Factor Price Equalization with More Industries Than Factors

Abstract

This chapter discusses factor price equalization with more industries than factors. The local version of factor price equalization is that small changes in factor endowments leave factor prices unchanged, given that goods prices are fixed. Factor prices are locally constant as functions of factor endowments. A global version is that two countries whose factor prices are locally constant and that face the same international prices and have the same technology also have exactly the same factor prices. Factor price equalization, both local and global, depends critically on the comparison of the number of industries and the number of factors. For example, on the negative side, if the number of factors exceeds the number of goods, small changes in factor endowments will change factor prices, and local factor price equalization does not hold (Samuelson, Diewert and Woodland, and Jones and Scheinkman). On the positive side, both local and global factor price equalization results have been shown for the cases where there are exactly as many factors as industries. A big difference between the cases of equal and unequal numbers of industries and factors is that in the former case, the cone of factor price equalization is unique, whereas it need not be in the latter, more realistic, case.