Econometrica: Mar, 1971, Volume 39, Issue 2

The Output Limit Function in General and Convex Programming and the Theory of Production

https://doi.org/0012-9682(197103)39:2<309:TOLFIG>2.0.CO;2-L
p. 309-339

S. N. Afriat

Programming theory is treated initially without any assumptions about the functions and with interpretation for production and activity analysis. By proof of a general theorem about optimal and support solutions and subsequent introduction of convexity assumptions, a new method for obtaining standard propositions and an amplification of their content becomes possible. Properties entirely peculiar to linear problems are noted. Two "shadow price" interpretations are discussed, one being the standard one in which support solutions appear as prices in a fictitious market. Consideration is also given to the law of diminishing returns. Finally, vector output, with emphasis on a concept of irreducible limit output, is treated.