Modelling Commodity Balances: A Derivation of the Stone Model

Abstract

This paper is the first of two essays on the modelling of commodity balances in which a path is traced from the representation of commodity balances in a social accounting matrix framework to the modelling of such balances in the context of a computable general equilibrium. From the outset, commodity balances are expressed at market prices. Therefore, in addition to the usual make and absorption matrices, a third matrix, referred to here as the ‘marketing matrix’, is needed to provide a complete description of commodity balances at this level of accounting. This description is then specialized by imposing the law of one price and assuming that activities produce bundles of products i.e. by assuming a general form of commodity technology. A linear model of commodity balances is explored in the next stage. Also, Stone's commodity technology model is shown to be a special case which can be derived via the reduced accounting framework obtained by eliminating the accounts for final commodities from the original matrix using the method of apportionment. It is suggested that various problems which may arise in using Stone's model can be ignored on the grounds that the model remains a reasonable approximation, or the database should be reviewed with a view to improving the data themselves or to adopting some alternative (more detailed) classification of activities and products.