A Dynamic Model with Import Quota Constraints
This paper develops a continuous-time two-sector model to study the economic effects of an import quota during the period of time over which it is imposed. One of the sectors is protected by a quota, which in our setup manifests itself as an integral constraint on the flow of imports of the protected commodity. In sharp contrast to the existing literature, our small open economy exhibits distinctly different economic behavior depending on whether the country is importing the protected good, exporting it or refraining from trade in it. The domestic price of the protected good exceeds the world price in import and no-trade regions, even when the quota is underutilized -- in contrast, the workhorse quota model predicts no economic effects of a quota unless it is binding. Within a general equilibrium world economy consisting of one quota-constrained and one unconstrained country, under logarithmic preferences, the constrained country becomes wealthier at the expense of the unconstrained. Moreover, the stock price of the protected industry increases in the quota-constrained and decreases in the unconstrained country. Keywords: Quota, International Economics and Finance, Asset Pricing, Integral Constraints.
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additional cost agent's marginal utility Basak cN(t conditional expectation consumer consumption allocations convex country is importing country Q cQ(t cumulative imports X(t current endowment decreasing density and endowment density or endowment domestic price domestic state price dw(t dynamic economic effects effects of quotas Electronic Money endowment process eQ(t equation expectation export less geometric Brownian motion Hence imply import constraint Import Quota Constraints import region integral constraint interest rate Karatzas Lagrange multiplier log(c London Business School market price market risk multiplier no-trade region normal country numerical analysis optimal consumption past cumulative imports period-by-period constrained country pQ(t price density associated price of risk Proof of Proposition protected commodity Q exports Q imports Q.E.D. Proof quota binds quota-constrained country quota-constrained economy quota-protected commodity quota-protected industry quota-type constraint Section small open economy solves stock price terminal consumption three regions total wealth unconstrained economy volatility world price world state price WQ(t