In this chapter we begin to make use of the analytical techniques developed in the previous one. Our aim is to establish some of the most basic propositions concerning the pattern of trade and the gains from trade. To this end, we first set up models for one country in autarky, and in a trading equilibrium. Simple ‘revealed preference’ comparisons allow us to prove the results concerning gains from trade. Then we consider a model of two countries in a trading equilibrium, which gives some insights into the reasons for trade, and the patterns of trade. Finally, we derive various well-known models as special cases, and compare their properties. The general model will be the workhorse for later chapters, where we study some further properties of trade equilibria, and carry out some comparative statics and policy analyses.

The exposition will proceed from very simple models to successively more complex ones: from one consumer to many, from inelastic factor supplies to variable ones, and from all goods being tradeable to some being non-tradeable. The simpler models serve to introduce concepts and techniques in settings where they are more easily understood; this familiarity will then make the more complex and more realistic cases easier to grasp. In later chapters, we sometimes revert to simpler models for similar reasons; when the complication is not material to the particular purpose, allowing it only confuses the issue.

All models of this chapter, and those of Chapters 4–7, share two important underlying assumptions: (1) each agent, consumer or producer, is a price-taker, (2) prices adjust instantaneously to levels which clear all markets.