220 PONTIFITIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 
~ 8 
For example, in designing a road, we may need shadow prices for 
the saving of lives or for the saving of time that would result from 
designing and building the road to higher standards. 
SCHNEIDER 
If you would call this additional cost the shadow price, then 
[ am in agreement with you; I have understood shadow prices as 
prices that are not paid on the market but which are calculated for 
internal deliveries from one firm to another firm. 
KOOPMANS 
The term and concept of shadow price has caught on very much, 
and like Prof. SCHNEIDER, I am all for its use. I would only point 
out that the theory on which the concept is based does not cover as 
many conditions and circumstances as our tendency to use the term 
would suggest. In particular there is the tase of choices in which 
important indivisibilities are present. I would surmise that the 
concept of shadow prices can be precisely and carefully extended 
to such cases, but I have not seen it worked out in the literature. 
There is one article by BaumorL and Gomory (« Econometrica », 
July 1960) that goes in this direction, but it does not go all the way. 
Prof. MAHALANOBIS asked: is there a specific study of a steel 
mill from this point of view. I may mention a study not of a steel 
mill, but of a fertilizer plant — the question of whether in the Latin 
American area there should be one, two, three or up to five or six 
plants, and if so, for each number what are the best places to put 
them. There is a study by MaNNE and VIETORISZ devoted to this 
question in a volume called « Studies in Process Analysis », edited 
by Manne and Markowitz (Wiley, 1963). That study used combina- 
‘orial methods because of the indivisibilities of the plants concerned. 
Again the shadow price concept has not been fully elaborated, and 
‘hat is how the reference occurred to me in this context. 
31 Dorfman - pag. 34