∂W
да
(H' - U')
sA Fhh - кη . лв
Sb- Fh - k',) “AS ` лв
B- rAh
Jb- Aai
KdAdB
Bl hAh г/ .-, s λ s s Γb+ ( S Blh lKl'∖ ‘Ah Fh-Kh ʌ jγ>
/в- ʃ" [(f - K)] dAdB Bb- (JF - K ‘ -< к)d-b
(33)
JBB- Shh KdAdB SB- (fh - кh) '.dB
Now consider the second term in the square brackets. It is:
(f h - k h) λa-fa
- Kh
Kh
cov
- кh)
dAh Fh - Kh
da Kh
dη dB.Γ - B ∖ dB
da ) B в- V K )
Rearrange:
ιF [(fh - Kh) ⅜') dB
SB- Fh - kh) AdB
f ka
SB- ((fh - kh) ¾h)dB
BB Fh-Kd),lB
where the LHS is the second term is square brackets of equation (33). Now
rewrite equation (33):
∂w ry h h cov
—— = Ω r - rh--
(Fh - кh) ‘Ah Fh-Kh
(Fh - Kh) ‘"h
with r = fkK the average return per capital unit, rh
per capital unit of the most productive firm and
= (f~kK~) the return
Ω = (H' - U')
Sbb- u (F ^kh) - kh) d"hdB
SB- (u (fh - kh) ‘-"h > dB
B3+ "hh
B B- Aa1
uKdAdB > O
some scale factor.
17