model. Symmetry of Q implies that these commodity relationships be
exactly equal between two commodities. For example, if we have two
commodities and two demand functions of the following form:


 P1 1 11l 12 2

 P2 2 '21x! W22x2

then w12 must equal ',i if the interaction between the two commodities
is to be correctly specified by QP.
 In practical econometric work, the chances of such interaction
coefficients arising naturally from statistical estimation are very remote
unless one superimposes the symmetry condition stated above in the esti-
mator. Thus, we are left with a need for a modeling procedure which
allows a more general set of demand and supply functions (i.e. an asym-
metric Q matrix), and still preserve the economic rationality of the model
(chapters 14 and 18 of [5]).


2.4 Linear Complementarity Programming


 Solution of QP problems involves a simplex type algorithm, however,
the basis change decisions cannot be made with direct reference to the
objective function as in linear programming. QP type algorithms proceed
to find an optimal solution by finding a solution which satisfies the
conditions (Q4) and (Q5) (i.e. the Kuhn-Tucker necessary conditions for
solving a quadratic programming problem). The problem may be stated in
the following manner.
 Find x, p, w,' w2

which satisfy


(LCP2) 1 +
 w2 -A Q x

(LCP2) w'p = 0 and w x 0


x, p, w1, w2 non-negative.


(LCP3)