A Note on Musgrave's Diagrammatic Explanation of Tax Liabilities under Various Sacrifice Formulas

In his monumental work, The Theory of Public Finance. Professor Richard A. Musgrave has used a diagram to explain tax liabilities of two individuals under equal absolute sacrifice formula, equal proportional sacrifice formula and equal marginal (or minimum aggregate) sacrifice formula. The purpose of this note is (1) to show the economic inconsistency in the relation between total utility and income which is present in his diagram and (2) to suggest some modifications in his diagram so as to satisfy the logical relation between the total utility and income and support his conclusions which he has drawn on the basis of his diagram.