Our original reason for writing this book was the desire to write down
in one place a complete summary of the major results in du- ality theory
pioneered by Ronald W. Shephard in three of his books, Cost and
Production Functions (1953), Theory of Cost and Produc- tion Functions
(1970), and Indirect Production Functions (1974). In this way, newcomers
to the field would have easy access to these important ideas. In adg,
ition, we report a few new results of our own. In particular, we show
the duality relationship between the profit function and the eight
equivalent representations of technol- ogy that were elucidated by
Shephard. However, in planning the book and discussing it with
colleagues it became evident that such a book would be more useful if it
also provided a number of applications of Shephard's duality theory to
economic problems. Thus, we have also attempted to present exam- ples of
the use of duality theory in areas such as efficiency measure- ment,
index number theory, shadow pricing, cost-benefit analysis, and
econometric estimation. Much of our thinking about duality theory and
its uses has been influenced by our present and former collaborators.
They include Charles Blackorby, Shawna Grosskopf, Knox Lovell, Robert
Russell, and, not surprisingly, Ronald W. Shephard. We have also
benefit- ted over the years from many discussions with W. Erwin Diewert.
