Optimal Tax Policy when Firms are Internationally Mobile

5 Appendix

This appendix shows how to derive equation (30). First, recall equations (23) and
(24). Given the level of B, how do и and a affect A^h7

dA^h

du

dA^h

da

B=const

F(A^h,K^h) - aK^h

F_a (A^h, K^h) (1 - u) - F_a (A^h, K^h*) (1 - t)

-uK ^h

B=const

F_ah (A^h, K^h) (1 - u) - F_ah (A^h, K^h*) (1 - t) > ⁰

Note that

dA^hda

dA^h / uK^h

du ∖F (A^h,K^h)

aK ^h

(32)

Given the level of B, how do u and a affect A^z?

dA

du

dA

da

B=const

B=const

F (A^l,K^l) - aK^lFa (A,K^l)(1 - u)
-uK^l

F (A,K^l)(1 - u)

With (32) it follows for equation (28):

^{dw h}'^-^u'>B' £^(F^-^k>^dAdBh'£(^u⁽^F'^-^k`^da)^dB

Solve for H'

<g ^,-u '> U' tf‘ l<f-K>dAdB
J_sC⁺ ((F ^h-κ^h) ^c^∙_{f d}B

and replace H' in equation (29):

∂W
da

B++ rA^h

(H' - U') u uKdAdB

Jb- A a

(H' - U') J+B⁺ JAA^h [(F - K)] dAdB

B⁺⁺ ∂A^h

,B ^{u f}^{h -}^k^ft) -dA^dB

fB⁺ U (F^h - K^h) ^tA AA-} dB
JB ∖ V t da uK^ft /

Rearrange and write:

16

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