Growth, Resource Extraction and Production in a Small Open Economy

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Growth, Resource Extraction and Production in a Small Open Economy

I. Introduction

One of the distinguishing features of exhaustible resources is the uneven distribution of their stocks among nations. Due to this fact, international trade plays a crucial role in the transfer of these resources from resource-rich to resource-poor economies.

With this essential feature in mind, a number of economist have studied, with different emphases, the optimal extraction policies of these economies engaged in international trade. The contributions by Vousden [1974], Long [1974], and Kemp and Suzuki [1975] examined, under different conditions, the dynamic aspects of resource extraction in open economies. However, they often omitted the discussion of capital accumulation and other optimal growth related topics in their models. Subsequently, aarrestad [1978] investigated optimal extraction policies of a resource exporting economy by concentrating on the intraction between optimal savings and optimal depletion policies. Dasgupta, Eastwood and Heal [1978] considered optimal extraction and export policies in the case of a resource monopolist open economy with technical change. La Grandville [1980] used a multisectoral growth model with exhaustible resources to investigate the optimal paths by extending the relation between the rate of interest and the own rate of a commodity in the tradition of capital theory. Moussavian [1985] generalized these results in the presence of non-traded goods. elbers and Withagen [1984] analyzed resource extraction and trade in a two-country general equilibrium model that incorporates conversion costs.

In this context, the purpose of this paper is to introduce a simple Ramsey-type open economy model, whereby we can analyze simultaneously the optimal of capital acculation, resource extraction and consumption.

In the first part of the paper, a Ramsey-type one sector model is developed to study the optimal growth of the economy (1). The small open economy will be assumed to produce a consumption-investment good by using capital and labor and export the resource in exchange for other goods in international markets. In other words the country will extract the resource only for export purposes. Subsequently, the model is modified to incorporate the resource as an input in addition to labor and capital. Besides the analysis of the time paths of the variables of interest and the characterization of the steady-state of the economy, the paper attempts to investigate the impact of the changes in the resource price on the optimal policies in question.

II. Production without the Resource

The model, as mentioned above, describes the optimal behavior of a small open economy that exchanges its resource for other foreign products in the world market. It is based on the assumption that the resource is extracted only for export purposes the economy produces the aggregate output by using capital and labor. Due to the small country assumption the relative price of the resource is exogenously given. The optimization problem of the economy is to mazimize the present value of total social welfare, subject to the dynamic constraints of capital accumulation and resource extraction.

The economy is assumed to use only capital and labor to produce the composite commodity that can either be consumed or invested to increase future production. Therefore the economy is represented by a neoclassical aggregate production function y(t) such that:

[Mathematical Expression Omitted]

Capital depreciates at a constant rate and the labor force growns exponentially at a constant rate n so that,

[Mathematical Expression Omitted] (1)

where the dot denotes the derivative with respect to time.

The resource is extracted at a rate R(t) and the remaining stock of the resource is denoted by S(t). Therefore,

[Mathematical Expression Omitted] (2)

The current account of the economy is always balanced since it is assumed that all net earnings from resource extraction M(t), are used for import. …