Chapter 14-Efficient and Equitable Taxation Public economics
1 Chapter 14 – Efficient and Equitable Taxation Public Economics
Optimal Commodity Taxation Assume that the goal is to finance expenditures with a minimum of excess burden Assume lump sum taxes are infeasible ·3 commodities Good x.y and leisure Prices Px, Py, and w
2 Optimal Commodity Taxation • Assume that the goal is to finance expenditures with a minimum of excess burden. • Assume lump sum taxes are infeasible. • 3 commodities: – Good X, Y, and leisure – Prices PX , PY , and w
Optimal Commodity Taxation Time endowment is fixed at T The full budget constraint can be written as WT=PX+PY+wl
3 Optimal Commodity Taxation • Time endowment is fixed at: T • The full budget constraint can be written as: wT P X P Y wl = X + Y +
Optimal Commodity Taxation Case 1-All goods can be taxed If all commodities can be taxed, imposing equal ad-valorem tax rates yields W7=(1+)fX+(1+)P+(1+)wt WT -PX+Pytwl 1+
4 Optimal Commodity Taxation: Case 1 – All goods can be taxed • If all commodities can be taxed, imposing equal ad-valorem tax rates yields: wT ( t)P X ( t)P Y ( t)wl = 1+ X + 1+ Y + 1+ ( ) wT t P X P Y wl X Y 1+ = + +
Optimal Commodity Taxation Case 1-All goods can be taxed In this case, the inability to impose a lump sum tax is irrelevant The government can effectively take away a lump sum amount through equal taxes on all commodities(including leisure) · No excess burden
5 Optimal Commodity Taxation: Case 1 – All goods can be taxed • In this case, the inability to impose a lump sum tax is irrelevant. • The government can effectively take away a lump sum amount through equal taxes on all commodities (including leisure). • No excess burden
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
