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

(3.C. 3)
,(3.C.6)
The monopolist's profit function is then
4 .
'2 T; - Y." Q2 F(Q2 ) , - e(Q2 ),
and his profit maximizing quantity, is given by the solution of
(3.C.4)
dQ2 F(Q2 ) + Q 2 F'(Q 2 ) -
(marginal revenue equals marginal cost), so long as
d 2H
(3.C.5) — ■ 2 2 . F'(Q
2 ) + Q
2 F"(Q
2
) -
dg
2
-r -
T 2 ■ F(Q 2 ).
2
) < 0.
The rate which he must charge to carry this quantity is then given by
To investigate how we would expect the monopolist to react to a
change in any of the underlying functions we again add our shift para-
meter, a, to equation (3.C.1). The equilibrium relationship (3.C.4)
then becomes
P(Q2 ,a) + Q2 FQ2 (Q2 ,0 - 0'(Q 2 ) ■ O.
Differentiating (3.C.7) totally with respect to a yields
(3. C. 8) •
[2 F
Q2 (Q 2' a) + Q 2 F Q2,Q2 (Q 2' a) - e"(Q 2
• -[Fa (Q2 °) Q2 FQ2,a (Q 2 ,a)].
dQ2
)] da --
Or, defining the first bracketed expression in (3.C.8) as W
• dQ2
1
-
(3.C.9) rw in -% n w In %1
da 171 "a"2"" '2 'CI
2'
a`"2"/".
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