Optimal commodity Taxation Case 2-Not all goods can be taxed May be impossible to tax non-market work Assume only taxes can be applied to goods X and Y In general, some excess burden is inevitable. Key question is how to select rates on x and y to minimize excess burden subject to the revenue constraint
6 Optimal Commodity Taxation: Case 2 – Not all goods can be taxed • May be impossible to tax non-market work. • Assume only taxes can be applied to goods X and Y. • In general, some excess burden is inevitable. Key question is how to select rates on X and Y to minimize excess burden subject to the revenue constraint
Optimal Commodity Taxation Ramsey rule Consider the idea of marginal excess burden The additional inefficiency from incrementally raising a tax by a small amount Figure 14.1 shows the initial excess burden as a triangle(abc), and the marginal excess burden as a trapezoid (fbae)
7 Optimal Commodity Taxation: Ramsey Rule • Consider the idea of marginal excess burden – The additional inefficiency from incrementally raising a tax by a small amount. – Figure 14.1 shows the initial excess burden as a triangle (abc), and the marginal excess burden as a trapezoid (fbae)
Figure 14.1 P0+(u1+1)8 Marginal excess burden b Po+l Ax △X X per year
Figure 14.1
Optimal Commodity Taxation Ramsey rule The marginal excess burden of taxing good X is approximately: AX The marginal tax revenue raised is approximately: X1 Therefore the marginal excess burden per dollar of tax revenue is △X X
9 Optimal Commodity Taxation: Ramsey Rule • The marginal excess burden of taxing good X is approximately: ΔX. • The marginal tax revenue raised is approximately: X1 . • Therefore the marginal excess burden per dollar of tax revenue is: X X1
Optimal Commodity Taxation Ramsey rule Similar reasoning is used for good y. Optimization therefore leads to △X△Y X Y Ramsey rule says that to minimize total excess burden. tax rates should be set so the percentage reduction in the quantity of each good demanded is the same 10
10 Optimal Commodity Taxation: Ramsey Rule • Similar reasoning is used for good Y. • Optimization therefore leads to: X X Y 1 Y1 = • Ramsey rule says that to minimize total excess burden, tax rates should be set so the percentage reduction in the quantity of each good demanded is the same