Answer the following questions:

a)Suppose there are two goods (X and Y) that are unrelated in consumption. The compensated demand elasticity of good X is greater than that of good Y. Assume society only cares about efficiency. Applying your knowledge of optimal commodity tax theory, describe the efficient tax rates on good X and Y.

b) Now suppose that society cares about equity (some egalitarian preferences), and that good X is consumed more by high-incomes and good Y is consumed more by lower-incomes. Does this change the result from part (a)? Explain.

c) Is it possible to design a tax that does all of the following: i) leaves behaviour unchanged so that the quantity demanded of goods and services does not change, ii) creates no excess burden, iii) is not regressive, and iv) is welfare enhancing?