The Viner-Wong Envelope Theorem.

The envelope theorem, now the fundamental tool in modem duality analysis, had its beginnings in Jacob Viner's classic 1931 article on shortand long-run cost curves. It seemed wrong to Viner that at any given point along the long-run cost curve, the long-run average cost curve should have the same slope as the short-run curve, where capital was being held constant. This is still a puzzle to many people, along with the various other envelope theorem results (see, for example, the discussion of a related issue by Sexton, Graves, and Lee 1993). Viner instructed his draftsman, Wong, to draw the long-run curve through the minimum points of the short-run average cost curves. Curiously, Samuelson's resolution of the puzzle in Foundations (1947) dealt only with a simple unconstrained maximum problem, maximize y = f(xl2 ... .. n, a), where the xi's are the decision variables and a is a vector of parameters. Its relation to the original Viner-Wong diagram seems a bit remote at first, and, curiously, a discussion of the envelope theorem in the explicit Viner-Wong context seems missing from the literature.' This is unfortunate because it is possible to communicate the essence of this result (and more general results) with a simple cost diagram that goes back to the roots of cost theory.