# The envelope theorem and Viner's draftsman

In 1931 Viner wrote the paper "Cost Curves and Supply Curves" that famously contained the following mistake: Viner had asked the draftsman to draw the long run average cost curve so that it was tangent to the minimum of the short-run average cost curves. His draftsman told him this was impossible and it was only until after the publication of the paper that Viner realised his draftsman was right. (To see this is trivial because to be tangent to a minimum means having zero gradient, and a function with zero gradient everywhere is constant. So unless LRAC is constant it cannot be achieved.)

I have two questions:

1. Firstly, I have seen it commonly stated that this is related to the envelope theorem. I understand the envelope theorem as a piece of mathematics but I don't see the precise connection to Viner's mistake.
2. Secondly, in later prints of the paper Viner kept the mistake in so that others could use it for teaching purposes though he doesn't explain what point such a teacher would be trying to make. The (somewhat surprising) implication is that operating at long-run average cost doesn't generally minimise short-run average cost. Though surprising I don't immediately see its significance.