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

                   countries.  Capital  will  keep  moving  away  until   Hence, the welfare-maximizing tax rate t  must
                   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
                   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
                   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-
                   domestically owned capital,  of  ρk .  Meanwhile,   shot stance. If t  (t is part of t_ ) is changed, assuming
                   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
                   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
                      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
                   – f '(k )k and net return to domestically owned   W (t ,t_ ) when .  For instance, if
                      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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