We use Grayson's binary multicomplex presentation of algebraic K-theory to give a new construction of exterior power operations on the higher K-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a λ-ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial functors is the universal λ-ring on one generator.

The authors would like to thank Frantisek Brocek and David Eiser of the Fraser of Allander Institute at the University of Strathclyde for producing revenue and spending figures for Scottish local government finance, to enable comparisons with figures for England. In addition they would like to thank Graham Atkins of the Institute for Government for kindly sharing its 2019 edition of the Performance Tracker so that insights could be included in Chapters 2 and 3. The authors would also like to thank consortium members, Nicola Morton from the Local Government Association, as well as Paul Johnson from IFS and Neil Amin-Smith who was at IFS until July 2019, for helpful comments and suggestions. However, the views presented in this report are those of the authors alone. Any errors or omissions are also their responsibility. ContentsExecutive summary 1. Introduction 2. Councils' revenues and spending: levels, trends and choices 2.1 Local government revenues and spending in 2019-20 2.2 How different is this picture from the one seen a decade ago? 2.3 How different are the choices councils have made in the face of funding cuts? 2.4 How have councils coped with the cuts? 2.5 Summary 3. The outlook for councils' funding: is austerity over? 3.1 The government's plans for 2020-21 3.2 The longer-term outlook 3.3 Summary 4. The impact of business rates retention and the New Homes Bonus on council funding: the story so far 4.1 The BRRS and NHB policies 4.2 How has the BRRS affected council funding? 4.3 How has the NHB affected council funding? 4.4 What evidence is there of an impact on councils' behaviour? 4.5 Summary 5. Conclusion Appendix A. Methodology Appendix B. Changes to councils' revenue and spending in Scotland Appendix C. Regression output References

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As in high-income countries, reduced rates of vat and vat exemptions ("preferential vat rates") are a common feature of indirect tax systems in lmics. Many of the goods and services that are granted preferential ratessuch as foodstuffs and kerosene-seem likely to receive such treatment on the grounds that they provide a means for the government to indirectly target poorer households, for whom such expenditures may take up a large proportion of their total budget. We use microsimulation methods to estimate the impact of preferential vat rates in four lmic countries, considering their effect on revenues, poverty, inequality, and across the consumption distribution. We consider whether other policy tools might be better suited for the pursuit of distributional objectives by estimating the impact of existing cash transfer schemes and a hypothetical scenario where the revenue raised from broadening the vat base is used to fund a universal basic income (ubi) in each country. We find that although preferential vat rates reduce poverty, they are not well targeted towards poor households overall. Existing cash transfer schemes are better targeted but would not provide a suitable means of compensation for a broader vat base given issues related to coverage and targeting mechanisms. Despite being completely untargeted, a ubi funded by the revenue gains from a broader vat base would create large net gains for poor households and reduce inequality and most measures of extreme poverty in each of the countries studied-even if only 75% of the additional vat revenue was disbursed as ubi payments.

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