trade gains in the short run: a reply to mr. kemp

Trade Gains in the Short Run: A Reply to Mr. KempAuthor(s): Stephen EnkeSource: The Canadian Journal of Economics and Political Science / Revue canadienned'Economique et de Science politique, Vol. 27, No. 4 (Nov., 1961), pp. 522-526Published by: Wiley on behalf of Canadian Economics AssociationStable URL: http://www.jstor.org/stable/139439 .

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522 Canadian Journal of Economics and Political Science

Reservation has one particularly objectionable feature, in that it contains within it a sort of "pocket veto." The federal government is not obliged to do anything at all about a reserved bill. If no action is taken at all, then the bill has been effectively vetoed. Since the bill under consideration would expire in any event on December 31, 1961, inaction would have destroyed its effect completely. Such a course of action is not without precedent, and could be justified by the argument that any action would be interference with provincial jurisdiction. As long as the disallowance power remains in existence, reservation is in any event an unnecessary prop to the federal power. The continu- ance of reservation merely makes it possible for the federal government to be involved by inadvertence in local issues in which it may have no direct interest.

TRADE GAINS IN THE SHORT RUN: A REPLY TO MR. KEMP

STEPHEN ENKE

Duke University

MR. Murray Kemp's commentsl on my "Gains and Losses from Trade in the Short Run"2 provide a welcome opportunity to explain the nature of my theorem more maturely. The main idea is that there are national gains to be derived from some degree of international trade even when national output is fixed and households are unlike as regards tastes and initial assets. Moreover, no trade, as against completely free trade with an unchanged production mix, will always be worse if the "open" income distribution is the norm. These ideas are neither demonstrated nor considered in Professor Samuelson's cele- brated article in this JounrAL of twenty-two years ago.3 However, now that the issue has been raised by Mr. Kemp, the most constructive course may be to indicate where my article, despite its many imperfections, may usefully sup- plement Professor Samuelson's masterly contribution of 1939.4

Samuelson considers two broad classes of cases: (1) where all members of the economy are identical as regards tastes and ownership of assets and are made better off by free trade;5 (2) where all individuals are unlike in these respects and could be made better off by some trade.6 In the second case he is explicitly considering only situations in which output changes. His treatment of the first case is also in long-run terms, but it includes the special case of no output change. Of the four possible combinations that arise from distinguish- ing between fixed and altered production and between like and unlike people, the Samuelson article considers all save the one that I alone analysed (that is, fixed production and unlike people) .7

1This JOURNAL, XXVII, no. 3, Aug., 1961, 382-3. 2This JOURNAL, XXVII, no. 1, Feb., 1961, 41-54. 3And in a recent letter Samuelson suggests that these are important points to prove. 4p. A. Samuelson, "The Gains from International Trade," this JOURNAL, V, no. 2, May,

1939, 195-205. References here will be to the article as reprinted in Howard S. Ellis and Lloyd A. Metzler, eds., Readings in the Theory of International Trade (New York, 1950).

UIbid., Sections [6]-[8]. OIbid., Section [9]. 7So Mr. Kemp could not be more wrong in supposing we considered similar situations.

Vol. XXVII, no. 4, Nov., 1961



Notes and Memoranda 523

Why it is difficult to prove that some trade could be better than no trade for all unlike persons in a country, assuming unchanged output, can be under- stood by reviewing very briefly how Samuelson and others have proved a gain from trade in the "changed output-unlike persons" case and how one can prove it for the "unchanged output-like persons" instance.

Assuming unlike persons, but output adjustments, Samuelson argues as fol- lows. With open prices, assuming an economy has suitably modified its output mix from that which prevailed with closed prices, its international command over every kind of good is potentially greater than under autarky. With com- plete free trade its consumption of every kind of good may not increase. But some degrees of trade must enable the open output, at external prices, to command more of each and every good. And this makes adequate or over- compensation of injured individuals possible. It is important to realize that this entire proof depends on a change in production mix that increases domestic output value assessed at open prices.8 The short-run case that I analysed excludes any change in production.

Assuming like persons, Samuelson proved that all persons are better or no worse off with free trade, and he goes on to suggest that the gain from trade will be greater the more open prices deviate from closed prices.9 Samuelson's demonstration was altogether novel and general and has become historic. But the enormous advantage to the analyst of assuming persons having like tastes and assets can best be appreciated from considering a special case that he mentioned in passing.10

Suppose there are two commodities, X and Y. Each person has the same supply of X and Y-received perhaps from outer space-as every other person. And they have the same ordinal preference schedules for these goods. The effective marginal rate of substitution between X and Y, given initial personal supplies, is the same for all individuals. In a closed economy this will deter- mine the price. Indeed, there can be no internal trade under autarky, for a price that would induce one person to sell (or buy) X would induce everyone to sell (or buy) X and there would be no one to buy (or sell) X. Opening trade brings open prices and a chance for all domestic residents to import the same good and export the other. The greater the difference between open and closed prices the greater the gain of each and every person in the country." If at open prices p' a person consumes some mix of goods q', whereas at closed

8Cf. Samuelson, "Gains from International Trade," Section [9]. 9Mbid., Section [7]. '0"It will be noted that the proof is still valid in the case where there exist no resources

transferable between different production uses. Indeed, if the commodities are not produced at all, but fall from heaven in fixed amounts per unit time, the theorem still applies." (Ibid., pp. 249, 250.) Then one can consider the commodity market alone and ignore factor prices and quantities.

llGeometrically, with no one buying or selling, all persons can be imagined to have such tastes and initial X and Y supplies that the effective slopes of the highest individual indifference curves they attain are equal. This slope will be the internal exchange rate between X and Y and will instigate no internal trade. Any change in prices, which can only occur through introducing foreign buyers and sellers into the market who have different tastes and assets, will enable each domestic resident to trade and so attain a higher indifference curve. And the greater the new price differs, the higher the just attainable indifference curves, and the greater the volume of trade.




Y~~~~~~~~~~~~Y

o ~ ~ ~ X x

0~~~~~ y

0X FIGURE 1

prices p he consumed another mix q, under these special assumptions it must be that he prefers q' to q. There is no possibility that he really prefers the q mix but cannot afford it at p' prices.'2 But all these remarkable conclusions stem from the assumption that people have like tastes and assets. And this facilitating supposition is one I never made.

How can one show that everyone would be made worse off by a change from some trade to no trade, even though they are unlike as regards tastes and initial supplies,'3 and despite no change in domestic output? Essentially, by showing that the fixed production point Yo (see diagram) must lie below the

12My former criticism ("Gains and Losses," 42) of this point in Samuelson's article (p. 249) was invalid. I was thinking of the more general case where households have uxnlike tastes and assets. It should have been obvious that at this point Samuelson was still analysing the case of like people.

13Actually, in my article, I went so far as to assume each household initially had supplies of either X or Y hut never both. Samuelson has kindly pointed out to me by letter that the argument fails if X-producing households only demand Y and Y-producing households only demand X. Physically, there is then no way of compensating whichever set is hurt by trade, because the imported good has no use value for competing domestic producers. But I was assuming, and did not mention it explicitly because it seemed so reasonable, that a closed economy can have all consuming households in satisfied equilibrium: that is, at a uniquely determined price, all households can have marginal substitution rates equal to the internal exchange rate. This supposition is now made explicit.



Notes and Memoranda 525

collective Scitovsky welfare contour4 1I' that is based on unrestricted trade. Such a curve is obtained by summing the community indifference curves that the X-producing households and Y-producing households attain with free trade but fixed outputs. These respective X' and Y' curves (see diagram) "overlap" in the sense that Y' lies between X' and the latter's origin at 0.15 Hence the curve F' must lie above and to the right of Yo, which indicates the total mix of X and Y produced and consumed under autarky, and so government termination of external trade would result in a loss of potential welfare for all.'6

A difficulty remains. It is conceivable that a combined Scitovsky contour I", passing through YO and tangent to the closed commodity exchange rate represented by Yoa", may pass above and to the right of Z'. This could occur if X" and Y", which when summed yield I", together had extreme curvature. The situation then is that a change to no trade from free trade with fixed outputs will lessen welfare for all if there is full compensation. But a change to free trade from no trade will also lessen welfare for all after compensation. Politi- cally, if a nation has to be at either Yo (no trade) or Z' (free trade), perhaps it had better continue its current policy.

But these two alternatives are not the only choices. Given open commodity exchange rates,17 there are many other possible consumption mixes, represented by the line passing through Yo and Z'. And, if I" intersects YoZ' at U, all consumption mixes represented from U to Yo are possible and can be made unambiguously preferable.

Consider the point Z between U and Yo. It lies above the curve I" by con- struction. And a Scitovsky curve based on Z (I,) will pass above and to the right of YO if government ensures a proper equilibrium. It must keep the economy's consumption on YOZ' by means of lump sum taxes or subsidies. And it must constrain trade from Z' to Z by means say of import or export taxes. In this way the price of X in terms of Y to private buyers can be increased so that the commodity exchange line becomes steeper than Yoa'. I, must then be tangent to the government imposed commodity exchange rate that results in only YOZ external trade. Hence 1 must pass above YO.18

14These curves represent the minimum alternative combinations of two goods, distributed as economically as possible, that will make each person of a group exactly as well off as at some stated initial position. See T. Scitovsky, "A Reconsideration of the Theory of Tariffs," Review of Economic Studies, IX, 1942.

'15Mr. Kemp complains that nowhere do I define my notion of a surplus. But I explicitly stated ("Gains and Losses," 46) ". . . the existence of a net surplus is confirmed by the fact that, with freer trade, . . . X' and Y' are both higher than other such curves, the tangencies of which comprise the intervening segment of the contract curve . ." And this notion of surplus is implied in several other places.

'6The curve I' lies above and to the right of Yo for the following reason. Suppose the whole family of Y-owning households' Scitovsky curves-of which there is one for each possible price-is shifted vertically upwards until curves X' and Y' are tangent. The point Yo, as origin of this family, will then move up to Y, on curve I'.

17Represented by the slope of Yoa'. 18The argument of this paragraph is novel to my article in this JOURNAL. Noteworthy is

the applicability of this same line of reasoning to cases of external trade by unlike people with changing output. Samuelson proved ("Gains from International Trade," section [9]) that some trade could then benefit all unlike persons. But, taking a simple two-commodity case, some trade in his model is limited to feasible consumption mixes that include more




Several important and novel conclusions seem to have been derived for instances of constant output and unlike people. Some trade must make everyone better or no worse off after suitable compensation. Free trade under these conditions can-but need not always-have the same outcome. Ternnination of free trade, after adequate compensation, must make everyone worse off in terms of the open welfare distribution.'9

X and more Y. If an unambiguous potential gain can be proved for various feasible mixes that do not include more of both commodities-e.g., those between YO and U in t:he "no output change" instance depicted here-there are more feasible consumption mixes with output changes that are unambiguously better than Samuelson's famous article intimated. (An attempt to show this more completely will be made in another place.)

19Mr. Kemp's point (2) needs to be answered and his point (3) conceded. On (2), as the open price begins to deviate from the "closed" one, the offer curves 0 and 0O diverge. Unless the X and Y households' respective indifference curves together lose most of their curvature, the "overlap" of X' and Y' will become greater, and I' will lie further above and to the right of the fixed production point. I am not at all surprised to leam from Mr. Kemp that his proof that this cannot happen does not apply when the consumption patterns and incomes of trade are not reproduced under autarky. On (3), I carelessly assumed that some of the trade volume that results without compensation must be due to changes in income rather than price; this invalidates parts of paragraphs 1 and 3 on p. 47. (In addition, on p. 46, line 3, the word "not" somehow fails to appear before the word "more.")



trade gains in the short run: a reply to mr. kemp

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