The Gains from Trade and the Gains from Aid: Essays in International Trade Theory

By Murray C. Kemp | Go to book overview

1

THE GAIN FROM INTERNATIONAL TRADE *

1

INTRODUCTION

In a brilliant paper of 1939 Paul Samuelson proved, under certain assumptions concerning technology, that for a small country unable to influence world prices, free trade is, in a clearly defined sense, better than no trade.

In this essay I shall offer a generalization of Samuelson’s theorem. In particular, it will be shown that free trade or trade distorted by (non-negative) import or export duties or quantitative import or export restrictions is, in Samuelson’s sense, better than no trade, regardless of the size of the trading country. The theorem will be shown to be valid whether or not the country imports raw materials, or is a net lender or borrower—possibilities from which Samuelson abstracted in his initial exposition.

For the most part my method of proof parallels that introduced by Samuelson. My indebtedness to his 1939 paper will, I hope, be abundantly clear.


2

SAMUELSON’S 1939 THEOREM

It will be convenient to begin with a bare statement of Samuelson’s theorem.

We shall consider a single economy consisting of one or more individuals enjoying a certain unchanging amount of technological knowledge, so that we may take as data the production functions relating the output of each commodity to the amounts of inputs devoted to its production. Any number of commodities is assumed; there may also be any number of inputs or productive services. These are not necessarily fixed in amount, but may have supply functions in terms of various economic prices. Moreover, for our purposes the differentiation of the factors of production can proceed to any degree; thus, labour services of the same man in different occupations are not regarded as the same factor of production unless the provider of these services is indifferent as between these two uses. [As a limiting case, factors may be occupationally completely immobile.] Similarly, in order that the productive services rendered by different individuals may be considered

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