Cost and production functions. Reprint of the 1st ed (Q1159553)

This book is a reprint of the original version published in 1953 (reviewed in Zbl 0052.15901). Consequently no new results in production theory can be found in it but almost all ideas laid down in this book were basic for the development of production theory in the last 25 years. The main topic of the book is worked out in the first six chapters: Some important implications from the first order conditions of the cost-minimization problem are deduced which are now well known in the literature as the ``Shephard lemma'' (chapter 3). Secondly it has been proved by Shephard using methods of ``convex analysis'' that the production function can be reconstructed from the (minimum)-cost function, the production isoquant (for a given output level) and the unit-cost surface are proved to be polar reciprocal transforms of each other (chapter 4, 5). In principle the same conclusions can be derived if the factors of production are constrained by linear resp. non-linear restrictions such that not all factors are allowed to vary freely (chapter 6). Chapters 7 and 8 are de-voted to a detailed analysis of the properties of homothetic production functions. It is proved in chap. 7 that such production functions ``generate'' (minimum)-cost functions which can be factored multiplicatively into two functions one of which depends on the prices and the other depends on the output level. In chap. 8 the properties of the Cobb-Douglas production function are analyzed especially with respect to the ``aggregation aspect'' arising from the fact that C.-D. production functions are often utilized in analyzing productive interrelationships between macroeconomic variables. In chapter 9 the aggregation problem is taken up again in a more general framework. To be more precise the book deals with aggregation over commodities exclusively the problem of aggregation over technologies is not included. Conditions are established which imply that the production and cost functions can be written as dependent solely on particular ``indices'' of input factors resp. factor prices. Finally the results concerning homothetic production functions are applied to a dynamic monopoly pricing problem (chap. 10). [See also the author's book `` Theory of cost and production functions. Princeton Studies in Mathematical Economics. 4. Princeton, N. J.: Princeton University Press (1970; Zbl 0244.90011).]