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We investigate the allocation and the effects of personal taxes and state and social security benefits in modern economies. The most prominent contributions are as follows: (1) We propose a unified framework in which to discuss the progressivity, redistribution and equity of taxes and benefits. Through this, we offer a general class of indices of horizontal inequity that complements existing classes of progressivity and vertical equity indices. We highlight throughout the analytical and empirical contribution of individual taxes and benefits to the effect of the whole system, using the features of the 1985 British tax and benefit system. (2) We analyse state benefit take-up and welfare programme participation in the presence of divergences between the assessment of entitlement made by the take-up analyst and that carried out by the government's agency. This explicit modelling helps remove important biases in the computation of take-up and participation rates. It also detects the presence of allocative errors made by the government in alleviating poverty. Our methodology -- which may be usefully extended to other microeconometric applications -- simultaneously identifies the distribution of costs to participating in welfare programmes. (3) We provide econometric evidence on the level of claiming inconveniences inherent to the British Supplementary Benefit (now Income Support) programme and on how they dampen the welfare impact of state support. Besides, we can illustrate the degree of misallocation of state support among the poor and the non-poor. These allocative errors are also respectively aggravated and mitigated by the deterrence effect of claiming costs. We also examine the impact of allocative imperfections upon the level of progressivity, equity and redistribution exerted by redistributive tools. (4) We model the optimal design of state support in the presence of heterogeneity in original incomes and in the costs incurred in granting state support. We see that some simple rules which hold when income redistribution and poverty alleviation are costless do not hold anymore in more general cases. This also has important consequences for the consideration of principles of vertical and horizontal equity.