SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMETRIQUE ETC. 
233 
is another concave function (Figure 5). The term convex pro- 
grammung 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 dif- 
ferentiable 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 indi- 
rectly 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), homo- 
geneons 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. «