Optimal Tax Policy when Firms are Internationally Mobile

∂W
да

(H' - U')

sA F^hh - кη . лв

Sb- ^F^h - ^k'^,) “AS ` ^лв

B- rA^h

Jb- Aai

KdAdB

Bl _hA^h г/ .-, ^s λ ^{s s} Γ^b+ ( S B^lh lK^l'∖ ‘A^h F^h-K^h ʌ jγ>

/в- ʃ" [(^f - K)] dAdB Bb- (J^{F - K} ‘ -< к)^d-^b

(33)

JBB^- Sh^h KdAdB SB- (f^h - к^h) '.dB

Now consider the second term in the square brackets. It is:

(^f^h - ^k^h) ^λa-^fa

- K^hK^h

cov

- к^h)

dA^h F^h - K^hda K^h

^dη dB.Γ - B ∖ dB
da ) B в- V K )

Rearrange:

^ιF [(f^h - K^h) ⅜') dB
SB- F^h - ^k^h) A^dB

f k^a

SB- ((^f^h - ^k^h) ¾h)^dB

BB F^h-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 - r^h--

(Fh _- кh⁾ ‘A^h F^h-K^h

(F^h - K^h) ‘"h

with r = ^fkK the average return per capital unit, r^h
per capital unit of the most productive firm and

= (^f~kK~) the return

Ω = (H' - U')

S^bb^- u ⁽F ^^k^h) - ^k^h) d"^h^dB

SB^- (u (^f^h - ^k^h) ‘-"h > ^dB

B3⁺ "h^h

B B- Aa¹

uKdAdB > O

some scale factor.