The geometry of global production and factor price equalisation
Résumé
We consider a production economy where commodities are partitioned into K irreproducible factors and L reproducible goods, and the production technologies have constant returns to scale. We examine the geometry of the global production set in the space of commodities, and we derive theorems of non-substitution type. We define the "factors values" of the different goods, we use them to characterize the efficient production plans, and we investigate in detail the relations between the prices of goods and the prices of factors. We show that the prices of factors uniquely determine the prices of goods, and that, generically, equalising the prices of 2K goods equalises the prices of factors.