Tax policy and endogenous factor supply in a small open economy.

• Author: Waschik, Robert G.

1. Introduction

   Since a paper by Kemp and Jones [6], there have been few attempts at modeling the effects of variable factor supply in a simple trade model, with almost all papers confined to a two-good, two-factor, small-open-economy model. Papers were typically concerned with the effect of variable factor supply on the shape of the economy's production possibility set, and with the result derived in Kemp and Jones [6] that when one factor is endogenously supplied in a simple two-good, two-factor general equilibrium trade model, output supply functions may no longer be upward-sloping, as in Frenkel and Razin [5], and Martin [7; 8], for example. A more general treatment is given in Dixit and Norman [3] and Woodland [14], where in an m-good, n-factor general equilibrium trade model, it is assumed that a subset of the factors of production are endogenously supplied, but very few comparative statics experiments are explored. A recent paper by Mayer [9] synthesizes much of this earlier work in a two-good, two-factor general equilibrium model, and provides an initial attempt at modeling the employment effects of tariff changes.

   Since the existence of variable factor supply in even a very simple general equilibrium trade model has been shown to complicate the simplest comparative statics results, the literature has paid very little attention to the exploration of the effects of various tax policy changes on factor supply. As a result, an important channel of the effects of trade tax changes on equilibrium has been largely ignored, that being the effect of trade tax changes on factor market equilibrium, and the concomitant effects on equilibrium in the small open economy. The question of the effects of variable factor supply is also important given the obvious attention that policy-makers and various interest groups pay to the employment effects and industry output effects of trade and factor tax policy changes.

   Another important implication of the lack of attention paid to endogenous factor supply in international trade models is the inability of trade models to analyze the effects of taxes on factor supply. In the standard Heckscher-Ohlin trade model of a small open economy with an endowment of factors of production, factor taxes can have no real effects.

   The objective of this paper is to use the general equilibrium trade model with endogenous factor supply developed in Dixit and Norman [3] and Woodland [14] to illustrate the implications of the presence of endogenous factor supply for many familiar tax policy experiments. We will also examine the effects of tax policy changes on factor market equilibrium. Results will be derived using duality theory in an m-good, n-factor trade model, so that the analysis will not be restricted to the case where there are only two goods and two factors. Assumptions of constant returns to scale, perfect competition, and the absence of externalities will be retained so as to concentrate on the effects of variable factor supply. The model is presented in section II.

   In order to raise revenue, many governments collect taxes on factors of production whose level of supply ought most appropriately be modeled as being endogenous. For example, tax on labor income collected in Canada in 1986 implied an average tax rate of 17.8% of value added by labor. When some factors are endogenously supplied, these taxes will have real effects on equilibrium factor supply, so our first step must be to determine the employment effects of factor tax changes on endogenously supplied factors in a general equilibrium trade model. These effects are derived in section III, where we show that factor taxes will always reduce variable factor supply when those factors are normal. Since taxes on international trade will also affect equilibrium factor supply, it also becomes necessary to determine the way in which trade taxes distort the market for endogenously supplied factors. We determine the effects of trade taxes on the supply of endogenous factors in section III, and describe conditions under which trade tax changes will either raise or lower factor supply. Results in this section imply a generalization of results in Mayer [9], which uses a two-good, two-factor general equilibrium trade model with one endogenously supplied factor, and only considers the effects of tariffs on imports.

   Once the effects of trade and factor taxes on general equilibrium have been determined, we can consider the welfare effects of trade and factor taxes when some factors are endogenously supplied. In section IV, we show that zero trade and factor taxes still constitute a Pareto-optimal equilibrium for a small open economy, so that increases in trade or factor taxes starting from an initial equilibrium with no taxes must reduce welfare. However, if there exist trade and factor taxes, then a reduction in trade taxes may lower welfare. We derive the characteristics of the vector of optimal second-best trade taxes when there are taxes on endogenously supplied factors, for a small open economy, and show how trade taxes can offset or augment the factor-market distortion imposed by a factor tax in a small open economy.

   The volume of trade effects of trade and factor tax changes are given in section V. For a given trade tax change, volume of trade effects are derived when all factor supplies are fixed and when the supply of some factors are determined endogenously. The presence of variable factor supply is shown to magnify the volume of trade effects whenever the cross-price elasticities between an endogenously supplied factor and traded goods are sufficiently small. This result is particularly important when considering results from general equilibrium trade models describing the volume of trade effects of trade tax changes, such as those implied by the recently completed uruguay Round of the GATT or the North American Free Trade Area between Canada, the U.S., and Mexico, since these predicted volume of trade effects would generally be underestimated. Concluding comments are offered in section VI.

2. Dual Trade Model with Endogenous Factor Supply

   In constructing the trade model, we must keep in mind the ultimate objective of carrying out some comparative statics experiments. To this end, we will not consider the case where there are more goods produced in equilibrium than there are factors of production, since then the equilibrium vector of output supplies would not be unique, and the local analysis using differentiation in subsequent sections could not be applied. In the interest of simplicity, we will also not consider the case where there are more factors than goods, since not much insight is added at the expense of a considerable degree of complication.(1) Instead we concentrate solely on the case where the number of factors equals the number of goods produced in equilibrium. In this "even" model, for a small open economy (SOE) unable to affect world output prices, the production sector will take output prices as given by world terms of trade, level of supply of the endogenous factors as given by the solution to the consumption sector's utility maximization problem, and the level of supply of the remaining factors as being exogenously given, and will determine input prices and level of output supply. The consumption sector will take output prices as given by world terms of trade, input prices as given by the solution to the production sector's cost minimization problem, and will determine the level of output demand and level of supply of the endogenous factors, subject to an income constraint given by the endowment of factors.

   We describe an economy with m perfectly competitive industries producing outputs y[prime] = ([y.sub.1], [y.sub.2], ..., [y.sub.m]) with n factors of production. The consumption vector for the economy is represented by the vector [Mathematical Expression Omitted]. We let [Mathematical Expression Omitted] be the vector of domestic output prices corresponding to y and z. Suppose that a subset e [is less than or equal to] n of the factors of production are endogenously supplied, while the remaining n - e factors are exogenously supplied. The endowment vector can be written as:

   [Mathematical Expression Omitted],

   with v [is an element of] [R.sup.+], [Mathematical Expression Omitted]. We correspondingly decompose the factor price vector into [Mathematical Expression Omitted], [Mathematical Expression Omitted]. To incorporate the presence of endogenously supplied factors into the demand side of the economy, assume that there exists a single representative consumer in the economy who owns all of the productive factors, some of which he directly consumes. Since the consumer can substitute between consumption of some factors and consumption of goods...