¹ This Journal, XXVII, no. 3, Aug., 1961, 382–3.

² This Journal, XXVII, no. 1, Feb., 1961, 41–54.

³ And in a recent letter Samuelson suggests that these are important points to prove.

⁴ Samuelson, P. A., “The Gains from International Trade,” this Journal, V, no. 2, 05, 1939, 195–205.Google Scholar References here will be to the article as reprinted in Ellis, Howard S. and Metzler, Lloyd A., eds., Readings in the Theory of International Trade (New York, 1950).Google Scholar

⁵ Ibid., Sections [6]–[8].

⁶ Ibid., Section [9].

⁷ So Mr. Kemp could not be more wrong in supposing we considered similar situations.

⁸ Cf. Samuelson, “Gains from International Trade,” Section [9].

⁹ Ibid., Section [7].

¹⁰ “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.

¹¹ Geometrically, 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.

¹² My 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 unlike tastes and assets. It should have been obvious that at this point Samuelson was still analysing the case of like people.

¹³ Actually, in my article, I went so far as to assume each household initially had supplies of either X or Y but 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.

¹⁴ These 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 Scitovsky, T., “A Reconsideration of the Theory of Tariffs,” Review of Economic Studies, IX, 1942.Google Scholar

¹⁵ Mr. 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.

¹⁶ The curve I′ lies above and to the right of Y ₀ 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 Y ₀, as origin of this family, will then move up to Y ₁ on curve I′.

¹⁷ Represented by the slope of Y _0α ′.

¹⁸ The 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 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 Y ₀ and U in the “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.)

¹⁹ Mr. 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 O _∞ and O _v 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 he further above and to the right of the fixed production point. I am not at all surprised to learn 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.”)