tion technology F is well-behaved (Fκκ < 0 < Fκ). After-tax profits are:
πi -(1 — u) f Çk {Ai, Bi), Ai, Bl^ — (1 — ua) K (Ai, Bi) (1)
where u is the statutory tax rate and a the rate of tax depreciation allowances.8
Optimal investment implies
∂F{K(Ai,Bi) ,Ai,Bi} _ 1 — uα
∂K (Ai,Bi) - 1 — u
(2)
which implies the optimal choice of K. In the following, K without tilde
denotes the optimally chosen K. It is straightforward to show that Ku — ^K < 0
and Ka — ^K > 0. a — 1 implies undistorted investment.
Firm 1 is assumed to have a high firm-specific profitability Ai and a low
location-specific profitability Bi. Firm 2 has a low A2 and a high B2. Roughly
speaking, firm 1 is internationally mobile and firm 2 is not. Mobility means, that
firm 1 leaves the country if its after-tax profits π are smaller than the profits which
could be earned abroad π*.
The government maximizes the utility of the households according to the social
welfare function
(3)
W - U (c) + H (д')
where c is private consumption and д is a publicly supplied good. Consumption
c is the after-tax income of the two firms. д is financed by the tax revenues.
The government has the choice between two general strategies. The first is
to levy high taxes, accepting that firm 1 will leave the country. In this case,
the standard result of the taxation of locally fixed profits is valid: Investment is
undistorted and the tax rate can reach 100%.
The second is to choose the optimal tax policy subject to the constraint that
firm 1 stays in the home market. In the following we will focus on this case. The
maximization problem is:
W — U Ç( (Fi (1 — u) — (1 — au) K^ + H Çu ( ( (Fi — aKi)^ (4)
8Any other taxes than source taxes are ruled out.