A note on the envelope theorem

The purpose of this note is to discuss the envelope relationship between long run and short run cost functions. It compares the usually presented relationship with one of different form and implications, resulting from a simple production function and constant prices. It points out in particular that the tangency condition between the short and long run total cost functions does not necessarily hold always. The note also shows that a given value of the fixed factor might support in the long run a whole range of levels of output.