of uncertainty: pursuance of managerial goals; and strategic entry deterrence. In the lirst of these the traditional prediction of reduced surplus for domestic consumers is no longer assured.
1. Introduction The traditional analysis of ‘dumping’ in the export context has always defined that tern? to mean selling a homogenecaus product in both overseas and domestic markets, with a higher price in the latter. In effect it is a synonym for price discrimination by a domestic monopolist in an international context. The analysis rests crucially on the assumption of a Ushaped cost curve and, although it allows the possibility that goods may be ‘dumped’ on foreign markets at a price lower than average costs, it presumes that the net export price is always equal to marginal cost. Two predictions emerge from the model: assuming that discrimination is feasible and profitable, it leads the domestic monopolist to expand his total output whilst raising his domestic price. So, for domestic consumers, dumping le,ads to a welfare loss. This analysis is described more fully in section 2. Our interest in this paper is to explore the possibility that discrimination might lead to dumping in the more obvious ‘lay’ sense that goods arc sold on the export market at less than marginal cost.’ At the same time we shall ‘We suggest that this interpretation of the term is more in keeping with the popular view of dumping (as represented in press reports and allegations of ‘unfaime.ss’ by produlcers and/or unions In afflict& industries).
0022_1996/82i ‘m/$02.75
0
1982 North-Holland
170
’
SW! Dmies and A.J. McGuinne~v, Dwpiny
at less than marginal cost
assume a horizontal (or L-shaped) cost curve in order to encompass those real world circumstances where the nature of technology makes U-shaped costs unlikely. In section 3 we suggest three reasons why goods may be sdd at less than marginal cost on the world market: in circumstances of uncertainty, pursuance of managerial goals, and strategic entry deterrence. We also explore the welfare consequences for domestic consumers. 2. The conventional analysis The traditional analysis mentioned above is described by Caves and Jones [ 1973, pp. 212-215). It may be summarised briefly as follows. Cuihsider a profit-maximising monopoly seller in the domestic market facing an upward sloping marginal cost (A4C) curve, demand curve p =4(x) and marginal revenue curve MR(x) in fig. 1. In the absence of an export market. optimality implies the choice of the x0, p. combination.
F
d
x2
xo
x1
x3
D
Fig. 1
However, suppose there exists a large world market for the product concerned and that, net of transport costs and/or tariffs, he is abIe to export at price pt. (Thus, the world market is large enough for the domestic: monopolist to be able to sell any quantity within the relevant range without depressing pt.) Assuming that effective price discrimination is physically and legally possible, the monopolist will choose to distribute his output between the two
S.W. Davies and A.J. AlcGuinness, Dumping ut fess than marginal cost
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markets so as to equate marginal revenue (MR) in both to MC. Since marginal revenue in the export market is pt, this does require, of course, that pl> MR(X,). As drawn, this condition is fulfilled and the monopolist will expand output up to the point where p,= MC. Total output is therefore OX, and, if marginal revenues in the two markets are to be identical, dolmestic output is now OX, and X,X, is exported. Domestic consumers now pay a higher price and have experienced a loss in surplus. 6;rt we should qualify this statement by pointing to the special case where the average cost curve lies everywhere above the domestic demand curve. In those circumstances, and if average costs are Falling sufficiently to be less than pd at X,, it stray be that the export option has enabled the achievement of sufficiently low unit costs for domestic production to be now profitable. In this case, then, consumers will receive sonze surplus [as opposed to none without trade -see Basevi ( 197011. Three features of this model are of relevance for present purposes. First, the ‘net’ export price must exceed MC at non-trade optimal output if exports are to oc:cur at all. Second, the p, line must intersect MC at some point if the level of exports is to be determinate. (In turn, these two points dictate an upward-sloping MC curve.) Third, exports are not sold at a loss in the sense that the marginal unit incurs a cost in excess of price. In that sense, then, exports are not dumped. On the other hand, the net export price may be less than average costs: this is true where AC> MC at output OX,: in other words, scale economies are not fully exploited at OX,. Given the assumption of rising MC, this does not imply an L-shaped average cost curve, but, only that minimum AC is attained at some scale in excess of OX,.* 3. Ilumping at price below marginal cost In this section we consider our two questions. Can dumping still occur without rising MC and where the net export price is below marginal costs? We conduct the analysis in terms of fig. 2, ir which costs are assumed to be L-shaped. More specifically, we assume a fixed cost element, F, and constant marginal costs, c. We also ilssume pt to be below marginal costs, i.e. p,
*Our exposition of this traditional model follows standard textbook practice in assuming rising MC. A determinate solution with consstcmtcosts could be achieved by relaxing the assumption that world price is insensitive to the scale of the domestic monopolists exports. Equally, as suggested by a referee, one might assume that domestic factor prices are bid up as the monopolist’s scale increases, Rut. either way, the central prediction would remain: exports are not dumped at price less than MC.
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S.W Davies and A.J. McGuinness,
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cost
D
MR
Fig. 2
rates. Ex-ante, he sets output on the basis of a subjective probability distribution describing different p, outcomes; the density function is denoted by fjp,) and is continuous with the following restrictions: (i) b >p, z=-a, i.e. the monopolist behaves that pr will fall within finite upper and lower bounds; (ii) E(p,) CC, i.e. his expcctatiou of p, is less than marginal costs (thus, In this case, the p, line in fig. 2 may be interpreted as E(p,)); and (iii) 1: f(p,)dp,>O, i.e. he attaches a positive probability to pt>c. Thus, he believes there is some chance, 110matter how small, that exporting will be profitable. To keep things simple, we assume risk-neutrality and a strict one period analysis - all output must be sold. Therefore ex ante the monopolist selects optimal X, say X*, so as to equate expected marginal revenue to costs. Expost, with X* now given, he will equate marginal revenue in the two markets - if possible. This will be possible if MR(X*)
S.W Davies and A.J. McGuinness, Dumping at less than marginal cost
II :‘3
marginal costs: MRiX*)
b
M W(A *)
W
The second-order condition for a maximum is satisfied given strict concavity of revenue, R =X4(X), with respect to X, which we shall assume throughout. We also assume non-negative profits at the optimum (i.e. fixed costs are covered). It is also easily shown ,that the optimum is an interior one in the sense that b > MR(X*)>U.~ We can now move fairly easily to two results, (A) The
dumping possibility encourages the monopolist to expand beyond the no-trade optimum output level (X0 in fig. 2), i.e. X* > X0.
output
Proof. The no-trade optimum is defined by MR(X,)=c. But, given the dumping option, this output yields an expected marginal revenue [from (1)-l:
cj f(p,kbt + j ptf(ptkbt a
(2)
C
=c~f(p,)dp,-cjf(p,)dp,+jp,fL (I E
-PI
(3)
C
=c+;ip,-c)ftiJdpt. P
(4)
From assumption (iii), the second term in (4) is positive and so expected marginal revenue at X0 exceeds c. Since c is expected marginal revenue at. X*, concavity of the revenue function therefore confirms that X* > X0. This is, of course, the same result as in the traditional important, it leads directly to our seconld rea:ult.
analysis, but, more
(B) There will be circumstances when dw rprng will occur ut net export price less than marginal costs. (More correctly, the subjective probability of this is 1zon-zero.) I?Td*ooJ
The probability
that export price is less than costs (i.e. p, CC) but
‘To see this, define MR(X1)=b and MR(X,)=a. From (l), at X,, expected marginal revenue is 6 (If(p,)dp, +O= bx [from assumption (iii)]. At X2, expected marginal revenue is a ! p, J(p,)dp, = E(pJ
G
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S.U! Davies and A.J. McGuinness, Dumping at less than marginal cost
more than MR(X*), i.e. that dumping will occur at J+*rc, is: j
(5)
f @,)dp,-
MR(X*)
Since we have already found that X* >X,, and thus MR(X*)< MR(X,) =c, this probability is positive given a continuous probability distribution. The intuition of these results is fairly obvious. The monopolist is persuaded to produce an output level greater than X0 by the possibility that pr may exceed marginal costs. Ex-post, with all costs already sunk, output is disposed of as profitably as possible between the two markets. In some cases (where pI is ‘not too far’ below c) this will involve ‘selling at a loss’ on the export market. In other cases, of course* (where p,>c) actual profits will be higher than those achieved without the dumping option.4 Let us now turn to the implications for domestic consumers. Domestic price is 4(X*) where no dumping occurs [i.e. where: MR(X*)> pJ and 4(X,) otherwise [i.e. where MR(X*)
W = 4(X*)
“p”fhbbt a
+ i
(6)
4(X&%&h
MR(X*)
where MR(X,J = pI for MR(X*) c pt. Consider this expression for the family of demand curves which satisfy I$(X)=~,+~,MR(X)
for all X,
(7)
where kO and kl are constants. It is easily confirmed that both the linear demand curve and the constant elasticity demand curve satisfy (7). Substituting (7) into (6), noting that +(X,J= k, + k,p,, we have MR(X)*
W)=ko +k, Mw*)
J a
fO+)dpt+ i z-+fh)dptI . Mi(XW)
1
Since the term in brackets is expected marginal revenue, from (I), it follows that E(p)=k,-tk,c.
(3
4Similar results emerge if we substitute an uncertain domestic demand curve for uncertainty concerning p,. A further cause of uncertainty might involve the yield achieved from given inputs. This is of direct relevance to allegations of dumping agricultural produce. In that case an analysis of hoti dumping at less than marginal cost can occur is sufliciently obvious intuitively to require no further elaboration here.
S.W Davies and A1.J. MeGuinness, Dumping at less than marginal cost
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Given that the no-trade optimal output also satisfies MR(Xo)=c, it follows that the expected price is identical to p. in fig. 2 [since p. =kO +krc from (7)J So E(P)= PO.
(10)
Thus, in contrast to the analysis of section 2, the dumping option has led to no increase in the (expected) price faced by domestic consumers. We should qualify this by noting our (slightly) restrictive assumption concerning the form of the demand function (7). [It should also be clear that, in this instance, the assumption of constant costs is crucial. If, on the other hand, we re-consider the case of rising marginal costs, then MC(X*)>MC(X,) since X* > X, and thus E(p)= k, + k, MC(X*) > p. = k. + k,MC(X,,).] At any event, a simple comparison of E(p) with p. tells us little about the relative magnitudes of consunret surplus. In general, an expression for the expected consumer surplus associated with X* will depend not only on the form of the domestic demand curve, but also on the second and higher order moments of the probability distribution. This prevents us from providing any general conclusion on the domestic welfare implications of dumping. However, the linear demand curve is a special case with interesting (and perhaps intuitively surprising) results. Let us now suppose therefore that p=&X)=a-px.
(W
It is an easy matter to show that at price p, consumer surplus is (ct-~)~/2fl. Thus, the no-trade certainty surplus associated with price p. is CS = a2/W - @/B)po + (MOP&
(12)
On the other hand, expected consumer surplus associated with X* where domestic price varies depending on the actual pt outcome is E(CS) =( 1/‘2j)E(a2-2ap +p”) =(a2/2/?) -(a/fl)E(p) +(1/2/3)E(p2)(13) Substituting (12) into (13), it follows that E(CS)=CS--a/fl{E@)-PO} +(~/~B){E(P~)-P&
(14)
and from (10)
-CS+(l/2/?)var(p).
(1%
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marginal cost
this special case, then, aithough the dumping option leaves domestic consumers facing the same price on average, it will generate a larger expected consumer surplus given any variability in domestic price, this being assured by the uncertainty concerning pr. As stated above, once we move beyond the linear demand curve, the comparison between E(CS) and CS will involve higher moments of the probability distribution which may be negative or positive and thus no general conclusions are possible. It should also be clear that the above result is limited to horizontal cost curves: as already seen, with rising MC, E(p)>po and there is no certainty that E(CS)> CS.’ In
3.2. Dumping
by the sales maximising f;rm
Consider now the case where the domestic monopolist acts so as to maximise sales revenue rather than profits. Perhaps this is due to a divorce of control from ownership, but let us suppose that owners inr:ist on profits of at least x0 being earned. Fig. 3 is a fairiy standard representation of the circumstances under which the constraint is effective. We assume that the sales revenue maximising output exceeds output level X, (thus the total revenue function, not shown, is still rising at this point) but that managers are unable to expand scale further because to do so would violate the profit constraint. n
xo
‘d
xs
x1
x
i_rg. 3
5Needless to say, the possibility of risk-averre consumers and/or s recognition that the utility of foreigners may also be of interest, further qualify our result.
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But let us now introduce the world demand curve of fig. 2, where p, is now certain but, as shown there, below c. Under certain circumstances the dumping option will allow managers to increase total sales and output beyond X, before encountering the profit constraint. These circumstances may be shown graphically as follows. The slope of the profits function is, of course, MR-MC and thus the level of profits at which the marginal revenue curve cuts the pt line is given by the point at which the profit function has slope pt- MC. Since ptc MC by assumption, this must occur to the right of X0 in fig. 3. So long as this point lies to the left of X,, then dumping is desirable from the manager’s point of ;iew. In the diagram this is shown as occurring at output X,. Clearly, the firm is now able to supply Xd to the domestic market whilst selling on the export market until the line AA’ intercepts the no line at X1. Exports are XdXl, domestic price is 4(X,) which exceeds the no-trade price 4(X,). Quite simply, the effect of the dumping option has been to shift the profits function to the right at scales of output in excess of Xd, leaving shareholders no worse OR, but yielding managers greater utility. Thus, again we have dumping at ;price below MC, but this time with an unequivocal loss in consumer surplus. Signilicantly, we do not need to invoke the assumption of rising MC as in the traditional model.6 From fig. 3 it is clear that such dumping is more likely, (a) the closer is pt to c and (b) the lower is the profit constraint. The magnitude of dumping is determined, in addition, by the curvature of the profits function - being greater the less elastic is domestic demand. 3.3. Dumping as an entry deterrent Thus far, implicit in the analysis is the assumption that domestic entry is blockaded, i.e. the domestic monopolist is able to price domestically without attracting new firms into his industry. Bf we now relax this assumption another motive for loss-making dumping emerges, namely that of discouraging new domestic entry. The argument is again easily explained using a simple profits function diagram, fig. 4. Exactly as in fig. 3, ODEB shows profits, absent both dumping and the threat of domestic entry. The dumping option involves an upward shift in the AB portion of the curve to AA’, exactly as above. But let us now suppose a pool of potential entrants into the domestic industry. Suppose they are deterred from entering only if the incumbent sets price no 6Having said this, a qualitatively similar result emerges with rising MC. We now re-define if costs are rising at all scales beyond X0. pc< MC(X,) and point A has slope pt - MC(&)<0 The AA’ line is now no longer linear but is, rather, concave but always to the right of the original profits function. This means that interception with the rrr,line lies to the left of A’, but, necessarily, at an output level >X,. Thus the output expansion is less pronounced than for horizontal costs, but dumping will still occur at a loss and domestic price will still rise.
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S.W Davies and A.J. MeGuinness, Dumping ac less ban marginal cost
n
Fig. 4
higher than the limit leueI, pL, and thus output no less than XL, where pL =&XL).’ At all Iower outputs entry will occur and thus the ODE portion of the curve is now unattainable. (Let us leave open, for the moment, the question as to what profit levels are attainable by the incumbent should entry occur.) As drawn, the diagram shows XL to the right of Xd [defined, as above, by pI= M&X,)]. This means t!lat a more profitable means of achieving limit output is now pocsible: thz incumbent may supply X, to the domestic market (at a pric.: in excess of PL) and XdXL to the export market. So long as Xd
S.W
Davies und
A.J. MeGuinness, Dumping at less than marginal cost
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decide to deter entry (i.e. set limit output), it leads to a higher domestic price and loss of consumer surplus. Whether or not entry deterrence is the most profitable option will depend on the shape of the profit function to the left of E, given entry. But what we have established (assuming the threat of switching from export to home market is credible) is that dumping may make entry deterrence more profitable, and thus more likely. At this point we should acknowledge a close affinity between this simple analysis and that of recent work in Industrial Economics concerning the deliberate creation of excess capacity as an entry deterrent [see Spence (1977)]. In the Appendix we explore this affinity a little further. 4. Summary The standard textbook analysis described in. section 2 suggests that a domestic monopolist will only dump on an export market (a) if marginal costs are rising at all scales beyond the no-trade profit maximising output and (b) if the net export price exceeds marginal cost at that output. Moreover, it interprets the term ‘dumping’ to mean merely price discrimination, one consequence of which is that goods are never dumped at below marginal costs. By modifying this model to allow, in turn, for uncertainty, managerial objectives and strategic entry deterrence, we have suggested a range of motives for dumping. In the circumstances described in section 3, we have shown how dumping may still occur given an L-shaped costs curve and at a price below marginal costs. In two of our three modifications (sales maximising or entry deterring firms) one result of dumping is that domestic consumers are charged a higher price, as in the conventional analysis (this holds for rising or constant costs.) In the third modification (uncertainty concerning the export price), consumers’ surplus is less clear-cut. Interestingly, however, given constant marginal costs, dumping leads to no change in expected domestic price, at least for a given family of demand curves, including the linear. Moreover, for the linear demand curve only, this leads to an increase in domestic consumers’ expected surplus. We conclude from these results that the traditional economic analysis of dumping, because it has been defined so restrictively, may be totally inappropriate as an aid to understanding a practice which may be quite commonplace in the real world (and increasingly so if public pronouncements by aggrieved parties are to be believed). Appendix:Dumping and excess capacity as entry deterrents In this appendix we briefly explore how the dumping option impinges on the use of deliberate excess capacity as an entry deterrent.
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S.W Davies und A..!.
McGuinness, Dumping ut less than marginal cost
Much of the contempo:ary academic interest in excess capacity as an entry deterrent can be traced to Spence (1977) who models this possibility in a purely domestic framework. The basic idea is that incumbent firms ‘choose capacity in a strategic way designed to discourage entry’ (p. 534). In the preentry period some of this capacity may be left idle in order to raise price, whilst maintaining a credible threat to expand output and reduce price when entry is threatened, thereby reducing prospective profits of new entrants (operating on a residual demand curve) to zero. In much the same way in our third case, subsection 3.3, we have suggested that where dumped output, oversea*;, can be easily switched back to the domestic market, this may provide a means by which an incumbent may deter entry, without actually supplyirrg the entire limit output to the home market. In what follows we shall assume that both threats are credible, although quite clearly in some circumstances this may not be so for either one or both threats. Most of the interesting points of comparison between the two strategies can be explained using the following simple cost function which can be introduced into our main text analysis with little extra complication. Suppose the incumbent’s total costs are TC=F+c,Y+c,K,
(A4
with F and X defined as earlier; K is capacity, C~is the marginal cost of
expanding capacity and c, is the marginal cost of expanding output. (This is e!;sentialiy Spence’s model 1 (pp. 543-547).-j K is assumed to place an upper limit on X, i.e. K 2 X. With no threat of entry, capacity will always be fully used, K = .Y, and our profits function in fig. 4 and fig. 5 now has a slope of MB(X)=-c,-c,. Introducing the threat of entry, potential entrants are assumed to believe that the incumbnt will produce at full capacity, K =X; should they enter. As such, limit cupucity (K,) in thts model has the same value as limit output, XL (under the Sylos postulate), in the conventional limit model. But, having installed that capacity, and so deterred entry, the incumbent may decide to restrict output to less than XL (and leave some capacity idle). It is not diCf”rcuitto see the circumstances under which this will occur. If marginal revenue at XL is less than the mar&al cost of ourput c,, it will be profitable to restrict output back to the point where MR(X)=c,, the costs of capacity now being fixed. Turning to fig. 5(a), this is assumed to be the case and optimal output, given capacity K,, is X, corresponding to the point on the unconstrained proiit function having slope MR(X,)-c,-c,= -c,. This is shown as point F. [Note, however, that since this involves X,-X, excess capacity, profits are lower by c,(X,-X,) than those shown at point F.] Returning to our analysis of dumping, fig. 5(b) repeats fig. 4. [But note that now c =c,+c,,
and so the slope of the profits function is MR(X)-c,-c,
S.W Davies and A.J. McGuinness,
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181
‘d
Fig. 5 (a) Excess capacity strategy:
MR(X,)=c,, MRW,.hc,, slope
at F = - c,.
(b) Dumping:
MR(X.,l= P,, MR(Xd< ~rq slope at A=p,-c,
-c,.
and the assumption that the export price is less than marginal cost is expressed as pt < c, + c,.] Dumping was shown to be profitable Jvhere Xd
A lies to the left of F (the situation
depicted in the figure), i.e. pI >c,>MR(X,). Here, without the dumping option.. it wouid be profitable to hold excess capacity, but given that the option is open, it is even more profitable to dump. In this case capacity is used to the full, dumping leads to an even greater restriction of domestic supply (and higher domestic price) than would be so given excess capacity. (And. of course, :profits are higher.) (2) c,>p, 3 MR(XL) (i.e. F to the left of A and both to the left of E). Here, while dumping is more profitable than supplying the entire limit output to the domestic market, it is even more profitable to leave idle capacity. So the dumping option is not taken. up (unless a policy of switching sales from the overseas to the domestic market is considered more credible than that of bringing into play previously idle capacity, should entry be threatened). (3) p,>MR(X,)>c, (A to the left of E, but F to the right of E). Here, while excess capacity is not profitable, dumping is. As in case 1, the dumping option will lead to a restriction of domestic output and an increase in price. (I)
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S. W;Davies and A.3. MeGuinness, Dumping at less than marginal cost
Quite clearly, the likelihood of these (and other cases) will depend on the magnitudes of c,, c, and pt as well as MR(X,). For example, remembering that p, cc =c,+cx (by assumption), case 2 is more likely when marginal costs are predominantly output-related, rather than capacity-related, whilst case 3 is rather the reverse. Finally, we note that, in a second variant of Spence’s model (pp. 538-541), marginal output costs are assumed to depend on the level of capacity. This gives rise to a fairly conventional analysis, in terms of upward sloping shortrun marginal costs curves, in which it can be shown that the dumping option may lessen the extent of excess capacity held, whilst leading to an increase in domestic price (case 1 above). This is quite closely related to Blattner’s (1973) earlier, but rather confusing, analysis of this question. Acknowledgements
Thanks for helpful comments are due to Roy Houghton, Bruce Lyons, Mike Waterson and an anonymous referee, none of whom is responsible for remaining errors. The referee has drawn our attention to an unpublished paper by Wilfred Ethier entitled ‘Dumping’ which apparently overlaps only slightly with our own. At the time of writing we were not aware of that paper.
References Basevi, G., 1970, Domestic demand and ability to export, Journal of Political Economy ‘18,330337. Blattner, N., f973, Domestic competition and foreign trade: The case of the excess capacity barrier to entry, Zeitschrift fur Nationalokonomie 33,403-412. Caves, R. and Jones, R., 1973, World trade and payments (Little, Brown, Boston). Spence, A.M., 1977, Entry, capacity, investment and oligopolistic pricing, Bell Journal of Economics 8.534-544.