Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

(3.8) Q
(3.9) Tc ■ •q.
(3.10) Tc ■ T;
(3.11.1)
(3.12.1)
(3.13.1)
(3.14.1)
(3.15.1)
Q1 Q2
1
-& (Ql' a2 )
equilibrium conditions.
Since we are, primarily interested in investigating the effects of
rate and associated cost changes upon quantities and shipper costs, we
first invert (3.2) and (3.3) to express rates as functions of quanti-
ties. Then the definitions and equilibrium conditions can be utilized
to reduce the model to a set of five equilibrium relations in five
endogenous variables.
(3.11)
(3.12)
(3.13)
(3.14)
(3.15)
Q 1 Q 2 18 D(Tc' AB)
T r
E 1 1)
1
r 2
T 2 E (Q 2 )
c r
T - Ti °
1
(Q1 )
c r
T - T 2 ° Z 2 (Q2 )
Equations (3.11) through (3.15) can be solved for Q 1 , Q 2 , T c ,
Tr and Tr ' Knowing the values assumed by these variables, we can then
1 2
utilize equations (3.6) through (3.10) to find Q, 4, T;, T: and 11.
Now, to perform our qualitative analysis we rewrite (3.11) through
(3.13 adding a shift parameter to each function.
-D(Tc )
+ T r
. 1
■ 0
0
55