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This paper examines the tax schedule for low income families with children.We take an optimal tax approach based on a structural labour supply model which incorporates unobserved heterogeneity, fixed costs of work, childcare costs and the detailed non-convexities of the tax and transfer system. The motivation is the British earned income tax credit reform (WFTC) and its interaction with the tax and transfer system for lone parents. Our analysis also examines the case for the use of hours-contingent payments. The results point to a tax schedule which depends on the age of children, with tax credits only optimal for low earners with school age children. The results also suggest a welfare improving role for hours-contingent payments although this is mitigated when hours cannot be monitored or recorded accurately by the tax authorities.Acknowledgements: This study is part of the research program of the ESRC Centre for the Microeconomic Analysis of Public Policy at the IFS. We thank Stuart Adam, Mike Brewer, Guy Laroque, Ian Preston, Emmanuel Saez, seminar participants at MIT, Jerusalem, NIESR, participants in the Mirrlees Review and the referees for helpful comments. We are responsible for all errors and interpretations.

SUMMARY Regulation of neuronal excitability and cardiac excitation-contraction coupling requires proper localization of L-type Ca2+ channels. We show that the actin-binding protein α-actinin binds to the C-terminal surface targeting motif of α11.2, the central pore-forming CaV1.2 subunit, to foster its surface expression. Disruption of α-actinin function by dominant negative or shRNA constructs reduces CaV1.2 surface localization in HEK293 and neuronal cultures, and dendritic spine localization in neurons. We demonstrate that calmodulin displaces α-actinin from their shared binding site on α11.2 upon Ca2+ influx through L-type channels but not through NMDAR, thereby triggering loss of CaV1.2 from spines. Coexpression of a Ca2+-binding deficient calmodulin mutant does not affect basal CaV1.2 surface expression, but inhibits its internalization upon Ca2+ influx. We conclude that α-actinin stabilizes CaV1.2 at the plasma membrane, and that its displacement by Ca2+-calmodulin induces Ca2+-induced endocytosis of CaV1.2, thus providing an important negative feedback mechanism for Ca2+ influx.

Optimal tax rules are used to evaluate the optimality of taxation for lone mothers in Germany and Britain. The theoretical model is combined with elasticities derived from the structural estimation of lone mothers' labour supply. For both countries we do not find that in-work credits with marginal tax rates are optimal. However we show that when the government has a low taste for redistribution, out-of-work transfers and transfer for the working poor are very similar, implying very low marginal tax rates. Further, the current tax and transfer systems in both countries are shown to be optimal only if governments have a much higher welfare value for income received by the non-workers than the working poor. Copyright � Institute of Fiscal Studies. Journal compilation � Royal Economic Society 2009.