Optimal Tax Policy when Firms are Internationally Mobile

where Fi denotes F (K_i, A_i, B_i), subject to

F₁ (1 — u) — (1 — au) K₁ ≥ π*                      (5)

The optimality conditions are:

W_u = 0 = (H' — U') ∑ (Fi — aKi) + H' (u ∑ (F_Kt — a) K_iU}        (6)

^{+a [(F}1 ^{— aK}1^)]

^Wa = 0 = ^{— (H}' ^{— Uf)} ^^ ^(uKi⁾ + ^H' (^u ^^ ^(FK ^{— a) K}ia^ + ^{A [—uK}1^] (⁷)

W_λ  =  0 = (F1 (1 — u) — (1 — au) Ki) (1 — u) — π*                      (8)

where A is the Lagrangian shadow price. Note that with immobile firms the
optimality conditions are the same with A = 0. In this case, the public good
provision is efficient (H' = U') and investment is undistorted (a = 1).

With A > 0, it follows from (6) and (7) that the closed economy result H' = U',
a = 1, u > 0 cannot be an optimum anymore. Therefore try the solution with
undistorted investment but underprovision of the public good (H' > U', a = 1,
u > 0).

Given that W_u = 0 is satisfied, it follows from equation (6) that:

(H¹ — Uɔ ∑ (Fi — Ki)
^(Fi ^{— K}i⁾

Now replace A in (7) and rearrange.

with Ω = (H' — U') ^k^_f> 0. The welfare effect of varying a, evaluated
at a = 1, depends on whether the term in square brackets is positive or negative.
To get the intuition, interpret the first term in the square brackets as the average
return per unit of capital in the overall economy and the second term as the return
per capital unit of firm 1. That means, that a = 1 is an optimal strategy if the
mobile firm is as profitable as the immobile one.

However, if one assumes that the mobile firm is more profitable than the rest

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