econ 551 government finance: revenues fall...

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


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

http://faculty.arts.ubc.ca/kmilligan/teaching/ECON551/econ551.htm


Agenda for today:

1. Four-slide history of the field

2. Basic welfare economics review


What is Public Economics?

Alan Auerbach and Martin Feldstein:

“The positive and normative study of government’s effect on the economy.”

[source]

http://store.elsevier.com/Handbook-of-Public-Economics/isbn-9780080544199/


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…..


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

http://en.wikipedia.org/wiki/Richard_Musgrave_(economist)


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.

http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1996/mirrlees-bio.html

http://economics.mit.edu/faculty/gruberj/

http://www.rajchetty.com/

http://eml.berkeley.edu/~saez/


Agenda for today:

1. Four-slide history of the field

2. Basic welfare economics overview


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.


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?


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)


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


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.


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.)


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.

http://en.wikipedia.org/wiki/Vilfredo_Pareto


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)


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.


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.

�̂��̅� > �̂��̂�


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. ∎


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.


Trading at the price vector �̂� takes us from initial endowment at 𝜔 to competitive

equilibrium at �̂�.

𝑥11

𝑥21

𝑥22

𝑥12

�̂�

𝜔

𝑥


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.


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….


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.”


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.


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.

econ 551 government finance: revenues fall...

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