From (21) we have:
∂c
∂E
ξ (1 - a)
(1 - δ) (ξ - α)
a ¢(1 — a)
∕dd∖ ~ л ξ ¢(1-a) _1 ¢(1-") ∕β (1 — δ)(1 — βδ)∖ —
— A■ E (1-δ)(ξ-a) 1L ξ ------—----'
U J к (1 + β — 2βδ)2 J
• (a (ξ + θ) - ξ)
g(ξ+ff)-ξ
αη
(αη)a- (α (ξ + η + θ) - ξ)
α(ξ+η+θ)-ξ
ξ-a
" a "
(αd∖ ξ-a
ш
ξ a(l -ξ) + δ(ξ -a) ¢(1-")
Aξ-a E (1-δXξ-a) L ξ-a
¢(1 —a)
μ β (1 — δ) (1 - βδ) λ ξ a
I (1 + β — 2βδ)2 )
"(¢ + 0) —ξ aη
α(ξ+n + θ)-ξ
• (α (ξ + θ) — ξ) a-ξ (αη)a-ξ (α (ξ + η + θ) — ξ)
ξ-a
and then:
∂c
∂L
ξ (1 — a) ξ — α
------------------------------------- . -----------------------
" a ɪ
(αd∖ ξ-a
ш
. ξ ξ(1-a) ¢(1-a) _1
Aξ-a E(1—δ)(ξ-a) L ξ-a
(β (1 — δ)(1
I (1 + β — 2βδ)
_

¢(1-a)
∖ ¢-a
a(C+£2-€ aη "(¢+^ + 0) -¢
• (α (ξ + θ) — ξ) "- (αη)"- (α (ξ + П + θ) — ξ) ,e" =
. ¢ ¢(1-a) "(W)
A¢-" E (1-5)^-a) L ¢-"
( β (1 — δ)(1 — βδ) ∖ ⅛"2
I (1 + β — 2βδ)2 )
"(¢+0) -¢ aη a(€+n + ^)-€
• (α (ξ + θ) — ξ) a- (αη)"- (α (ξ + η + θ) — ξ) ^a
and also:
∂c
∂A
a ,∖ ɪ
α αd∖ ¢-ɑ
ш
. ⅞ _1 ^1-a) ⅞(1-a)
At' a E(1-≡-a) L t' a
8β (1 — δ) (1 — βδ)
I (1 + β — 2βδ)2
¢(1-a)
- - a
a(C+£)-C aη "^+п + ^) -¢
• (α (ξ + θ) — ξ) "- (αη) "- (α (ξ + η + θ) — ξ) ^"
a ¢(1 -a) ¢(1-")
A¢-" E(1-δ)(¢-a) L ¢-"
ββ (1 — δ) (1
к (1 + β — 2βδ)
_

ъ1
¢(1-")
ʌ ¢-"
"(¢ + 0) -¢ aη "(¢+^ + 0) -¢
• (α (ξ + θ) — ξ) "- (αη) "- (α (ξ + П + θ) — ξ) ^"
and finally:
∂c
∂d
-1
α i ɪ .. ¢(1-") τ
—A ¢-" E x-'XW-") L
ξ
¢(1-")
¢-"
μβ (1 — δ) (1 — βδ) ∖ ⅛""2
1 (1+ β — 2βδ)2 )
"(¢ + 0) -¢ aη
• (α (ξ + θ) — ξ) "- (αη) "- (α (ξ + П + θ) — ξ)
ɑ(¢+η+θ)-¢
¢-"
2a-¢
α2 α adʌ ^"
ё Ш
; ξ(1-a) ξ(1 -a)
A¢-a E (1-δ)K-" L ¢-a
∕β (1 — δ) (1 — βδ) ∖ ';-"
к (1+ β — 2βδ)2 )
"(¢ + 0) -¢ aη
• (α (ξ + θ) — ξ) "- (αη) "- (α (ξ + П + θ) — ξ)
a(¢+η+θ)-¢
¢-"
36
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