– Figure 14.1 shows the initial excess burden as a triangle (abc) and the marginal excess burden as a trapezoid (fbae)
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Figure 14.1
Optimal Commodity Taxation: Ramsey Rule
Chapter 14 – Efficient and Equitable Taxation
Public Finance
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Aaron S. Yelowitz - Copyright 2003 © McGraw-Hill
Optimal Commodity Taxation
• Assume that the goal is to finance expenditures with a minimum of excess burden.
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Optimal Commodity Taxation: Ramsey Rule Reinterpreted
• Recall the formula for excess burden for good X:
EBX 12PXXtX 2
• Planner’s optimization problem is to minimize total excess burden by choosing taxes on goods X and Y, subject to a revenue constraint.
• The government can effectively take away a lump sum amount through equal taxes on all commodities (including leisure).
• No excess burden.
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Optimal Commodity Taxation: Case 2 – Not All Goods Can Be Taxed
• 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.
per dollar of tax imal Commodity Taxation: Ramsey Rule
• Similar reasoning is used for good Y.
• Optimization therefore leads to:
X Y X 1 Y1
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Optimal Commodity Taxation: Ramsey Rule Reinterpreted
• Setting up the LaGrangian:
m t X i ,t n Y , L 1 2 X P X X t X 2 1 2 Y P Y Y t Y 2 R P X X t X P Y Y t Y
w T 1 t P X X 1 t P Y Y 1 t w l
wT
1t
PXXPYYwl
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Optimal Commodity Taxation: Case 1 – All Goods Can Be Taxed
• In this case, the inability to impose a lump sum tax is irrelevant.
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Optimal Commodity Taxation: Ramsey Rule
• Consider the idea of marginal excess burden
– The additional inefficiency from incrementally raising a tax by a small amount
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Optimal Commodity Taxation: Ramsey Rule Reinterpreted
• The full budget constraint can be written as:
w TP XX P Y Y w l
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Optimal Commodity Taxation: Case 1 – All Goods Can Be Taxed
• If all commodities can be taxed, imposing equal ad-valorem tax rates yields:
• Assume lump sum taxes are infeasible. • Three commodities:
– Good X, Y, and leisure – Prices PX, PY, and w.
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Optimal Commodity Taxation
• Time endowment is fixed at: T
• The marginal excess burden of taxing good X is approximately: ΔX.
• The marginal tax revenue raised is approximately: X1.
• Therefore the marginal excess burden
• May be impossible to tax nonmarket 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.