We construct a general equilibrium model of international trade where each government agent has a system of tariffs as his strategic variables. Our general equilibrium model follows recent contributions allowing incompleteness and intransitivity of consumer preferences. Government agents are assumed to have incomplete information on the preferences of domestic consumers and the availability of commodities. The behavior of each government agent is to choose a system of tariffs to maximize the estimated preferences of domestic consumers with a constraint on an estimated availability of commodities. We introduce an equilibrium concept so that (a) estimated preferences and an estimated available set of commodities are compatible with an observed state of the world economy and (b) a consumption bundle intended by each government agent coincides with a consumption bundle chosen by its domestic consumers. Our major goal is to provide the existence of such an equilibrium.

THE MAIN PURPOSE of this paper is to investigate properties of production possibility sets when technology sets are neo-classical. By neo-classical technology we mean (i) externalities in production are absent and (ii) nonproducible commodities or primary factors are fixed in their supply. Production possibility sets are defined to be those derived from technology sets when constraints on the supply of nonproducible commodities are added. Our model is a fairly general one where, in particular, intermediate commodities and joint products are allowed. Of course, individual technology sets will provide us with enough information when we are only interested in individual behavior. In such a case, we may not need the concept of production possibility sets. But when we are concerned with more global pictures of an economy and when the supply of nonproducible commodities is assumed to be fixed, then production possibility sets can provide us with a nice summary of production sectors and it is possible to obtain more qualitative information from our models. In the next section, we shall describe our model and give the main assumptions. Section 3 will be devoted to a characterization of production possibility sets which turns out to be a generalization of the well-known nonsubstitution theorem of Samuelson. Three applications of the result in Section 3 will be discussed in Section 4. In Section 5, we shall show that when technology sets satisfy a condition called the weak indispensability of nonproducible commodities, then production possibility sets have the desirable properties of closedness and boundedness.