I. Introduction, 353. — II. The neoclassical postulate and its neoclassical solution, 355. — III. The technology frontier in the linear-technique model, 358. — IV. The choice of techniques in the linear-technique model, 366. — V. The nature of empirical production functions under the neoclassical postulate, 374. — VI. The technology frontier and the substitution parameter, 376.— VII. Concluding remarks, 382.

BROWN AND CHANG [2] have sought the exact conditions of aggregation within and across sectors in a general equilibrium model of production. Complete intrasector aggregation of nonlabor inputs requires all gross rental rates to change in the same proportion, while complete intersector aggregation requires all prices of products and rental rates on capital aggregates to vary in the same proportion. Then, the full aggregation is to be established when all prices change in the same proportion, provided that all nonlabor inputs depreciate at the same rate [2, Theorems 1 and 8]. The necessary and sufficient condition for it is that labor's shares in total value of product are equal in equilibrium across sectors. This condition fails when nonlabor inputs depreciate at different rates because gross rental rates no longer change in the same proportion even if all prices change in the same proportion. Brown and Chang have derived a condition for the equiproportionate changes in gross rental rates [2, Theorem 8]. Though the condition allows intraand intersector aggregation of nonlabor inputs, it no longer permits intersector output aggregation because product prices do not vary at the same rate.

A country's exports are conventionally explained by its export prices relative to competitors' prices and by importing countries' real income. Except for its export prices, the demand for its exports is determined by factors beyond its control. It is thus usually assumed that the country passively responds to the multiplier effect that export demand generates in its domestic economy. This view is common both in macroeconomic theories of short-run income determination and long-run growth of an open economy. However, competition is imperfect in international trade. Apart from barriers set up artificially by importing countries, there are non-price factors in product quality, marketing, and services that make competition imperfect in international markets. Just as sellers can influence their demand curves in domestic markets by advertising, exporters can affect foreign demand through non-price competitive activities, e.g., export promotion. Moreover, imperfect availability of information gives a strong edge to well-established trading connections, which should become firmer as the exporting country expands in scale. In a dynamic world, process and product innovations are continually introduced; old goods are improved in quality and new goods come into existence. A country that leads others in initiating these innovations enjoys a dynamic comparative advantage. Thus, we can make a strong case that non-price competitiveness is significantly associated with an exporting country's growth performances. This argument suggests that domestic growth is an important determinant of the growth potential of a country's industrial exports. A fast-growing country could increase its exports more rapidly than a slow-growing country. While the former enjoys trade surpluses, the latter suffers from trade deficits. The balance of trade could be divergent rather than convergent in the process of growth. The experiences of industrial countries in the two decades preceding 1971 seem to be consistent with this interpretation. We wish to test our hypothesis and to evaluate how far it can account for differences in individual countries' export performances. This article presents such an empirical test by examining export records of major industrial countries over the 1955-1970 period through estimating a cross-country export demand function. Our investigation indicates that domestic factors were a particularly important determinant of export demand. We emphasize that the omission of these factors from the export demand function can make trade projections err and, consequently, lead to wrong policy prescriptions. We introduce export demand and supply functions in section II, examine data and variables in section III, present cross-country estimates of the export demand function in section IV, account for intercountry variations in the conventionally estimated world-income elasticity of export demand in section V, discuss a few econometric problems in section VI, and give concluding remarks in section VII.

RICE and quantum indexes (P, Q) are dual to each other if PQ = E where E is the expenditure index. They satisfy the weak factor reversal test.' If they share an identical weighting formula as weighted averages of price and quantity relatives, they satisfy the strong factor reversal test, that is, they are ideal. The most celebrated ideal economic index is the one associated with the name of Irving Fisher though it was discovered before him. No ideal index as simple as Fisher's has been discovered since. Log-change index numbers have become increasingly popular in recent years, particularly as an approximation to the theoretically desirable Divisia index. Theil (1973) proposed a new log-change index number that alhnost satisfies the strong factor reversal test. I derived several alternative formulas that improve in the degree of approximation (Sato, 1974b). But neither Theil nor I was able to obtain the ideal log-change index. In section II, I report its discovery. Our pessimism has proved premature. Indeed, the formula was self-evident from the very beginning -we simply failed to see it.2 There are dual dualities between economic indexes and homothetic preferences (Samuelson and Swamy, 1974). A price or quantum index is associated with a homothetic indirect or direct preference ordering. If P and Q are dual to each other, so are the direct and indirect preference orderings corresponding to them. If P and Q are ideal, the latter are not only dual but also share an identical mathematical form. They are strictly self-dual as I call them elsewhere.3 An obvious example is the association of Cobb-Douglas indexes and preferences. A less obvious example is the association of Fisher's ideal indexes and quadratic preferences. The association itself was discovered by Konuis and Buscheguence a half century ago in 1926.4 Note that homothetic quadratic preferences are self-dual. Then, what is the selfdual preference ordering that corresponds to our ideal log-change index? We shall show in section III that it is the CES function that has become so popular in the economic literature, originally discussed by Bergson (1936), rediscovered by Solow (1956), and popularized by Arrow et al. (1961). The CES function is known to be self-dual (Samuelson, 1965) and yet the economic index associated with it has eluded discovery until now. Economic indexes are useful because they apply even when underlying preferences are not homothetic.5 We shall show in section IV that the ideal log-change index corresponds to the addilog preference ordering introduced by Houthakker (1960).

i vt= it yjtyjtV(( ) where viVi is nominal value added in industry i and yjYj the nominal GNE on good j. We have vitVit qitQ t mitMit (2) where qQ is the value of gross product and mM the cost of materials.' We wish to maintain the fundamental national-income identity (1) in constant prices, too. This is possible when we evaluate both outputs and inputs in uniform prices, say, of the base year. Then, we have

The reswitching phenomenon brought to light the fact that the neoclassical production system need not be well behaved. This means that the central proposition in neoclassical production theory, namely the monotonic relation between the round-aboutness of production and the interest rate, need not always hold. There are two ways to cope with this situation. One is to accept what is true, however cumbersome it may be. The other is to look for conditions which rule out perverse phenomena in the hope that such conditions are empirically acceptable. Lowell Gallaway and Vishwa Shukla (abbreviated as G-S henceforth) have taken the second approach and claimed to have discovered a new sufficient condition that rules out the reswitching of techniques in a neoclassical production system, a condition which may be called the capital-intensity condition. Unfortunately, their claim is unfounded; their analysis is faulty. Rather than showing where it has gone astray, I shall present a counterexample that satisfies their capital-intensity condition and yet permits reswitching.1 Though there are conditions that warrant the neoclassical production svstem to be well behaved, the capital-intensity condition is not among them.