Econ 551 Government Finance: Revenues Fall 2019 Given by Kevin - - PowerPoint PPT Presentation

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 𝜕𝑘

ℎ

consumes amount 𝑦𝑘

ℎ

Each firm produces: 𝑧𝑘

𝑔

(inputs are negative values of 𝑧𝑘

𝑔)

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: 𝜕 = ∑ 𝜕ℎ

𝐼 ℎ=1

(with 𝜕ℎ now representing the vector of 𝜕𝑘

ℎ across all goods j)

𝑧 = ∑ 𝑧𝑔

𝐺 𝑔=1

𝑦 = ∑ 𝑦ℎ

𝐼 ℎ=1

ECON 551: Lecture 1 13 of 26

Definition: Feasible allocation

An array of consumption vectors {𝑦ℎ} is feasible … …if there exists a production array {𝑧𝑔} such that: 𝑦 ≤ 𝑧 + 𝜕. Note that {𝑦ℎ} just means {𝑦1, … , 𝑦ℎ, … , 𝑦𝐼}, and 𝑦ℎ includes all goods for household h, 𝑦1

ℎ to 𝑦𝐾 ℎ.

ECON 551: Lecture 1 14 of 26

Definition: Pareto Optimality

A feasible consumption array {𝑦 ̂ℎ} is a Pareto optimum if…. …there does not exist an array {𝑦̅ℎ} such that: 𝑉ℎ(𝑦̅ℎ) ≥ 𝑉ℎ(𝑦 ̂ℎ) ∀ ℎ and 𝑉ℎ(𝑦̅ℎ) > 𝑉ℎ(𝑦 ̂ℎ) 𝑔𝑝𝑠 𝑏𝑢 𝑚𝑓𝑏𝑡𝑢 𝑝𝑜𝑓 ℎ (Note: We’ve just simply assumed there is some utility function 𝑉ℎ over 𝑦ℎ.)

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
• ff.

 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, 𝑞𝑘. Definition: An array [𝑞̂, {𝑦 ̂ℎ}, {𝑧 ̂𝑔}] 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 𝑦 ≤ 𝑧 + 𝜕 (i.e. allocation is feasible)

ECON 551: Lecture 1 17 of 26

First Welfare Theorem: Statement

Let [𝑞̂, {𝑦 ̂ℎ}, {𝑧 ̂𝑔}] be a competitive equilibrium with no household locally satiated. Then [{𝑦 ̂ℎ}, {𝑧 ̂𝑔}] 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 [{𝑦 ̂ℎ}, {𝑧 ̂𝑔}] is not a Pareto optimum. 1) Then there must exist some feasible alternative allocation that is Pareto preferred. ∃ [{𝑦̅ℎ}, {𝑧 ̅𝑔}] with 𝑦̅ ≤ 𝑧 ̅ + 𝜕 ̅ 𝑉ℎ(𝑦̅ℎ) ≥ 𝑉ℎ(𝑦 ̂ℎ) ∀ ℎ 𝑉ℎ(𝑦̅ℎ) > 𝑉ℎ(𝑦 ̂ℎ) 𝑔𝑝𝑠 𝑏𝑢 𝑚𝑓𝑏𝑡𝑢 𝑝𝑜𝑓 ℎ 2) No local satiation and utility maximizing households mean that {𝑦̅ℎ} which was not chosen but is preferred, must not have been affordable. 𝑞̂𝑦̅ > 𝑞̂𝑦 ̂

ECON 551: Lecture 1 19 of 26

3) No local satiation means budget fully exhausted; holds at equality. 𝑞̂𝑦 ̂ = 𝑞̂𝑧 ̂ + 𝑞̂𝜕 4) Firms are maximizing profit at 𝑧 ̂𝑔, so they make weakly less at 𝑧 ̅𝑔than at 𝑧 ̂𝑔. 𝑞̂𝑧 ̂ ≥ 𝑞̂𝑧 ̅ 5) Do some math…. Substitute result from (3) into (2): 𝑞̂𝑦̅ > 𝑞̂𝑧 ̂ + 𝑞̂𝜕 Substitute result from (4) into above: 𝑞̂𝑦̅ > 𝑞̂𝑧 ̂ + 𝑞̂𝜕 ≥ 𝑞̂𝑧 ̅ + 𝑞̂𝜕 ⇒ 𝑞̂𝑦̅ > 𝑞̂𝑧 ̅ + 𝑞̂𝜕 6) Divide by 𝑞̂: 𝑦̅ > 𝑧 ̅ + 𝜕 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 𝑞̂ takes us from initial endowment at 𝜕 to competitive equilibrium at 𝑦 ̂.

𝑦1

1

𝑦2

1

𝑦2

2

𝑦1

2

𝑞̂ 𝜕 𝑦 ̂

 

ECON 551: Lecture 1 22 of 26

Second Welfare Theorem: Statement

Suppose [{𝑦 ̂ℎ}, {𝑧 ̂𝑔}] 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. ∃ 𝑞̂ such that [{𝑦 ̂ℎ}, {𝑧 ̂𝑔}] 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 𝜕 that could be support 𝑦 ̂ 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

• ptimum 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.