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 Ah7

dAh


du


dAh


da


B=const


F(Ah,Kh) - aKh

Fa (Ah, Kh) (1 - u) - Fa (Ah, Kh*) (1 - t)


-uK h


B=const


Fah (Ah, Kh) (1 - u) - Fah (Ah, Kh*) (1 - t) > 0


Note that


dAh
da


dAh /     uKh

du F (Ah,Kh)


aK h


(32)


Given the level of B, how do u and a affect Az?

dA


du


dA


da


B=const


B=const


F (Al,Kl) - aKl
Fa (A,Kl)(1 - u)
-uKl

F (A,Kl)(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
JsC+ ((F h-κh) ^c^∙f dB


and replace H' in equation (29):


∂W
da


B++ rAh

(H' - U')     u uKdAdB

Jb- A a

(H' - U') J+B+ JAAh [(F - K)] dAdB

B++            ∂Ah

,B u f h - kft) -dAdB


fB+ U (Fh - Kh) tA AA-} dB
JB V            t da uKft /

Rearrange and write:

16



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