use (7) to substitute for Wn■ Rearrange it to get:
p(i)1 e
Φn (i) LnAn (i)σ
_ r fθ an (j Γ dj
use an(j) = an (i) [⅛⅛J] /( σ
to elimnate An («)■ Integrate i over the interval
[0,1], use (3) and rearrange:
r = |(LNr jθ φN (i)
-∣ 1— σ
σ
1-σ di
+ (ΘLs)σ J1 Φs (i)
σ
1-σ di
- 1—σ ^Vσ
Finally, use (22) to substitute for fj t Φs (i)σ^1 σ^ di^ The Euler equation g = r — ρ
then yields equation (23) in the text
35
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