In the open Leontief system, the term we
obtained as the solution of **x** is as follows:

x= (I-A｢)^{-1}c

This is also known as the "*matrix multiplier*" since it
relates consumption to output in an almost Keynesian
fashion. Letting D be the difference operator so that D **x** is a change in output and D**c**
is a change in consumption, then:

D

x= (I-A｢)^{-1}Dc

which simply states that growth in consumption must be met by growth in output as proportioned by the inverse of the technology matrix.

This "Keynesian" result has interesting implications if we wish
to think about employment and capacity utilization. If primary inputs are not producible,
by definition, then one might think that they are endowed and thus *limited* in
supply. Consequently, one may conjecture that the supply of endowed factors might
constrain the level of activities** x** below equilibrium or, more interestingly,
remain in excess. Let **v** be a vector of primary input supplies, **v**｢** **= [v_{1}, ..., v_{m}], then we now have a
new quantity condition that states:

B｢x｣v

i.e. the demand for primary inputs cannot exceed their supply. In Figure 1
below we see the implications of this assumption. Allowing for inequalities **x** ｳ **Ax** + **c**, so that we can set out the Leontief system as a linear programming problem, we obtain, in
the two-sector case, the familiar L_{1} and L_{2} lines acting as
constraints. However, the endowment restriction implies that we must add a *third*
line, denoted V in the diagram, which places an upper bound on the possible output
combinations in the economy. This arises from the equation **B｢
x** ｣ **v** which, in a two-sector case with one primary
factor, translates into:

b

_{01}X_{1}+ b_{02}X_{2}｣ v

where b_{01} and b_{02} are unit input coefficients of the
primary factor into the two industries while v_{0} is the exogenously-given factor
supply. Thus, the line V has vertical intercept v_{0}/b_{02} > 0,
horizontal intercept v/b_{01} > 0 and slope -b_{01}/b_{02} <
0. Thus, only areas *below* V are feasible according to the primary endowment
constraint. As a result, combining the restriction imposed by L_{1}, L_{2}
and V, the only feasible area remaining is the shaded area in Figure 1. All other areas
have output combinations which violate one of the three conditions.

Figure 1- Excess Capacity and Effective Demand

If we choose the output combination at point E (where output is (X_{1}*,
X_{2}*)), it is obvious that L_{1} and L_{2} constraint are
binding, but constraint V is not binding, thus there is excess capacity. As a result, if
we think of v_{0} as the labor supply, then the output combination (X_{1}*,
X_{2}*) at E is *not* efficient: as V does not bind, then we have obviously
left a good amount of endowed labor unemployed.

The solution to this problem is, in fact, a Keynesian one: as the horizontal and vertical
intercepts of L_{1} and L_{2} contain C_{1} and C_{2} in
them respectively, then if we increase consumption of good 1 (shifting L_{1} to
the right to L_{1}｢_{ }) and/or increase
consumption of good 2 (shifting L_{2} to the left to L_{2}｢_{ }), then our intersection would be at a point such as F
which lies on the V constraint in Figure 1. This would be the more efficient outcome as we
would eliminate the excess supply of the primary input - and we would have also increased
consumption in the process. This an exogenous increase in final demands (e.g. consumption)
will help us eliminate unemployment and excess capacity in the economy. There is nothing
within the Leontief model which forces equilibrium to be at F - thus, being at E, is
equivalent to a Keynesian unemployment equilibrium. The impetus to move to F, as John
Maynard Keynes (1936) proposed, must come
externally from an increase in effective demand.