each row generally represents a 'resource" or "flow" where the bi assoc-
iated with that row is the fixed exogenous quantity available of the
"resource." If that "resource" is not exhausted (i.e. strict equality
does not hold for a given row) then the resource is assigned a zero
"price" because it is in excess supply.

 The condition (L3) is less transparent than (L4) but has a similar
interpretation. Each element of c represents the cost associated with
an input or the revenue associated with an output. In the first part of
condition (L3) we can interpret each row as follows. For a given row of
AT we can consider each element to be the amount by which a primal act-
ivity adds to or subtracts from the availability of a resource or flow.
For inputs, this means that the cost should be allocated so that the
shadow prices reflect the amount that the input adds to each "resource"
or "flow." For outputs, it means that the shadow prices should reflect
the value of the output and the contribution of each resource to the
output.
 The second part of (L3) merely states that if the price relation-
ships do not hold with equality, then the input is not economical to use
or the output is not profitable enough to produce, so the associated
activity should be zero.
 Condition (NL3) is a natural condition and trivially met. Condition
(NL4) is trivially met in this case since f(x) E c'x is a concave
 n
function and b. a..x. E g.(x), i = 1, 2, ..., m, is also a concave
 1 j=l 13 3 1
function. Condition (NL5) is not trivial in practice as one can easily
formulate an LP problem which has an empty X. Since (NL6) is not met in
this case, the uniqueness of a solution is not guaranteed.


2.3 Quadratic Programming


 Quadratic programming has been used for some time in engineering
applications, but has only recently come into use with problems which
are fundamentally economic in nature. For economic modeling purposes,
the landmark work in the use of quadratic programming is the book Spatial
and Temporal Price and Allocation Models [5]. This volume contains an
exhaustive treatment of a broad range of models which use mathematical