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DDTC Working Paper 1416

                      The existing  theoretical  research thus needs   to the model.
                   to be followed by a  series  of empirical proof.
                   Too  simplified  theory  might  not  just  nullify  the   The profit generated from production function
                   theoretical relevance, but  could also provide   of country i is then deducted by t . Tax treatment
                   policies that  exacerbate the  problem.  And to   here is  assumed  to depend  only on the location
                   know what assumptions are relevant, one should   of the investment, as the countries are assumed
                   understand how to connect the role of theoretical   to use “source”  based principle.  Accordingly,  in
                   and empirical research.                          equilibrium, all investors  must achieve the same
                                                                    after-tax rate of return on capital, denoted by ρ. Put
                      Thus, in this paper, I present  the theoretical   it mathematically,
                   explanation  in the following  order. First, I
                   explain  the traditional  but  useful model that  are
                   broadly used by other researchers to derive more
                                                                       Here, we should acknowledge that, since capital
                   contextualized  theory  for  recent  issues.  Second,
                                                                    is freely mobile, world capital-labor ratio is fixed at
                   I continue with relaxing  the assumption used
                                                                    , causing market clearing condition
                   in the basic  model to get  the theory closer to
                   practical world. I do it by incorporating two base
                   of adjusted assumptions, which are: (i) taking into
                   account the possibilities for firms to shift the profit   Where
                   without moving the whole capital; (ii) considering
                                                                       Equation (2)  is necessary  to emphasize  that
                   the consequence  of implementing  differentiated
                                                                    capital  and labor can always  choose  place to go
                   corporate tax rate in dealing with tax competition.
                                                                    so that  there is balance  in capital  market. Or in
                   Third, for further case, I make it possible for the
                                                                    other words, equilibrium  condition can  always
                   countries to integrate the case when countries
                                                                    be achieved.  Although  realistically the balance  is
                   actually can develop the tax  system not only by
                                                                    never equalized – and will never be –, we believe
                   determining the tax  rate, but  also  by setting  the
                                                                    that the flow movement of labor and capital across
                   regime used in country, which are source principle
                                                                    border  moves  in a way as continuously nearing
                   and residence principle. Fourth, with the generated
                                                                    the equilibrium state. Thus,  (1)  and (2)  jointly
                   findings,  I  try  to  take  several  policy  implications
                                                                    determine the amount of capital allocated to each
                   that can be insightful for policy makers to deal with
                                                                    country and the common net of return.
                   tax  competition.  Lastly,  the  paper  is  completed
                   with the conclusion.                                Now  suggest that  one of country  changes its
                                                                    tax rate, while the rest (n – number of countries)
                   2. Basic Model                                   do not. Adjusted equation (1) then holds for n – 1,
                                                                    which  represents  all  other  countries  that  do  not
                      When we analyze the capital owner’s behavior,   increase the tax rate, that
                   we should keep in mind that  the decision  is
                   governed by the objective to maximize the return.
                   In formalizing the logical framework of tax policies
                   and investment decision,  utilizing model built     We can infer from equation (3) that the added
                   by  Zodrow  and  Mieszkowski  (1986)  and  Wilson   value of increasing one unit of capital is intrinsically
                   (1986)  – or usually mentioned as ZMW model –    determined by the ratio of capital itself in respect
                   can be a good start to generate insightful ideas.  with  the associated labor  involved in production
                                                                    process. Put it alternatively, the net return of capital
                      The model considers a world economy consisting
                                                                    is generated after deducting it by labor wage and
                   of n “countries” (i = 1, ... , n) that have investment
                                                                    tax.  Accordingly, through mathematical  routine
                   opportunities represented by production function
                                                                    worked by Zodrow, Mieszkowski, and Wilson, this
                   f (k ), where k  denotes aggregate capital ratio and
                    1  1       1                                    gives  us a matrix system  from which  following
                   f   represents  the aggregate  output. Thus,  f (k )
                    1                                     1  1      conditions follows:
                   represents that  the amount  of output  produced
                   is  influenced  by  the  capital  invested  in  the
                   production. There are other numerous factors that
                   can also influence the production function, such as
                   law, bureaucracy, politics etc, but here, the reality
                   is simplified by removing other irrelevant aspects   An increase in the tax rate in any country i thus
                                                                    reduces  the capital  employed in the production
                                                                    function, and thus increases  capital  in all  other
                   16. Michael Keen and Kai A. Konrad, “The Theory of International Tax
                   Competition and Coordination,” Max Planck Institute for Tax Law and Public
                   Finance Working Paper, No. 06 (2014). I partially follow the sequential
                   step of the modelling in this paper.             17. Ibid.
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