Professor Sten Malmquist constructed the Malmquist quantity index and in doing so developed a distance function defined on a consumption space. This function is the consumer analog to the Shephard input distance function of producers and is used in ratio form to define the quantity index. This volume contains new contributions based on Malmquist's work nearly 50 years ago and provides modern perspectives on the value of this research.

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...

The format of this monograph is three essays, which we arrived at after spending a year writing over one hundred pages of what we even- tually realized was a tedious reworking of old material. So we started over determined to write something new. At first we thought this approach might not work as a coherent mono- graph, which is why we chose the essay format rather than chapters. As it turns out, there is a common thread--namely the directional distance function, which also gave us our title. As you shall see, the directional distance function includes traditional distance functions and...