I. II. SOME BASIC REMARKS ON TAXATION 2 11. 1 Foundations 3 I I. 2 Data 11. 3 Principles of Taxation 3 I I I. TAX PROGRESSION I I 1. 1 Preliminary Definition 6 7 I I I. 2 Reasons for Progressive Taxation of Incomes IV. MEASURING THE DEGREE OF PROGRESSION IV. l Notation 10 IV. 2 Measures Suggested by Musgrave/Thin 12 IV. 3 Comparison of these Measures 14 IV. 4 A Reason for Using the RIP 17 IV. 5 The Way to Go 17 V. DIFFERENT CONCEPTS OF INEQUALITY V. l Lorenz Curves 19 V. 2 Absolute Inequality-Aversion 19 V. 3 Mixed Inequality-Aversion 20 VI. LOCAL MEASURES OF TAX PROGRESSION VI. l Building Blocks 23 VI. 2 Directly Inequality-Equivalent Tax Functions 26 VI. 3 Directly Inequality-Preserving Tax Functions 29 VI. 4 Scale Invariance 31 VI. 5 Type A 32 VI. 6 Implications 33 VI. 7 Type B 44 VI. 8 Implications 46 VI. 9 Further Desiderata for Type A Measures 50 VI. 10 Conclusions 59 VI VII. PROGRESSION AND THE DESIGN OF TAX FUNCTIONS VII. l Introduction 62 VII. 2 Constant Progressivity Tax Functions 62 VII. 3 Tax Revenue Conditions 71 VI I. 4 The German Income Tax Function and Income Distribution 1981 73 VII. 5 #-Cocop Tax Functions for Germany 78 VIi I. GLOBAL MEASURES OF TAX PROGRESSION VIlLi The Problem 83 VIII. 2 Desirable Properties 84 VIII. 3 Suggestions in the Literature 85 VIII.