SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMETRIQUE ETC.

233

is another concave function (Figure 5). The term convex programmung
 derives from the fact that the feasible set, and each
set of points on which the maximand attains or exceeds a given
value, are convex (!). Linear programming is a special case
of convex programming.
With any optimal point in a convex programming problem
one can associate a hyperplane H through that point, which
separates the feasible set from the set of points in which the
maximand exceeds its value in the optimal point (H is a line
in Figure 5). The direction coefficients of such a hyperplane
define a vector of relative prices implicit in the optimal point.
One interpretation of the implicit prices is that the opening up
of an opportunity to barter unlimited amounts of commodities
at those relative prices does not allow the attainment of a higher
value of the maximand. Moreover, if the maximand is a differentiable
 utility function, one may be able, by treating utility
as an additional « commodity » and choosing its « price » to
be unity, to interpret the implicit prices of the other goods as
their marginal utilities either directly in consumption, or indirectly
 through the extra consumption made possible by the
availability of one more unit of that commodity as a factor of
production.

|

A ONE-SECTOR MODEL WITH CONSTANT
STEADILY INCREASING I ARBOR Fore

TECHNOLOGY AND

We assume that output of the single producible commodity
is a twice differentiable and concave function F(Z, L), homogeneons
 of degree one. of the capital stock Z and the size o

1 : . __. .
(') A convex set is a set of points containing everv line segment con
necting two of its points

., Koopmans - pag. «