12.9 Ad valorem taxes Throughout this chapter's analysis of taxes we have used per-unit taxes-that is, a tax of a fixed amount for each unit traded in the market. A similar analysis would hold for ad valorem taxes-that is, taxes on the value of the transaction (or, what amounts to the same thing, proportional taxes on price). Given an ad valorem tax rate of t (t = 0.05 for a 5 percent tax), the gap between the price demanders pay and what suppliers receive is given by P = (1+1)Ps-

a. Show that, for an ad valorem tax, d In Pp dt es d In Ps and = dt es- "D

b. Show that the excess burden of a small tax is DW=-0.5- epes es-ep Polo

c. Compare these results to those derived in this chapter for a unit tax.