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

(4.15)
(4.16)
(4.17)
(4.18)
• •
We now substitute equations (4.8) through (4.14) into equations
(4.1) through (4.7) to eliminate Q d , T T a (i • 1, 2, 3). The
reduced equilibrium system then appears as
Q1 + Q2 + Q 3
T 1
T 2
w D(Tc ,A)
w E 1 (QM)
■
2 0 2' 10
T• w3(Q3'M) .
3
(4.19) Tc - Tr Z 1 (Q 1 ,M)
1
r
(4.20) T c - T 2 • Z 2 (Q 2 ,M)
(4.21) Tc - Tr 3 Z3 (Q3' M)
Two specifications are now imposed upon the system.
1. The equations are linear in all included variables.
2. The Qi do not appear in equations (4.16), (4.17) and
(4.18)
Specification 1 is necessary due to the nature of the model and the
estimation problems involved. The second specification recognizes
that rates for the commodities we are concerned with are fixed by law
and that the regulatory process may cause the process of rate adjust-
ment to be both long and complex. As will be seen below, it also
allows the empirical work to be separated into two distinct parts.
(4.22)
(4.23)
(4.24)
(4.25)
With these specifications the model may be written as
Ql + Q2 + Q3 wa+0T c +yA
c r
T - T l w a l + b l Q l + c l M
Tc - Tr wa
2
+b
2 Q2 +c 2 M
2
C r
T - T w a + b Q + c M
3 3 3 3 3
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