Shepherd R.W. Theory of Cost and Production Functions

Princeton: Princeton University Press, 1971. - 324 p.A sequel to his frequently cited Cost and Production Functions (1953), this book offers a unified, comprehensive treatment of these functions which underlie the economic theory of production.
The approach is axiomatic for a definition of technology, by mappings of input vectors into subsets of output vectors that represent the unconstrained technical possibilities of production. To provide a completely general means of characterizing a technology, an alternative to the production function, called the Distance Function, is introduced.
The duality between cost function and production function is developed by introducing a cost correspondence, showing that these two functions are given in terms of each other by dual minimum problems.
The special class of production structures called Homothetic is given more general definition and extended to technologies with multiple outputs.