Below are lecture notes from my graduate course in taxation and local
public sector economics. Some are newer and more complete than others.
I expect to add to this site as this semester goes on.
The material here is covered in a number of sources, but I do have some
minor innovations here and there. I point those out in comments below
and in the notes. I do not give credit for canonical results, but
it should be understood that I am not taking credit for that material.
If there is any evidence that anyone is using these notes I will add bibliographic
material. The canonical ("textbook") material is a melange of Atkinson-Stiglitz,
Tresch, Auerbach, and Myles. I do cite journal articles when I draw
directly from them.
I'd like to hear about errors of any kind, big or small, and (notwithstanding
the previous paragraph) anything that comes across as such wholesale appropriation
that it ought to be beneath my dignity (ahh, but perhaps you do not know
me that well).
1. Gross and net prices
2. Unit tax
3. Ad valorem tax
4. General equilibrium: Consumer and
5. Budget sets with taxes: Net trades
and taxation of net trades
I like to introduce producer and consumer prices early on, so they appear
in the technical machinery (indirect utility, profit functions, etc.) from
the start. Adding them in later makes it difficult to give clear
explanations for the various normalizations that are done.
I emphasize that there is no loss of generality in representing preferences
in "net trades" space instead of "gross consumption" space, and one can
easily represent the taxation of net trades in gross consumption space.
Restricting taxes to net trades does have important implications, how one
represents preferences does not.
1. Leisure-income and labor-income models
2. Basic structure of the optimal tax model
6. A digression on technology
1. Optimal commodity tax problem with a single
consumer: The general problem
2. Walras Law
3. Tax vector normalization (uses CRS)
4. Problem I: general CRS technology
5. Problem II: linear technology
6. Ramsey rule for the linear technology model
7. Interpretation of the Ramsey rule
8. Inverse elasticity rules
Here I move from a general optimal tax problem to the particular optimization
problems, rather than the other way around. I think this makes it
clear how the various properties of the model (Walras Law) and assumptions
about technology lead to the different problems. In particular, it
becomes clear why the use of a revenue constraint, while quite natural,
is valid only under the most restrictive assumptions.
1. 3-Good Case (Corlett-Hague rule; follows
2. Optimal taxation with any CRS technology:
the Ramsey Rule again
3. Production efficiency with public and private
(any CRS technology; following
Auerbach, p. 100)
1. Many-person Ramsey Rule (follows Myles)
2. Commodity taxes and income taxes (synthesizes
Myles and Atkinson-Stiglitz)
3. Indirect taxes and direct taxes (owes a
lot to Atkinson-Stiglitz)
4. Kaplow, JPubE 2006, "On the undesirability
of commodity taxation even when income taxation is not optimal."
1. On the "underprovision" and "overprovision"
of public goods
2. Atkinson-Stern model
3. Comparing "rules" at the optimum
4. Comparing "levels" at the optimum
2. The "indirect compensation function" (or
"money metric indirect utility") and the equivalent variation
3. Excess burden of commodity taxes (the "standard"
1. Characterizing total excess burden at given
fixed utility measure
2. Single price change: trapezoids and
3. Many prices change: trapezoids
4. Many prices change: not just triangles!
5. Marginal excess burden with the fixed utility
1. Optimal tax problem as minimizing total
excess burden with the fixed utility measure
2. Marginal excess burden using the variable
utility measure (graph only)
3. Optimal tax problem as minimizing total
excess burden with the variable utility measure
4. Total excess burden one more time (general
equilibrium or "oR" measure)
5. Introduction to special cases
6. Quasi-linear preferences (compensated and
regular demand coincide)
7. Homothetic preferences (money value of
a utility change)
8. Leontief preferences (vertical compensated
9. Vertical regular demand
1. Wilson (1991)
2. Gronberg-Liu (2001)
1. Jorgenson and Yun (1991)
2. Slesnick (1991)
3. Feldstein (1999)
1. Overview of tax incidence analysis
2. The representation of taxation
3. Incidence in a partial equilibrium model
(Kotlikoff and Summers)
4. Taxation and oligopoly
1. Two-sector model: derivations
1. Two-sector model: results