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 1 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 2 of 26
Agenda for today: 1. Four-slide history of the field 2. Basic welfare economics review ECON 551: Lecture 1 3 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 4 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 5 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 6 of 26
The last 5 decades…. 1970s/1980s: 1990s: 2000s/10s: Theories of optimal Empirical Revolution Theory-empirical synthesis taxation 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 7 of 26
Agenda for today: 1. Four-slide history of the field 2. Basic welfare economics overview ECON 551: Lecture 1 8 of 26
Review of Welfare Economics: We will quickly go over some basic results: 1 st and 2 nd 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 9 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 10 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: ℎ 𝜕 𝑘 has endowment of goods ℎ 𝑦 𝑘 consumes amount 𝑔 𝑔 ) 𝑧 𝑘 (inputs are negative values of 𝑧 𝑘 Each firm produces: ECON 551: Lecture 1 11 of 26
Setup Let’s now make some useful vectors out of this so we can manipulate things more cleanly. Consolidate the notation: 𝐼 ℎ across all goods j ) 𝜕 ℎ (with 𝜕 ℎ now representing the vector of 𝜕 𝑘 𝜕 = ∑ ℎ=1 𝐺 𝑧 𝑔 𝑧 = ∑ 𝑔=1 𝐼 𝑦 ℎ 𝑦 = ∑ ℎ=1 ECON 551: Lecture 1 12 of 26
Definition: Feasible allocation An array of consumption vectors {𝑦 ℎ } is feasible … … if there exists a production array {𝑧 𝑔 } such that: 𝑦 ≤ 𝑧 + 𝜕 . Note that {𝑦 ℎ } just means {𝑦 1 , … , 𝑦 ℎ , … , 𝑦 𝐼 } , ℎ to 𝑦 𝐾 ℎ . and 𝑦 ℎ includes all goods for household h , 𝑦 1 ECON 551: Lecture 1 13 of 26
Definition: Pareto Optimality ̂ ℎ } is a Pareto optimum if…. A feasible consumption array {𝑦 …there does not exist an array {𝑦̅ ℎ } such that: 𝑉 ℎ (𝑦̅ ℎ ) ≥ 𝑉 ℎ (𝑦 ̂ ℎ ) ∀ ℎ and 𝑉 ℎ (𝑦̅ ℎ ) > 𝑉 ℎ (𝑦 ̂ ℎ ) 𝑔𝑝𝑠 𝑏𝑢 𝑚𝑓𝑏𝑡𝑢 𝑝𝑜𝑓 ℎ (Note: We’ve just simply assumed there is some utility function 𝑉 ℎ over 𝑦 ℎ .) ECON 551: Lecture 1 14 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 g ood. 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 15 of 26
Definition: Competitive Equilibrium Introduce prices for each good, 𝑞 𝑘 . ̂ ℎ }, {𝑧 ̂ 𝑔 }] is a competitive equilibrium if Definition: An array [𝑞̂, {𝑦 a) Households are maximizing utility subject to their budget constraint. b) Firms are maximizing profit subject to production function. Market clears 𝑦 ≤ 𝑧 + 𝜕 (i.e. allocation is feasible) c) ECON 551: Lecture 1 16 of 26
First Welfare Theorem: Statement ̂ ℎ }, {𝑧 ̂ 𝑔 }] be a competitive equilibrium with no household locally satiated. Let [𝑞̂, {𝑦 ̂ ℎ }, {𝑧 ̂ 𝑔 }] is a Pareto optimum. Then [{𝑦 In words: Market economies that satisfy the stated conditions produce Pareto optimal allocations. ECON 551: Lecture 1 17 of 26
First Welfare Theorem: Proof Proof strategy: by contradiction. ̂ ℎ }, {𝑧 ̂ 𝑔 }] is not a Pareto optimum. Suppose [{𝑦 1) Then there must exist some feasible alternative allocation that is Pareto preferred. ∃ [{𝑦̅ ℎ }, {𝑧 ̅ 𝑔 }] with 𝑦̅ ≤ 𝑧 ̅ + 𝜕 ̅ 𝑉 ℎ (𝑦̅ ℎ ) ≥ 𝑉 ℎ (𝑦 ̂ ℎ ) ∀ ℎ 𝑉 ℎ (𝑦̅ ℎ ) > 𝑉 ℎ (𝑦 ̂ ℎ ) 𝑔𝑝𝑠 𝑏𝑢 𝑚𝑓𝑏𝑡𝑢 𝑝𝑜𝑓 ℎ No local satiation and utility maximizing households mean that {𝑦̅ ℎ } which was not 2) chosen but is preferred, must not have been affordable. 𝑞̂𝑦̅ > 𝑞̂𝑦 ̂ ECON 551: Lecture 1 18 of 26
3) No local satiation means budget fully exhausted; holds at equality. 𝑞̂𝑦 ̂ = 𝑞̂𝑧 ̂ + 𝑞̂𝜕 ̂ 𝑔 , so they make weakly less at 𝑧 ̅ 𝑔 than at 𝑧 ̂ 𝑔 . Firms are maximizing profit at 𝑧 4) 𝑞̂𝑧 ̂ ≥ 𝑞̂𝑧 ̅ Do some math…. 5) 𝑞̂𝑦̅ > 𝑞̂𝑧 ̂ + 𝑞̂𝜕 Substitute result from (3) into (2): 𝑞̂𝑦̅ > 𝑞̂𝑧 ̂ + 𝑞̂𝜕 ≥ 𝑞̂𝑧 ̅ + 𝑞̂𝜕 Substitute result from (4) into above: ⇒ 𝑞̂𝑦̅ > 𝑞̂𝑧 ̅ + 𝑞̂𝜕 Divide by 𝑞̂ : 6) 𝑦̅ > 𝑧 ̅ + 𝜕 By (1), this result is not feasible. QED by contradiction. ∎ ECON 551: Lecture 1 19 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 “Mark ets underprovide health care” , this can be reinterpreted to say here is some violation of an assumption so that the 1 st 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 20 of 26
2 𝑦 1 2 𝑦 2 ̂ 𝑦 𝑞̂ 𝜕 1 𝑦 2 1 𝑦 1 Trading at the price vector 𝑞̂ takes us from initial endowment at 𝜕 to competitive equilibrium at 𝑦 ̂ . ECON 551: Lecture 1 21 of 26
Second Welfare Theorem: Statement ̂ ℎ }, {𝑧 ̂ 𝑔 }] is a Pareto Optimum. Suppose [{𝑦 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. ̂ ℎ }, {𝑧 ̂ 𝑔 }] is a competitive equilibrium. ∃ 𝑞̂ such that [{𝑦 ECON 551: Lecture 1 22 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 23 of 26
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