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ECON 551: Lecture 1 1 of 26
Econ 551
Government Finance: Revenues
Fall 2019
Given by Kevin Milligan
Vancouver School of Economics
University of British Columbia
Lecture 1: Course Introduction + Review of Welfare Economics
ECON 551: Lecture 1 2 of 26
Course Materials:
These are all available on the course website:
http://faculty.arts.ubc.ca/kmilligan/teaching/ECON551/econ551.htm
Course syllabus
Reading list (preliminary)
Presentation guide
Paper guide
ECON 551: Lecture 1 3 of 26
Agenda for today:
1. Four-slide history of the field
2. Basic welfare economics review
ECON 551: Lecture 1 4 of 26
What is Public Economics?
Alan Auerbach and Martin Feldstein:
“The positive and normative study of government’s effect on the economy.”
[source]
ECON 551: Lecture 1 5 of 26
Public Economics vs. Public Finance
See Musgrave (1985) for a deep history of the field.
Dreze (1995) dates the transition of ‘Public Finance’ into ‘Public Economics’ around
1950.
Before then, the field was fairly normative involving a lot of principles about what
government ought and ought not to do, but it didn’t look much like what we think of
as economics. It was somewhat more like accounting.
After 1950, in part due to the neo-classical synthesis of Samuelson etc., there was a
growing use of standard microeconomic tools to analyze the public sector.
Which led to…..
ECON 551: Lecture 1 6 of 26
Richard Musgrave: The Theory of Public Finance (1959)
The first “modern” public economics text: used recognizable microeconomics to
study public sector.
Organizing framework for thinking about government:
Allocation Branch
Distributive Branch
Stabilization Branch
ECON 551: Lecture 1 7 of 26
The last 5 decades….
1970s/1980s:
Theories of optimal
taxation
1990s:
Empirical Revolution
2000s/10s:
Theory-empirical synthesis
e.g. James Mirrlees e.g. Jonathan Gruber e.g. Raj Chetty and Emmanuel Saez
…see Dahlby and Milligan (2017) for an accounting of the last fifty years in (Canadian)
public economics.
ECON 551: Lecture 1 8 of 26
Agenda for today:
1. Four-slide history of the field
2. Basic welfare economics overview
ECON 551: Lecture 1 9 of 26
Review of Welfare Economics:
We will quickly go over some basic results: 1st and 2nd welfare theorems.
You’ve seen this before, but we’ll be putting a particular interpretation on them; it’s
a good warmup.
ECON 551: Lecture 1 10 of 26
Setup
Standard microeconomic setup:
Utility maximizing consumers; profit maximizing producers.
All transactions take place at one point in time.
All agents take prices as parametric.
Markets are complete—no public goods or externalities.
Q: Why study such an abstract, stylized framework?
ECON 551: Lecture 1 11 of 26
Setup
Households indexed by h: 1 to H
Firms indexed by f: 1 to F
Goods indexed by j: 1 to J
Each household:
has endowment of goods 𝜔𝑗ℎ
consumes amount 𝑥𝑗ℎ
Each firm produces: 𝑦𝑗𝑓 (inputs are negative values of 𝑦𝑗
𝑓)
ECON 551: Lecture 1 12 of 26
Setup
Let’s now make some useful vectors out of this so we can manipulate things more
cleanly.
Consolidate the notation:
𝜔 = ∑ 𝜔ℎ𝐻ℎ=1 (with 𝜔ℎ now representing the vector of 𝜔𝑗
ℎ across all goods j)
𝑦 = ∑ 𝑦𝑓𝐹𝑓=1
𝑥 = ∑ 𝑥ℎ𝐻ℎ=1
ECON 551: Lecture 1 13 of 26
Definition: Feasible allocation
An array of consumption vectors {𝑥ℎ} is feasible …
…if there exists a production array {𝑦𝑓} such that:
𝑥 ≤ 𝑦 + 𝜔.
Note that {𝑥ℎ} just means {𝑥1, … , 𝑥ℎ, … , 𝑥𝐻},
and 𝑥ℎ includes all goods for household h, 𝑥1ℎ to 𝑥𝐽
ℎ.
ECON 551: Lecture 1 14 of 26
Definition: Pareto Optimality
A feasible consumption array {�̂�ℎ} is a Pareto optimum if….
…there does not exist an array {�̅�ℎ} such that:
𝑈ℎ(�̅�ℎ) ≥ 𝑈ℎ(�̂�ℎ) ∀ ℎ
and 𝑈ℎ(�̅�ℎ) > 𝑈ℎ(�̂�ℎ) 𝑓𝑜𝑟 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 ℎ
(Note: We’ve just simply assumed there is some utility function 𝑈ℎ over 𝑥ℎ.)
ECON 551: Lecture 1 15 of 26
Discussion: Pareto Optimality
Vilfredo Pareto (1848-1923; Italian)
Comments on Pareto criterion:
Everyone must be weakly better off – we need unanimity.
No notion of justice here—no uniqueness of result.
Do not have to make interpersonal utility comparisons.
Utilitarian theories generally trade off one person’s utility for the
greater good. Instead, here we look at every person’s utility as
inviolate. We do not make one person worse even if everyone would be much better
off.
Under standard preferences, unanimous approval to move to a Pareto improving
allocation. Exceptions possible: e.g., if your welfare depended on your neighbour’s
allocation, you might take smaller allocation just to spite her.
ECON 551: Lecture 1 16 of 26
Definition: Competitive Equilibrium
Introduce prices for each good, 𝑝𝑗.
Definition: An array [�̂�, {�̂�ℎ}, {�̂�𝑓}] is a competitive equilibrium if
a) Households are maximizing utility subject to their budget constraint.
b) Firms are maximizing profit subject to production function.
c) Market clears 𝑥 ≤ 𝑦 + 𝜔 (i.e. allocation is feasible)
ECON 551: Lecture 1 17 of 26
First Welfare Theorem: Statement
Let [�̂�, {�̂�ℎ}, {�̂�𝑓}] be a competitive equilibrium with no household locally satiated.
Then [{�̂�ℎ}, {�̂�𝑓}] is a Pareto optimum.
In words:
Market economies that satisfy the stated conditions produce Pareto optimal
allocations.
ECON 551: Lecture 1 18 of 26
First Welfare Theorem: Proof
Proof strategy: by contradiction.
Suppose [{�̂�ℎ}, {�̂�𝑓}] is not a Pareto optimum.
1) Then there must exist some feasible alternative allocation that is Pareto preferred.
∃ [{�̅�ℎ}, {�̅�𝑓}] with �̅� ≤ �̅� + �̅�
𝑈ℎ(�̅�ℎ) ≥ 𝑈ℎ(�̂�ℎ) ∀ ℎ
𝑈ℎ(�̅�ℎ) > 𝑈ℎ(�̂�ℎ) 𝑓𝑜𝑟 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 𝑜𝑛𝑒 ℎ
2) No local satiation and utility maximizing households mean that {�̅�ℎ} which was not
chosen but is preferred, must not have been affordable.
�̂��̅� > �̂��̂�
ECON 551: Lecture 1 19 of 26
3) No local satiation means budget fully exhausted; holds at equality.
�̂��̂� = �̂��̂� + �̂�𝜔
4) Firms are maximizing profit at �̂�𝑓, so they make weakly less at �̅�𝑓than at �̂�𝑓.
�̂��̂� ≥ �̂��̅�
5) Do some math….
Substitute result from (3) into (2): �̂��̅� > �̂��̂� + �̂�𝜔
Substitute result from (4) into above: �̂��̅� > �̂��̂� + �̂�𝜔 ≥ �̂��̅� + �̂�𝜔
⇒ �̂��̅� > �̂��̅� + �̂�𝜔
6) Divide by �̂�:
�̅� > �̅� + 𝜔
By (1), this result is not feasible. QED by contradiction. ∎
ECON 551: Lecture 1 20 of 26
First Welfare Theorem: Discussion
Fairly weak conditions needed for a breathtaking result. “Woah if true”.
When people say “Markets won’t provide clean air” or “Markets underprovide health
care”, this can be reinterpreted to say here is some violation of an assumption so that
the 1st welfare theory doesn’t hold—we are not getting the socially optimal outcome
along some dimension.
Not unique: How choose among Pareto optima? Do we get to choose?
If the assumption don’t hold, then what can we do? Well, we could just have some
decision maker / government make the allocations for us. Or, we could intervene in
the market using taxes, subsidies, or regulation. In other words, use market
incentives to push us back toward the social optimum.
Can be represented in standard Edgeworth box picture.
ECON 551: Lecture 1 21 of 26
Trading at the price vector �̂� takes us from initial endowment at 𝜔 to competitive
equilibrium at �̂�.
𝑥11
𝑥21
𝑥22
𝑥12
�̂�
𝜔
𝑥
ECON 551: Lecture 1 22 of 26
Second Welfare Theorem: Statement
Suppose [{�̂�ℎ}, {�̂�𝑓}] is a Pareto Optimum.
Take the same assumptions as before, but now add:
convex indifference maps
convex production sets
lump sum transfers of endowments.
Then there exists a set of prices that can support that Pareto optimum as a competitive
equilibrium.
∃ �̂� such that [{�̂�ℎ}, {�̂�𝑓}] is a competitive equilibrium.
ECON 551: Lecture 1 23 of 26
Second Welfare Theorem: Comments
In the Edgeworth box diagram earlier, we can just use lumpsum transfers to shift us
to the endowment point 𝜔 that could be support �̂� as a competitive equilibrium.
We can choose whichever Pareto optimum we want, and just shift around
endowments to get us to the one we want.
No efficiency-equity tradeoff, as we can get whichever allocation we like best
without sacrificing Pareto efficiency.
Assumptions are stronger here. Lumpsum transfers are hard….
ECON 551: Lecture 1 24 of 26
Lipsey and Lancaster: Theory of the Second Best
Review of Economic Studies, 1956
“The general theorem for the second best optimum states that if there is introduced into a
general equilibrium system a constraint which prevents the attainment of one of the Paretian
conditions, the other Paretian conditions, although still attainable, are, in general, no longer
desirable. In other words, given that one of the Paretian optimum conditions cannot be
fulfilled, then an optimum situation can be achieved only by departing from all the other
Paretian conditions. The optimum situation finally attained may be termed a second best
optimum because it is achieved subject to a constraint which, by definition, prevents the
attainment of a Paretian optimum.”
ECON 551: Lecture 1 25 of 26
Lipsey and Lancaster: Theory of the Second Best
In words: In a distorted economy, removing a distortion might hurt welfare; moving other
variables away from optimum may improve welfare.
Implications:
Can’t count number of distortions to gauge welfare.
Policy changes that remove distortions may not improve welfare.
ECON 551: Lecture 1 26 of 26
For next time…
We will be going through some basics on the topic of collective decision making.
Recommended reading….Boadway and Keen (2000) on the motivations for
redistribution.
After that, we’ll be ready to start optimal taxation.