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Article Excerpt
Abstract The purpose of this paper is to show that indeterminacy can arise in a simple competitive two-country dynamic model of international trade, free of externalities, imperfect competition, and government intervention. This seemingly surprising result is based on an assumption that there is no international credit market. As will be shown later, the assumption implies that dynamic equilibrium paths of our two-country, therefore heterogeneous consumer, model are not generally Pareto-optimal.
Keywords Indeterminacy * Two-country model * No distortion
JEL Classification Numbers E13 * E32 * F11 * F43
1 Introduction
This study investigates the dynamic behavior of the economic activities of multiple countries in a two-good, two-factor model in which there is no international credit market.
A dynamic general equilibrium model with heterogeneous agents was first studied by Becker (1980). In a perfect foresight model with many consumers, a competitive equilibrium path is well known to behave like an optimal growth path, as Bewley (1982), Yano (1983, 1984), and Epstein (1987) demonstrated.
Later, Nishimura and Yano (1993a,b) studied the interlinkage of business cycles between countries in a discrete-time, large-country model. Atkeson and Kehoe (2000) applied a large-country Heckscher-Ohlin (H-O) model to the analysis of development patterns. Bond, Wang and Trask (2003) characterized an integrated world equilibrium path in a dynamic H-O model. Ghiglino and Olszak-Duquenne (2001) investigated economic fluctuations in a two-country dynamic general equilibrium model. (See Wan and Majumdar (1980) for the problems arising in the large country model.)
Recently there has been a growing body of literature on the existence of indeterminate equilibria in dynamic general equilibrium economies. (1) Indeterminacy refers to the presence of a continuum of equilibrium paths starting from the same initial condition. While the earlier results on indeterminacy relied on relatively large increasing returns, Benhabib and Nishimura (1998) and Benhabib, Meng and Nishimura (2000) showed that indeterminacy can arise in multisector models with constant social returns to scale when a small wedge is placed between private and social returns. To justify this wedge, those papers assumed that factor-generated externalities are present in production sectors. (See also Majumdar and Mitra (1995) for dynamics in a small country model with increasing returns, but without externality.)
The purpose of this paper is to show that indeterminacy may arise in a simple competitive two-country dynamic model of international trade, free of externalities, imperfect competition, and government intervention. This seemingly surprising result is based on the premise that international borrowings and lendings are not allowed in the two-country model, which contrasts well with the Bewley-Yano model in which each consumer's utility optimization is subject to her wealth constraint alone. As will be shown later, this difference between the Bewley-Yano model and the present two-country model makes it possible that dynamic equilibrium paths of the latter model are not generally Pareto-optimal and it cannot be aggregated to a single-consumer world economy.
Moreover, the indeterminacy result has an important implication for the factor endowment theory of international trade, a core theory of trade patterns, in which owners of factors of production cannot earn factor income outside their country.
As Chen (1992) and Shimomura (1992) concluded, a large-country dynamic H-O model has multiple stationary states and it depends on the initial international distribution of factor endowments to which steady state the world trade equilibrium path converges. In particular, Chen contends that other things being equal, the initial distribution of factor endowments explains the long-run pattern of international trade in the Heckscher-Ohlin manner.
However, as we will see later, the indeterminacy result in this paper holds even under the assumption often made in trade theory such that existing factors of production are internationally immobile if each country is incompletely specialized without international market for any factor of production and factor price equalization (FPE) holds at each point in time. Since trade and production patterns may differ among stationary states, the indeterminacy result implies that initial international distribution of factor endowments does not necessarily determine the long-run trade pattern.
We have elsewhere derived a similar indeterminacy result by introducing factor-generated externalities into a dynamic two-country H-O model. (2). However, the indeterminacy result in this paper is not derived from any "distortional factors" such as externalities, imperfect competition, public goods, trade policies, and so forth. It comes from the intrinsic inefficiency of the dynamic trade model, due to the lack of international borrowings and lendings.
The remainder of this paper is organized into four sections. Section 2 formulates the two-country dynamic trade model; Section 3 characterizes its long-run equilibrium and obtains the characteristic equation evaluated at a long-run equilibrium; Section 4 derives the indeterminacy results; and. Sect. 5 gives concluding remarks.
2 The dynamic two-country model
In this section we formulate the continuous-time version of the dynamic two-country model. In what folllows, we call the two countries the home and foreign countries.
2.1 The production side
Two goods items, a consumption item and an investment item, are produced using two factors of production: capital and labor. The first item is a pure consumption item and the second a consumable capital goods item. The home and the foreign households own labor l, l* and capital stocks k, k*, respectively. (3) While capital is a reproducible factor, labor is a primary and time-invariant factor. Both factors are internationally immobile.
Let [a.sub.ij], i, j = 1, 2, be the amount of factor i to produce one unit of goods item j, where factor 1 is labor and factor 2 is capital. We assume Leontief technologies, which means that all the input coefficients, [a.sub.ij], are nonnegative and constant. Full employment conditions in the home country are
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)
Solving equation (1), we obtain
[y.sub.1] = [[a.sub.12]k - [a.sub.22]l]/[[a.sub.21][a.sub.12] - [a.sub.11][a.sub.22]], [y.sub.2] = [[a.sub.21]l - [a.sub.11]k]/[[a.sub.21][a.sub.12] - [a.sub.11][a.sub.22]]. (2)
The outputs of the foreign country are similarly given by
[y*.sub.1]...
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