Optimal tariffs and income taxes under imperfect and uncertain foreign investment.

• Author: Itagaki, Takao

1. Introduction

   International investment as well as international trade is now a wide phenomenon, and optimal policies to be selected in the presence of both international trade and investment have been a great concern. Jones |7~ and Kemp |9~ have done pioneering works in this area of study. Previous studies, however, have mostly postulated that international capital movements are perfect.

   While perfect capital mobility is expected in the long-run, Bhagwati and Brecher |2~ and Brecher and Bhagwati |3~ emphasized short-run sluggishness of foreign investment; that is, even in the presence of international differentials in rates of return to capital the amount of foreign capital existing in the host country is fixed in the short-run. A realistic case, however, will be between complete fixity and perfect mobility of foreign capital. This is especially true in the medium-run.

   In such a case the amount of foreign capital existing in a country at a particular future point in time may be reasonably conceived as uncertain to that country. Uncertainty may arise for various reasons. The case includes uncertainty about the level of the rate of return to capital in the world market, and also uncertainty about production technology employed by foreign investors. These cause amounts of foreign capital to be received by the host country uncertain to it even under perfect international capital mobility. Uncertainties in such a case are relevant when the host country government has a long-run perspective, and is concerned with the long-run consequences of its policies.

   This paper addresses the open question of levels of optimal policies to be chosen when foreign capital movements are uncertain as well as imperfect, and examines whether they modify or make intact the optimal policies established traditionally. Policies considered here are import tariff and income tax by the host country, since these are prevalent and have attracted much attention in the literature of international trade and investment.

   The schedule of the paper is as follows. In section II perfect international capital mobility is assumed. However, production technology of foreign investors or the world rate of return to capital is uncertain for the host country. In section III imperfect or partial capital mobility is assumed. But, the response of foreign capital to international differentials in rates of return to capital is regarded as uncertain for the host country. In section IV a brief summary is given.

2. Perfect Capital Mobility

   Let us first assume perfect international capital mobility, and examine that, in this case, uncertainty does not influence optimal policies for the host country.

   In light of the fact that most foreign direct investment is of industry-specific nature, in the following we shall use the specific-capital model developed by Jones |8~ and Caves |4~.

   Industry-specificity of capital is largely due to technical factors. It makes capital, whether it is domestic or from abroad, unable to move intersectorally for the relevant period of time. The case includes immobility observed even where intersectoral differentials in net returns to capital are changed, say, as a result of changes in tariffs or income tax rates. Industry-specificity, however, does not preclude international capital mobility within the same industries at all. Many observers will agree that international direct investment is mostly within the same industries.

   Perfect competition and non-existence of any distortion are assumed. Sector 1 consists of local producers only, and produces the first goods |X.sub.1~ employing a generic factor, i.e., labor, and specific capital |Mathematical Expression Omitted~. We denote the production function there by

   |Mathematical Expression Omitted~.

   Foreign investment occurs in Sector 2 which produces the second goods |X.sub.2~. Production of |X.sub.2~ is undertaken by both local producers and foreign investors. Let |Mathematical Expression Omitted~ and K denote the capital used by local producers and the capital owned by foreigners, respectively. Furthermore, let |L.sub.2~ denote the total labor employed in Sector 2.

   If the production technology of foreign investors is not known surely for the policy-maker of the host country, their production function takes the form |Mathematical Expression Omitted~, where |Mathematical Expression Omitted~ denotes the labor employed by foreign investors, and u the random variable.(1) Since the aggregate production function also becomes uncertain when the production function of foreign investors, |Mathematical Expression Omitted~, is random, it is convenient to incorporate randomness of the latter into the aggregate production function, and write it as

   |Mathematical Expression Omitted~.

   It is assumed that |Mathematical Expression Omitted~, |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~, where the superscripts denote partial derivatives of |F.sub.i~ with respect to j and k. j and k represent |L.sub.1~, |L.sub.2~, |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~. It is also assumed that |Mathematical Expression Omitted~. All the factors of production are fully employed.

   The host country is assumed to be a small country throughout the following analysis. That amounts of foreign investment become random when the production function is written as (2) is illustrated in Figure 1. There r* denotes the world real rate of return to capital. The MP|K.sub.a~ and MP|K.sub.b~ curves represent the marginal productivities of capital in the host country corresponding to capital stock chosen by foreign investors, when the realized values of random variable u are |u.sub.a~ and |u.sub.b~, respectively. When |u.sub.a~ is realized, foreign investment occurs at |K.sub.a~, and when |u.sub.b~ is realized, it is given by |K.sub.b~.

   On the other hand, let the world rate of return to capital, r*, be random while the production technology of foreign investors is surely known. This case is illustrated in Figure 2. If the world rate of return to capital, r*, takes the value of |r*.sub.a~, the amount of foreign investment is equal to |K.sub.a~, while if |r*.sub.b~ is the realized value of r*, it is given by |K.sub.b~.

   The policy-maker of the host country is assumed to maximize the expected indirect utility EU(p,y), where p is the domestic relative price of the second goods in...