Public goods production, nontraded goods and trade restrictions.

• Author: Michael, Michael S.

1. Introduction

   When lump-sum taxes are available, the first-best rule for public good production requires that the sum of the marginal rates of substitution be equal to the marginal rate of transformation (e.g., Samuelson [13, 387-89]). In this case, the social marginal cost of the public good equals its private marginal cost of production. When distortionary taxation is used to finance the production of public goods, Pigou [12] argues that the social marginal cost exceeds the marginal cost of production because of the induced indirect cost due to raising revenue through distortionary taxation. Stiglitz and Dasgupta [14, 151-74], Atkinson and Stern [3, 119-28], and Wildasin [15, 227-43] among others, demonstrate that in certain cases (e.g., when the taxed and public goods are complements in consumption), Pigou's argument fails and the social marginal cost may fall short of the marginal cost. A number of authors (e.g., King [10, 273-91], and Batina [5, 125-33]) examine these and related issues in a many-persons economy. In a trade theoretic context, Feehan [7, 155-64] derives the efficiency rule for the production of a pure public good when it is financed through tariff generated revenue. Abe [1, 209-22] examines the welfare effects of tariff reform programs when tariff revenue is used to finance the production of a pure public consumption good.

   We build a small open economy trade model where two traded goods, one exported and one imported, one nontraded private good, and one public consumption good are produced. The production of the public good is financed through lump-sum taxes. Imports are restricted through voluntary export restraints (VERs), quotas, or tariffs.(1) Within this framework, and relative to previous studies, the present paper makes the following contributions. First, it shows that the Samuelson's rule is valid under an import quota and violated under a tariff or a VER. Second, it offers a different interpretation as to why the social and private marginal cost of the public good may not be the same. Third, it shows that the difference between the social and private marginal cost of the public good not only depends on the complementarity/substitutability between the public and restricted (i.e., imported) good, but also on the complementarity/substitutability between the imported and nontraded and between the nontraded and public good. That is, it depends on the "general equilibrium" substitutability/complementarity between the imported and the public good. Specifically, when imports are restricted by VERs (respectively, tariffs) the marginal cost understates (overstates) the social marginal cost when the public and imported goods are general equilibrium complements, and overstates (understates) it when they are general equilibrium substitutes.

2. The Public Good Economy with Trade Restrictions

   Consider a small open economy with a representative consumer, producing three private goods - one exported, one imported and one nontraded good - and one public consumption good that is provided by the government to the representative consumer free of charge. Two internationally immobile factors - capital and labor - are used in the production of the four goods. The production functions are homogeneous of degree one and concave in the two factors. The full employment condition requires that

   [v.sup.p] + [v.sup.g] = v, (1)

   where [v.sup.p] and [v.sup.g] are the amounts of factors used in the production of the private and public goods, and v is the vector of fixed factor endowments (i.e., dv = 0).

   Good and factor markets are perfectly competitive and trade is subject to alternative import restrictions (VERs, quotas, or tariffs). As usually assumed, tariff revenue is lump-sum distributed to the consumer, VER rents are captured by foreign exporters, and quota rents are captured by domestic importers.(2)

   Let [p.sup.*] and p denote the world and domestic relative price of the imported good. The difference between the two prices, denoted by t(= p - [p.sup.*]), may be due to a tariff, an import quota, or a VER. Since the country is small in world goods markets, changing the import constraints or the level of public good production does not affect the world prices of the traded goods.

   Individual utility depends on the consumption of the four goods, which are assumed normal. The private expenditure function, E(p, q, g, u) represents the minimum expenditure needed to achieve a level of utility u at a relative price of the imported good p, relative price of the nontraded good q and level of public good consumption g. The derivatives of the expenditure function with respect to p and q (i.e., [E.sub.p], and [E.sub.q]) are the compensated demands for the imported and nontraded goods. An increase in the consumption of the public good reduces the expenditure on the private goods needed to achieve a level of utility u. Thus, [E.sub.g] is negative. In the public economics literature, -[E.sub.g] is called the consumer's marginal willingness to pay for the public good [10, 273-91]. Throughout the analysis, subscripts denote partial derivatives.

   The maximum value of private goods production, for given p and [v.sup.p], is represented by the gross domestic product function [R.sup.*](p, q, [v.sup.p]). The derivatives of this function with respect to p and q (i.e., [Mathematical Expression Omitted] and [Mathematical Expression Omitted]) are the supply functions of the imported good and the nontraded good, and with...