The name is absent



Examining terms on the right hand side and using the definitions of V(X) and Vt(X), we get

Xccc ∞                                  Xccc

I   V,(c + v + u)fι(u)du g(v)dv = /       [   [Bk 2[c + v + u]]fι(u)du g(v)dv

∞ √—∞                        √—∞ √—∞

Xccc


'∞


Bk 2c 2v 2


Zufι(u)du g(v)dv = /

∞                  - —


4.


Xccc


-∞


[-Bk 2c 2v] g(v)dv


[Bk + 2c]Φ Xc—--\+2^συφ(Xc—^-
σ σv J σ σv J

as well as

∞∞

X Xcc — -∞


∞∞

V,(c + r + v + u)f2(u)du g(v)dv = / I [Bk 2[c + r + v + u]]f2(u)du g(v)dv
X Xcc — -∞

Xc


cc


'∞


Bk 2c 2v 2r 2


Zuf2(u)du g(v)dv = /

∞                     ∙ΛX


∙∞


4.


X.


[Bk 2c 2r 2v] g(v)dv
ccc


[Bk + 2c+2r] 1

*i ⅛ )l

v φ(JXσV(1 )

and finally

V V (Xc + r + u)f2(u)du f
— -∞                    — —∞

V (Xc + u)fι(u)du


α Bk[Xc + r + u] [Xc + r + u]2] f2(u)du f α Bk[Xc + u] [Xc + u]2] fι(u)du
-∞                               -∞

BkXc


z∞                    fi∞)               ∞∞

f2(u)du [Bk + 2Xc] / [r + u]f2(u)du — / [r + u]2f2(u)du

∞                J—∞            J—∞


4.


4.


v

σ22 +r2


[a BkXc


4.


∞∞

fι(u)du +[Bk + 2Xc] / ufι(u)du + /
∞                 —-∞         ——


u2fι(u)du


4.


4.


σι


[Bk + 2Xc ]r


r2


σ;


.2


U2


+ σ'.


.2


U1


Putting things together, the first-order condition becomes

k


δ—φ f —c ^ Bkr + 2Xcr + r2 + σ;
συ συ J


U2


— σ(


U1


] δ[Bk + 2c]Φ χx- c


+2σ.δφ(XcσvC )


δ[Bk + 2c + 2r] 1


2avδφ(Xσ^ )


k


δ—φ f —c---ʌ Bkr + 2Xcr + r2 + σ,

σ21 ] δ[Bk + 2c] 2δr 1


συ \ συ y

30



More intriguing information

1. Cultural Diversity and Human Rights: a propos of a minority educational reform
2. Determinants of Household Health Expenditure: Case of Urban Orissa
3. AN EMPIRICAL INVESTIGATION OF THE PRODUCTION EFFECTS OF ADOPTING GM SEED TECHNOLOGY: THE CASE OF FARMERS IN ARGENTINA
4. The name is absent
5. The name is absent
6. The name is absent
7. The name is absent
8. The Nobel Memorial Prize for Robert F. Engle
9. The name is absent
10. The resources and strategies that 10-11 year old boys use to construct masculinities in the school setting