The Lens Condition with Two Factors

The authors give a simple, constructive proof that the lens condition implies the factor price equalization condition when there are only two factors. Taking stock of the conditions under which the lens condition is equivalent to the factor price equalization condition, there are the conditions of two factors or two goods or two countries, or the condition that the rank of the factor‐use matrix is equal to the number of goods. It is shown that, in an essential sense, there are no other such conditions.     

Why the Lens Condition Cannot Imply Factor Price Equalization

This paper explains why the lens condition cannot imply the factor price equalization condition when the rank of the factor use matrix is larger than two, but smaller than the number of goods. This arises from production substitution and the degeneration of the convex polyhedrons consisting of the possible output vectors of a country where the factor market is cleared. Two kinds of necessary and sufficient conditions for the factor price equalization condition are given. As a byproduct, a simple proof is given on equivalence between the lens condition and the factor price equalization condition in the case where the rank of the factor use matrix is two.     

SUFFICIENCY OF THE LENS CONDITION FOR FACTOR PRICE EQUALIZATION

Abstract.  Demiroglu and Yun (1999 ) and Wong and Yun (2003 ) gave counterexamples to show that the lens condition is not sufficient for factor price equalization. However, they leave the following two important problems untouched: why the lens condition is not sufficient for factor price equalization in general; and whether counterexamples can be given only in a very special case. This paper extends these papers to a framework without two input vectors being proportional to explain why the lens condition loses sufficiency and gives a lot of counterexamples which include those provided in above papers as special cases.     

Factor price equalization beyond a “cubic” world

Summary. The importance of factor price equalization (FPE) is widely recognized in economics. The FPE theorem states that, absent any factor intensity reversal, factor prices are equal across countries with identical technologies and product mixes. In a two-factor-two-good-two-country Heckscher-Ohlin model this is equivalent to countries factor endowments being contained in the diversification cone defined by goods factor intensities. This paper identifies a condition, stated in terms of the allocation of factor endowments across countries relative to the demand for and the factor intensities of goods, that is necessary and sufficient for FPE in a world with arbitrary number of countries, goods and factors.Received: 16 July 2004, Revised: 10 January 2005, JEL Classification Numbers: F1.     

Factor Price Equalization in a World of Many Trading Countries

Conditions sufficient for factor price equalization within any non‐trivial subset of trading countries are provided. The conditions are that (a) the factor endowment ratios of countries in the subset are all bounded by the factors‐in‐use ratios in an equilibrium of the hypothetical world economy in which factors are perfectly mobile within the subset, and that (b) in dimensions higher than two, either the rank of the factors‐in‐use matrix is 2 or products do not outnumber factors and the factors‐in‐use matrix is of full rank.     

Globalization and the Inequality–Unemployment Tradeoff

Over the last 20 years, advanced economies have experienced an “unemployment versus inequality” tradeoff that is critically uneven across countries. To explain this, we propose an extended HOS model in which: the factors are skilled and unskilled labor; there is a continuum of goods; the world comprises two North countries (one egalitarian and one nonegalitarian) and the South; there is no factor price equalization; globalization consists in the South cornering a growing share of world production. In the North, globalization entails an inequality–unemployment tradeoff and the adjustment to globalization is more painful for the country that was initially inequality‐oriented.     

Micro Convergence and Macro Convergence: Factor Price Equalization and Per Capita Income

Factor price equalization implies the equality of prices of the same productive factors across countries owing to free trade. The present paper examines the relationship between factor price equalization and the equality of per capita (per worker) incomes in the contexts of the static Heckscher–Ohlin trade model and the dynamic two-sector neoclassical growth model. Factor price equalization is shown to be neither necessary nor sufficient for equality of per capita incomes across trading countries.     

General equilibrium with trade balance and real interest rate parity

This paper demonstrates, in the context of a two-sector OLG neoclassical growth model, conditions under which international trade in consumption goods alone may be sufficient for the equalization of real returns to physical capital across countries; that is, under which commodity arbitrage is sufficient for real interest rate parity (RIRP). This role for repeated commodity arbitrage is established via a dynamic extension of the factor price equalization (FPE) theorem which is valid at all dates comprising the equilibrium path as well as its steady state. The results are at odds with the conventional view regarding RIRP which arises from open one-sector growth models, in which case steady state trade balance and RIRP are irreconcilable, and are also a contradiction to frequent assertions of lon-run specialization in two-sector frameworks. An equilibrium path for an integrated world economy yields an endogenous, time-variant cone of diversification which implies sufficient conditions for the dynamic paths of a cross-section of economies to exhibit FPE, and hence RIRP with trade balance, at all points in time. These conditions require that the savings rates and initial capital-labor ratios of individual countries do not deviate too significantly from world averages, and that both sectors absorb capital easily. The first of these requirements is sufficient to establish steady state FPE and RIRP in the general specification. The first two requirements are sufficient for the entire equilibrium path to be characterized by FPE and RIRP in a log-linear example. Received: September 22, 1998; revised version: February 10, 2000     

Jointness In Production and Factor-Price Equalization *

This paper argues that the presence of activities which yield outputs jointly does not damage the case for factor-price equalization. the crucial condition for equalization is similar to that in the no-joint production case: the number of common activities with independent input vectors that are actively used in both countries at least match the number of factors, and factor endowments lie sufficiently close. Indeed, joint production may increase the range of commodity prices for which factor prices are equalized by commodity trade.     

Trade,growth, and convergence in a dynamic Heckscher–Ohlin model

In models in which convergence in income levels across closed countries is driven by faster accumulation of a productive factor in the poorer countries, opening these countries to trade can stop convergence and even cause divergence. We make this point using a dynamic Heckscher–Ohlin model—a combination of a static two-good, two-factor Heckscher–Ohlin trade model and a two-sector growth model—with infinitely lived consumers where international borrowing and lending are not permitted. We obtain two main results: First, countries that differ only in their initial endowments of capital per worker may converge or diverge in income levels over time, depending on the elasticity of substitution between traded goods. Divergence can occur for parameter values that would imply convergence in a world of closed economies and vice versa. Second, factor price equalization in a given period does not imply factor price equalization in future periods.     

Similarity of endowments and the factor price equalization condition

Summary. We give a geometric interpretation of the lens condition, proposed by Deardorff as a shortcut for checking the factor price equalization (FPE) condition. We identify the conditions under which the lens condition implies the FPE condition. If the FPE zone is not a neighborhood of the diagonal allocations, however, the lens condition is irrelevant despite the implication since the FPE condition (hence the lens condition) is unlikely to be satisfied in that case. We give precise conditions under which the lens condition is equivalent to the FPE condition and simultaneously, the FPE zone is a neighborhood of the diagonal allocations. Received: January 2, 2002; revised version: July 1, 2002 RID="*" ID="*" The author would like to thank an anonymous referee, Bruce Dieffenbach and Michael Jerison for helpful comments.     

Pushing Economies (and Students) Outside the Factor Price Equalization Zone

Despite overwhelming empirical evidence of the failure of factor price equalization, most teaching of international trade theory (even at the graduate level) assumes that economies are incompletely specialized and that factor price equalization holds. The behavior of trading economies in the absence of factor price equalization is not well understood, and some major textbook treatments err. The authors map regions of specialization and diversification for standard competitive economies and show how outputs, goods, and factor prices change as economies move within and across different regions of diversification and specialization. Two examples of how the analysis can enrich graduate-level trade teaching are given: the substitutability of goods trade and factor movements, and debates over the trade and inequality.     

Regional Heterogeneity and China's Trade: Sufficient Lumpiness or Not?

This paper explores whether there is sufficient lumpiness or heterogeneity in the relative endowments (capital, labor, and skills) of the regions of China to affect China's specialization and trade patterns. It does so using both the lens condition to identify the violation of factor price equalization across regions, and direct evidence on regional trade and specialization. The results are sensitive to the level of regional aggregation. The paper concludes, however, that China was sufficiently lumpy as recently as 2004 to affect its pattern of international trade.     

Monopoly,intermediate goods and the pure theory of international trade

Conclusion In a model with two traded good sectors between which intersectoral flows of intermediate goods are allowed and with a monopolized non-traded good sector, the wage rate in terms of two traded goods increases and the rental of capital in terms of two traded goods decreases when the price of relatively more labor intensive traded good sector increases, though nothing definite can be said about the direction of change in the wage rate and rental in terms of the non-traded good. When prices of traded goods are kept constant and labor and/or capital increase(s), output of the non-traded good sector increases provided that the non-traded good is not inferior, having income elasticity of demand less than unity. The factor intensity condition for the traded goods is in general not sufficient for the validity of the Rybczynski theorem to hold with respect to net outputs of the traded goods. We have derived sufficient conditions for the magnification effect to be observed with respect to net outputs of the traded good sectors. Specifically, we have shown that the factor intensity condition (23) is sufficient for the magnification effect to prevail when only labor increases.     

Monetary Shocks and Real Exchange Rate Dynamics: a Reappraisal

This paper proposes a two‐country general‐equilibrium model incorporating a tradable sector with pricing‐to‐market as well as a nontradable sector. In that case, real exchange rate fluctuations arise from two sources: changes in the relative price of traded goods, that exemplify deviations from the law of one price, and movements in the relative price of traded to nontraded goods across countries. Our framework sheds light on the propagation mechanisms through which monetary shocks affect the real exchange rate. More specifically, the two components respond in opposite directions to monetary disturbances, which is consistent with data. Besides, the introduction of nontraded goods does not alter the predictive power of monetary shocks because the presence of nontraded goods magnifies the response of the deviation from the law of one price.     

Capital Accumulation and Convergence in a Small Open Economy

Outward‐oriented economies seem to grow faster than inward‐looking ones. Does the literature on convergence have anything to say on this? In the dynamic Heckscher–Ohlin–Samuelson model, with factor‐price equalization, there is no convergence of incomes. This is because with identical preferences and return to capital, irrespective of initial levels, the growth rates of consumption are the same. In the specific factors' model, there is factor‐price equalization in the long run, but incomes depend on endowments of non‐accumulable factors. Different specifications for the intersectorally mobile factors have different implications for development (as well as convergence).     

Factor Price Equalization when the World Equilibrium is not Unique

It is shown that, whatever the multiplicity of the integrated world equilibrium, (i) factor prices are equalized if and only if the distribution of primary factors between trading countries can be represented by a point in or on the boundary of a certain convex subset of R ^m , where m is the number of primary factors, and (ii) the likelihood of factor price equalization is independent of the multiplicity of the equilibrium.     

The Distributional and Allocative Impacts of Virtual Labor Mobility across Time Zones through Communication Networks

Using a specific‐factors' model, with two goods (a shift‐working good and a non‐shift‐working good), three factors (capital specific to shift‐working, land specific to non‐shift‐working and labor) and two countries (Home and Foreign), which are located in different time zones, we highlight the impact of trade in labor services via communication networks on factor prices and production patterns. If two countries are identical in size, then under free trade in labor services, all workers work only in their local daytime, and night shift in each country is performed by imported labor services supplied by residents of the other country in their local daytime. Night‐time wage becomes the same as daytime wage (a wage equalization result). Other factor prices are also equalized. In both countries, capital rental rate increases, while land rent decreases. However, if two countries are different in size, trade in labor services does not equalize wages: in the large country, wages for night‐shift workers are higher than daytime wages and some residents work at night; in the small country, daytime wages become higher than night‐time wages and no one works at night, and night‐shift work is done by imported labor services from the large country. Land rent in the small country decreases. Land rent in the large country may or may not decrease, but it is always higher than in the small country. Capital rental rates in both countries are equalized and increase.     

Monetary Policy with Sectoral Trade‐Offs

We formulate a two‐sector New Keynesian economy featuring sectoral heterogeneity along three dimensions: price stickiness, consumption goods durability, and the usage of input materials in production. These factors affect both inter‐sectoral and intra‐sectoral stabilization. We examine the welfare properties of simple rules that react to alternative measures of final goods price inflation. Due to factor demand linkages, the cost of production in one sector is influenced by price‐setting in the other sector. Therefore, measures of aggregate inflation weighting sectoral prices based on their relative stickiness do not allow one to keep track of the effective speeds of sectoral price adjustment.     

Foreign Factor Ownership and Optimal Tariffs

In the presence of foreign factor ownership tariffs change not only the terms of (goods) trade but also income flows between countries. Assume that only the home country owns factors abroad. Then the optimal tariff is negative if and only if foreign factor ownership entails trade-pattern reversals. Trade-pattern reversals are neither a necessary nor a sufficient condition for a negative optimal tariff if the foreign country owns factors in the home country. Changes in the home country's tariff shift the foreign country's offer curve. This adds a new dimension to optimal tariff analysis.