On cell problems for Hamilton-Jacobi equations with non-coercive Hamiltonians and its application to homogenization problems
We study a cell problem arising in homogenization for a Hamilton-Jacobi equation whose Hamiltonian is not coercive. We introduce a generalized notion of effective Hamiltonians by approximating the equation and characterize the solvability of the cell problem in terms of the generalized effective Hamiltonian. Under some sufficient conditions, the result is applied to the associated homogenization problem. We also show that homogenization for non-coercive equations fails in general.
Abstract This paper investigates whether it is possible to find Pareto-improving commodity tax reforms that harmonise taxes between two countries when governments supply public goods and thus have revenue requirements. We consider a Ricardian model of trade with elastic factor supply, and suppose that initial taxes are Nash equilibrium ones. Under weak conditions, a necessary and sufficient condition for a tax reform to be Pareto improving is that it increases the value of compensated (utility constant) demand for imports in both countries. A two-good example suggests that harmonisation is unlikely to be Pareto-improving if the revenue requirement is high, and the demand for imports is relatively price elastic, in both countries. © 1997 Elsevier Science B.V.