Page 6 - Working Paper (Optimal Corporate Income Tax Policy for Large Developing Countries in an Integrated Economy)

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DDTC Working Paper 1416
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countries. Capital will keep moving away until Hence, the welfare-maximizing tax rate t must
i
the increased scarcity of capital in i has increased fulfill following first-order conditions
the gross marginal product of capital there and
reduced the marginal product of capital elsewhere
by enough to bring the arbitrage condition back
into balance. We can see clearly here the impact of increasing
tax rate imposed by one unit. An increase in tax
On the consumption and welfare side of
rate would reduce rents to immobile factors due
the model, a representative consumer have
to capital outflow this would cause. Meanwhile,
preferences of private goods and public provision,
this change also increases revenue, thus increasing
which can be expressed as W (x,r) = x + G (r). is public provision, but reducing net income earned
1
1
private consumption and r is publicly provided
from capital endowment. Whether the decision to
good; G is strictly increasing, strictly concave and increase tax rate will improve the welfare or not
1
18
satisfying an Inada conditions which ensures
will depend on whether the increased government
that, in the absence of other source of revenue,
revenue can more than offset the reduced rents to
all countries will charge a strictly positive tax rate
immobile factors.
in equilibrium. Private consumption is financed
by the rents to domestic immobile factors – or in One should note that equation (6) is the case
short, wage – f (k ) – f '(k )k and the net return to when tax rate in other countries, t_ is taken as one-
1
1
i
i
i
i
domestically owned capital, of ρk . Meanwhile, shot stance. If t (t is part of t_ ) is changed, assuming
i
j
i
j
public goods in financed by per capita receipts t k strategic complementarity would increase, then it
i i
from capital located domestically, which means holds that:
r = t k . Thus, the typical consumer in country can
i
i i
be expressed as
Following the same logic, intuition might
suggest that, the best response to this is for i to
Each government maximizes its objective reduce its own rate too. But, realistically, this has
function by a choice of its tax rate, taking the tax not certain direction of value. As Keen and Konrad
rate choices of all other countries as given, and (2014) clearly stated: ‘A lower tax rate in some
anticipating the implications of their choice for other country j, for instance, moves capital out of
the allocation of and net return to capital. In the country i and so reduces its tax revenue and public
model, the tax rate is assumed as the single factor spending; whether the best response to this is for i
contributing to the allocation of capital across to raise or lower its tax rate depends, among other
border in international economy. On one side, tax things, on how large an increase in the marginal
rate positively affect the public goods provision, value of public spending this implies.’ 19
but on the other one, it negatively affect private
A solution to the system (6) is an intersection
production decision taken by capital owner.
of the best responses t (t_ ) and characterizes an
i
i
Considering the big picture suggested by the interior Nash equilibrium. In the system comprised
model, the government cannot solely consider of numerous countries, each of the economy
its objective by just maximizing tax revenue. stays at the state where there is no better gain in
The impact to the economic decision taken by making changes given the state of other countries’
private sectors is also an influential aspect for economy.
the government in shaping the national tax
The next question is whether such an
system. Welfare in country i is determined by two
equilibrium has any social optimality properties.
determining elements: private consumption –
which is funded by rents to immobile factors, f (k ) Potential inefficiency arises in a game with
1 1
i
i
– f '(k )k and net return to domestically owned W (t ,t_ ) when . For instance, if
1
i i i
capital, ρk –, and public provision G , which is
i i
determined by per capita receipts t k from capital
i i
located domestically.
then, country j would set tax rate that, from the
perspective of country i, is too low. For the model
ZMW model, (4) above implies that
18. Inada conditions guarantee that a production function is positively
related to the associated factors. The conditions are built by several
assumptions, which are: 1) the value of the function at 0 is zero, ; 2)
the function is strictly increasing in G, ; 3) the derivative of the function
is decreasing so that the function is strictly concave, ; 4) the limit of the
derivative approaches plus infinity when k goes to zero, lim ; and 5) the
limit of the derivative approaches zero when G goes to infinity, lim . See 19. Michael Keen and Kai A. Konrad, “The Theory of International Tax
Daniel Primont and Rolf Fare, “Inada Conditions and the Law of Diminishing Competition and Coordination,” Max Planck Institute for Tax Law and Public
Returns”, Discussion Papers, No. 3 (2001): 1-8. Finance Working Paper, No. 06 (2014).
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