Knowledge that Transforms

The comments of Kazuo Sato and P. Garegnani indicate a technical problem in our original analysis. Its effect is to make it possible for reswitching to occur even though what Sato calls our capital-intensity condition is satisfied, provided that the factor price contours in question are quite similar in nature. Thus, as Sato notes, our condition only definitely reduces the possibility of reswitching. Unfortunately, all this may be simply a minor exegesis of what is perhaps a trivial question. Let us explain that statement. Consider the standard case of a full-employment steady-state economy (constant population and labor force) in which alternative two-commodity indecomposable production systems are available. Assume that producers will choose the technique that is profitable. Conventionally, this is taken to mean that they will choose the productive technique that will provide the highest rate. For example, Luigi Pasinetti states: Clearly, on grounds of profitability, that technique will be chosen which-for any given wage rate-yields the higher rate of profit (p. 507). In a micro-economic context one would not quarrel with this proposition. A given investment in capital goods will be the higher the rate of return on the investment. However, at our highly aggregated (economy wide) level of analysis of the meaning of capital and the nature of the production function, this is not so obvious. At the heart of the Cambridge (England) criticism of neoclassical analysis is the proposition that capital in an aggregate sense can only be measured through the use of some pricing numeraire which itself is functionally related to the level of wage and (interest) rates. In this highly interdependent world (illustrated by the twocommodity indecomposable production systems under discussion), it is alleged that the straightforward neoclassical propositions break down because of the interrelationship between the value of capital and the (interest) rate. Unfortunately, the analysis upon which this conclusion has been based appears to have ignored the fact that at the aggregate level the phrase more profitable has an added dimension that is lacking at the micro-economic level. This added dimension is the opportunity to employ capital. In the models under analysis the rate of and the quantity (in value terms) of capital employed are simultaneously determined. Together, they explain the volume of profits per head associated with a given technique and wage-profit rate combination. Since net output per head for any technique is constant (at the level of the wage rate associated with zero rate), profits per head may be calculated by subtracting any wage rate on the factor price contour from the zero wage. We have done this for Sato's example (Garegnani's would do just as well) and the results are shown in Table 1. They are fascinating in that they indicate that at any rate the most technique from the standpoint of profits per head is technique I. But, how important is this? Quite; in a macromodel that assumes 1) full emplovment and 2) that capital is used solely for the purpose of producing the commodities included in the model.' Together, these conditions imply that profits per head are a measure of the total profits associated with the use of any technique. This means that switching from technique I to technique II in Sato's example as the rate falls below .595 involves adopting a production system that yields

Terutomo Ozawa's demonstration of the relationship between the commodity trade triangle, the factor trade triangle, and the equilibrium factor endowment ratio rays in two that initially trade with one another because of differences in tastes, is both logically correct and geometrically interesting. But while I admire his elegant proof, I must disagree with his assertion that ''we are not in a position to tell the exact locations of [the factor endowment ratio] rays unless we first know the exact amounts of labor and capital to be moved between the two countries (p. 668). This assertion not only runs counter to the general mathematical fact that the solution of a general equilibrium system requires that all unknowns be simultaneously determined, but as a specific proposition is demonstrably false as well. It is proved below that given the initial equilibrium commodity trade triangles, the equilibrium factor endowment ratio rays in the two can be determined without explicitly considering the exact amounts of labor and capital to be moved between the two countries. In Figure 1 (a simplified version of my earlier Figure 2), the initial common production vector is OP with OZf the consumption vector in the foreign country and OZd the consumption vector in the home country. The respective equilibrium triangles thus are CfFP and CdDP, and the equilibrium commodity price ratio given by the slope of Cf PCd. By the Stolper-Samuelson relation the factor price ratio is known once the commodity price ratio is known; and given factor prices, the optimal factor-intensity ratios OR, and OR, also are known. In Figure 2, point E represents the common factor endowment y

In a recent paper in this Review, Melvyn Krauss presented an interesting case of factor mobility under assumption that two countries have an identical factor endowment but differ from each other in tastes. A pattern of factor movements required under this set of assumptions is shown to be determinate in contrast to basic indeterminacy involved in a situation that assumes differences in factor endowments but identical tastes in two countries. To prove his point that there is only one unique pattern of factor mobility, Krauss starts by drawing from origin of a twofactor endowment (capital and labor) diagram two rays representing the factor endowment ratios in two countries that correspond to production vectors . . . required for mirror image solution (p. 801) in such a manner that each ray symmetrically deviates from initial common factor endowment ratio line from origin. He then proves with help of a parallelogram exact amounts of labor and capital to be transferred between two countries. Intuitively we know that such factor endowment ratio rays must exist. Yet we are not in a position to tell exact locations of such rays unless we first know exact amounts of labor and capital to be moved between two countries. Although Krauss's arbitrary way of drawing such rays does not invalidate his proof, it seems more logical as a geometrical proof that we directly find exact amounts of two factors to be transferred in a manner shown below, since only after we have done so, can rays used by Krauss be derived. The initial common factor endowment box is shown by O,COXL in Figure 1. The equilibrium production point achieved under free trade is indicated by point P. Let us subtract amount of labor-intensive good Y which home country would export Rd

In a recent issue of this Review, Robert Vogel extended to sixteen Latin American countries a technique used by Arnold Harberger to examine the chief causes of Chilean inflation. On the basis of pooled regressions for the sixteen countries, he concluded that with little heterogeneity, the different rates of inflation cannot be put to structural differences but must be attributed to varying rates of expansion of the money supply. Only monetary variables are employed and the link between inflation and the rate of money suppl growth rests essentially on R2 so high as to leave little of the variation in the rate of price increase for other variables to explain. This note contends that in coming to such broad conclusions on the basis of only monetary variables, Vogel has committed an error that the Harberger model was designed to avoid. Some regressions based on Argentine data are presented by way of illustration. As a partial justification for using only monetary variables, Vogel states the Harberger model is essentially monetarist. In his original study, however, Harberger focused specifically on the problem of multicollinearity between changes in the money supply and the wage rate. He suspected that the long history of Chilean inflation consisted of instances when increases in the quantity of money had brought rising prices in the absence of wage increases, other instances when wages had pushed up prices without being by expansion of the money supply, and still others when inflation had been accompanied by wages and prices rising together. Regression analysis cannot sort out these instances, he asserted, . . . but it can g,ive some indications of their relative importance, and can surely distinguish between the extreme positions that deny the explanatory power of either wage changes or monetary changes, once the other is taken into account (p. 228). Thus Harberger contended that if either nmonetary changes or wage changes are excluded, the regression analysis might not be able to distinguish between these extreme positions. A formulation such as Vogel's, using money supply changes and lagged values of the rate of inflation, can capture the variation in prices resulting from: 1) current and past instances in which money supply changes alone have driven up prices; 2) current and past instances in which monetary and structural variables have risen in step; and 3) past instances in which structural variables alone have been at work. The only instances that it clearly will not capture are those in which current structural variables have operated without accompanying money supply changes. Vogel's high k2 indicate that these instances have been few relative to all others. However, because Vogel's model will attribute to monetary factors the variation in prices due to both current structural causes which have been financed by increases in the money supply and past causes which have affected the lagged price variable, these R2 cannot say anything about the relative importance of structural and monetary factors. The Harberger model is designed to identify the relative inflationary impact of structural and monetary factors when each has operated alone. If it is true that in the majority of instances both have operated together and that in an important number of instances, each has forced up prices on its own, then either a totally monetary model, such as Vogel's, or a totally structural one will leave only a small portion of the variation in prices unexplained. Their relative importance as independent inflationary forces will only show up in an equation which uses both sets of factors. * Economic affairs officer, General Agreement on Tariffs and Trade. I assume sole responsibility for the views expressed here.

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.