SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMEIRIOUE ETC. 480 
APPENDIX 
Maximizing the quadratic preference function (3.7) subjec: 
to the constraint (3.4) can be done conveniently by using iui: 
constraint to eliminate the vector of noncontrolled variables 
The result is 
‘A.1) 
where 
‘A.2) 
a (à, Po +8) — 
F 
Tr 
k, rk oi 
Eo 
7xge, Rs 
‘= - R'R, 
x'Ka 
Che optimal decision is then 
‘A.3) x= -K k= (gd + RR)! (gx, 
which shows that our first task is to find the inverse of gA + R'KX 
Let us write 
A.4) 
Theil 
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