SUMMARYIn this paper, we apply two optimization methods to solve an optimal control problem of a linear neutral differential equation (NDE) arising in economics. The first one is a variational method, and the second follows a dynamic programming approach. Because of the infinite dimensionality of the NDE, the second method requires the reformulation of the latter as an ordinary differential equation in an appropriate abstract space. It is shown that the resulting Hamilton-Jacobi-Bellman equation admits a closed-form solution, allowing for a much finer characterization of the optimal dynamics compared with the alternative variational method. The latter is clearly limited by the nontrivial nature of asymptotic analysis of NDEs. Copyright

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We assess the stabilizing effect of progressive income taxes in a monetary economy with constant returns to scale. It is shown that tax progressivity reduces, in parameter space, the likelihood of local indeterminacy, sunspots and cycles. However, considering plausibly low levels of tax progressivity does not ensure saddle-point stability and preserves as robust the occurrence of sunspot equilibria and endogenous cycles. It turns out that increasing progressivity, through its impact on after-tax income, makes labor supply more inelastic. However, even when large, tax progressivity does not neutralize the effects of expected inflation on current labor supply which may lead to expectation-driven business fluctuations. Copyright � 2008 Blackwell Publishing, Inc..

This paper introduces general formulations for both technology (with input substitution) and non-separable utility (compatible with balanced growth and stationary worked hours) into a benchmark RBC model. It is shown that intertemporal substitution and input substitutability lead to local determinacy and rule out stationary sunspot equilibria when labor demand is downward-sloping, in contrast with recent results obtained under the assumption of separable utility. The main intuition behind this result is shown to work as follows: in contrast with separable preferences, increasing the elasticity of intertemporal substitution in consumption necessarily implies decreasing the elasticity of constant-consumption labor supply, when utility is non-separable and concave, which affects unfavorably the occurrence of local indeterminacy.