Economists traditionally tackle normative problems by computing optimal policy, i.e. the one
that maximizes a social welfare function. In practice, however, a succession of marginal
changes to a limited number of policy instruments are implemented, until no further
improvement is feasible. I call such an outcome a ”restricted local optimum”. I consider the
outcome of such a tatonnement process for a government which wants to optimally set taxes
given a tax code with a fixed number of brackets. I show that there is history dependence, in
that several local optima may be reached, and which one is reached depends on initial
conditions. History dependence is stronger (i.e. there are more local optima), the more
complex the design of economic policy, i.e. the greater the number of tax brackets. It is also
typically stronger, the greater the interaction of policy instruments with one another – which in
my model is equivalent to agents having a more elastic labor supply behavior. Finally, for a
given economy and a given tax code, I define the latter’s average performance as the
average value of the social welfare function across all the local optima. One finds that it
eventually sharply falls with the number of brackets, so that the best performing tax code
typically involves no more than three brackets.
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