4.7 In Example 4.3 we used a specific indirect utility function to illustrate the lump sum principle that an income tax reduces utility to a lesser extent than a sales tax that garners the same revenue. Here you are asked to:

a. Show this result graphically for a two-good case by showing the budget constraints that must prevail under each tax. (Hint: First draw the sales tax case. Then show that the budget constraint for an income tax that collects the same revenue must pass through the point chosen under the sales tax but will offer options preferable to the individual.)

b. Show that if an individual consumes the two goods in fixed proportions, the lump sum principle does not hold because both taxes reduce utility by the same amount.

c. Discuss whether the lump sum principle holds for the many-good case too.