1218 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
FISHER 
I have one or two points to make. Both of these are on issues 
brought up during the discussion, the one by Professor Koopmans 
and the other by Professor DORFMAN. 
Professor KoopmaNs raised the point that small changes in prices 
might induce large changes in action. This is, of course, a possibility, 
but it is less serious the more different ways there are of doing things. 
For example, even if the technology is a linear programming one, the 
production possibility frontier will approach a continuous surface if 
there are many different activities which cover the entire nonnegative 
orthant. 
Now the question of discontinuities of this type is also relevant to 
Professor DORFMAN’s remarks and indeed my comment here should 
pe taken as a comment on his paper rather than on FriscH’s. Pro- 
fessor DORFMAN wants to present policy makers with shadow prices 
when they are at a particular vertex and see what they will do. The 
discontinuity problem arises in this connection because there will ge- 
nerally be more than one set of shadow prices at a vertex. Each set 
will be associated with movement from the vertex one is at to another 
particular one. The alternatives must be presented to the policy 
maker therefore in a form which insures that once he has said he 
will move to another vertex he will not then also want to move back 
at a different but still appropriate set of shadow prices. One must 
‘herefore ask questions which bracket the range of admissible shadow 
prices. Once again, if there are numerous activities, this is not a 
serious problem because the sets of shadow prices associated with a 
given vertex will not be very wide. 
WOLD 
It seems to me that Professor ALLAIS is dramatizing the argument 
a little. It has not occurred to me that Professor FriscH nor anybody 
else believes that it is possible to arrive at something like the actual 
truth when setting up a utility function for a political decision at the 
17] Frisch - pag. 22