Richard Manning

Trade, Education and Growth: The Small-Country Case

This paper develops optimal educational and trade policies for a small open economy capable of growth. A theoretical structure previously used for the analysis of education and growth in closed economies (Manning [1975, 1976, 1978, 1979a, 1979b, 1981b]) is extended to do this. The analysis is aggregative. It differs from that of a similar problem by Aarrestad [1978] by allowing for heterogeneity of the labor force. Recently, Henry [1979], and Henry and Manning [1980], developed the model of this paper to permit the endogenous determination of international commodity prices, but only in the context of balanced growth. All of these papers belong to a small literature on aggregative aspects of education and growth, other examples of which include Aarrestad [1975], Hu [1976], Razin [1972a, 1972b], Tu [1969, 1970], and Uzawa [1965]. Oniki and Uzawa [1965] is the classic extension of the Heckscher-Ohlin theory of international trade to permit growth. In models of their type, production possibilities are given instantaneously and are altered over time by factor accumulation. Educational policy affects the production possibility set in two ways. An increase in educational activity reduces the factors available to produce traded goods, and so shrinks the production possibility set immediately: In the longer term the level of skill is altered, so changing the production possibility set. Both the size and shape of the production possibility set are determined statically and dynamically by educational policy. McMillan [1978] has recently presented a model of public intermediate goods, trade and growth with the same property. A problem like this is considered in Manning [1981a], for a general model of capital accumulation and growth. The structure of this paper is as follows. The model and optimality conditions are first presented. Growth is then analyzed, and it is found that specialization is the most likely pattern of production. A deeper investigation of the economics of the model explains this conclusion. Some concluding remarks are then made. Details of the lengthy mathematical proofs of two Propositions are relegated to a Mathematical Appendix.

On the shape of the single-country and world commodity-substitution and factor-substitution surfaces under conditions of joint production

Abstract In recent years trade theorists have completed the task of specifying necessary and sufficient conditions for the single-country and world transformation surfaces to be locally of any assigned degree of flatness. However those conditions are relevant only if the technology is of the no-joint-products type. In the present note we derive necessary and sufficient conditions for the single-country and world transformation surfaces to be of any assigned degree of flatness under conditions of joint production; and we also obtain, as a by-product, necessary and sufficient conditions for the single-country and world equal-product surfaces to be of any assigned degree of flatness.

The scale effect of public goods on production-possibility sets

Publisher Summary This chapter discusses the shape of the set of production possibilities in the presence of public goods that are inputs to production processes. Examples of such public intermediate goods are the production infrastructure—transport and communications services, irrigation, and flood control, pollution control, and technological knowledge. However, in an economy with non-convexities, existence and Pareto-optimality of competitive equilibrium cannot be assured. The free-rider problem means that in an economy with public goods, Pareto optima may not be attainable. When the public goods are intermediate goods rather than consumption goods, this reason for misallocation of resources loses much of its force because the problem of obtaining the information needed to compute how much public-good supply is optimal and is of lower order of difficulty. If, however, the public intermediate goods give rise to non-convexities in the production-possibility set, then there is a second source of misallocation of resources, separate from the free-rider problem. With non-convexities, even if the public intermediate good is optimally supplied by some mechanism, rational action by individual agents may not lead to an efficient outcome.

National Product Functions in Comparative Steady-State Analysis

The structural properties of steady state are well understood for multisector models, but the comparative dynamics of long-run growth are much less developed. By exploiting duality theory, this paper obtains conclusions about these effects for a small, internationally-trading economy. Arbitrary numbers of consumption and capital goods, and a very general technology, are admitted. Definite conclusions about the short-run and long-run impact on outputs and factor prices are not always available, but often correlations can be established between vectors of parameter changes and endogenous variable changes. Copyright 1991 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Nonsubstitution over the production-possibility frontier

Publisher Summary This chapter first presents a non-substitution theorem for the usual case of no joint products and a single primary resource. The concepts employed are then extended to establish a local non-substitution theorem for the general case. These two results establish the connection between competitive equilibria and the flat segments of the production-possibility frontier, along which no substitution of inputs occurs within industries. The chapter also explores the duality of competitive equilibria and efficient input selection. It is shown that in a market economy, the techniques that yield greatest profits also imply the highest real incomes to factor owners. These techniques are the efficient set described by the non-substitution theorem. The chapter also discusses a coherent exposition of the major concepts and results involving non-substitution theorems. The simpler proofs used for the simple and general non-substitution theorems highlight the nature of the results.

The Geometric Construction of Production Functions that Are Consistent with an Arbitrary Production-Possibility Frontier

The production-possibility frontier is strictly concave and negatively sloped if two commodities are produced according to linearly homogeneous, strictly quasi-concave production functions that use, with different intensities, two factors of production that are available in fixed supply. In this paper, it is shown that any arbitrary, concave, negatively sloped production-possibility frontier can be generated by a pair of linearly homogeneous, quasi-concave production functions given fixed total endowments of two factors. Thus, the construction of such arbitrary production-possibility frontiers places no other restrictions on the underlying production technology.