Lecture 1: Introduction to Public Finance

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1 IE Lecture 1: to Public Finance Beat Hintermann FS 2012, University of Basel 28 February / 54

2 Course limits Credits Fundamental questions of PF Course outline IE 1 Limits of the course Credits Fundamental normative questions of public finance Course outline 2 Government expenditure : Overview 3 Samuelson General Equilibrium Model 4 5 Inter-personal equity 2 / 54

3 Course limits Credits Fundamental questions of PF Course outline IE What is public finance? Synonyms: Public economics, public sector economics Study of government economic policy 3 / 54

4 Limits of the course Course limits Credits Fundamental questions of PF Course outline IE Focus on: Microeconomic of public sector Normative perspective positive where necessary Fiscal federalism Exclude: Macroeconomic ("fiscal policy") Financial market regulation Public choice Cost-benefit analysis 4 / 54

5 Credits for this course Course limits Credits Fundamental questions of PF Course outline IE 6 KP 4 Discussion sections 2 Homework sets (15 % each) Homework 1: expenditure (due April 4) Homework 2: tax and capital tax competition (due May 27) Written final exam (70 %), May 30 5 / 54

6 Course limits Fundamental normative questions of public finance Credits Fundamental questions of PF Course outline IE 1 Legitimacy and goals of government economic activity 2 Decision rules 3 Financing of expenditures 4 Government hierarchy and sorting of population 6 / 54

7 1.) Legitimacy and goals Course limits Credits Fundamental questions of PF In what economic activity should gov. be involved? What are goals of public policy? Course outline IE Government activity Starting point: Markets take precedence for solving economic problems and allocating resources Government activity legitimized by market failure Goals Primary goal: Maximize social welfare Proximate goals: Efficiency Equity (process, horizontal and vertical equity) 7 / 54

8 2.) Decision rules Course limits Credits Fundamental questions of PF Course outline How should government become involved? (public choice: How does gov. become involved?) What is the optimal level of involvement? IE Government-as-agent Limitation for political of government Useful for a Providing benchmark b Understanding efficiency-equity trade-offs c Analyzing market failures Legitimacy and decision rules: 8 / 54

9 3.) Financing of expenditures Theory of taxation Course limits Credits Fundamental questions of PF Course outline IE How should government finance expenditures? Taxation becomes relevant if A expenditure defines need for government intervention B does not specify how expenditures are to be financed Same principal goals as public expenditure Allocational of taxation: Efficiency design taxes that minimize distortions for given amount of required revenue (optimal taxation) Second goal of taxation: Equity Efficiency-equity tradeoff Tax incidence 9 / 54

10 4.) Gov. hierarchy and sorting "Fiscal federalism" Course limits Credits Fundamental questions of PF Course outline IE Taking 1.)-3.) as given: Which tasks should each level of government perform? Optimal sorting of consumers / voters / firms across jurisdictions Positive analysis: How do people sort? (income, tastes etc.) What are the welfare losses/gains relative to a centralized government? 10 / 54

11 Course outline Course limits Credits Fundamental questions of PF Course outline IE Check syllabus, incl. reading list! 1 under first-best Lectures 1-4 SWF, externalities, decreasing cost production 2 Theory of taxation Lectures 5-8 Commodity and income taxation, corrective taxation under second-best 3 Fiscal federalism Lectures 9-11 Capital, property and income tax competition; environmental federalism 11 / 54

12 Market failure Welfare theorems IE 1 2 Government expenditure : Overview Market failure The fundamental theorems of welfare economics 3 Samuelson General Equilibrium Model 4 5 Inter-personal equity 12 / 54

13 Market Failure Market failure Welfare theorems IE If a set of assumptions hold, competitive markets generate efficient allocation of resources If assumptions are violated: Market failure Government intervention to fix problem Market failure vs. government failure Inequality can be interpreted as market failure 13 / 54

14 Market assumptions "perfect competition" Market failure Welfare theorems IE a Large number of buyers and sellers in each market b No product differentiation within each market c Everybody has complete information d No barriers to entry or exit 14 / 54

15 Market failure Welfare theorems IE Technical assumptions Preferences and prod. activities "well behaved" 1 Non-Satiation i no consumer is satiated ii some consumer is not satiated 2 Preferences are convex 3 Preferences are continuous 4 Consumption possibilities set is convex 5 Individual utility is a function of own consumption and factor supplies 6 An individual firm s production possibilities depend only upon its own inputs and outputs 7 Aggregate production possibilities are convex 15 / 54

16 Market failure Welfare theorems Fundamental Theorems of Welfare Economics First Fundamental Theorem of Welfare Economics If assumptions 1i, 2, 4, 5 and 6 hold, then a competitive equilibrium is a Pareto optimum IE Second Fundamental Theorem of Welfare Economics If assumptions 1ii, 2, 3, 4, 5, 6 and 7 hold, then any Pareto optimum can be achieved by a competitive equilibrium with the appropriate distribution of income (Proof: G. Debreu, 1959) 16 / 54

17 Utility-possibilities frontier Market failure Welfare theorems IE U 2 A C E D B U 1 17 / 54

18 Utility-possibilities frontier Market failure Welfare theorems IE U 2 A C E D F B U 1 18 / 54

19 Relevance of Welfare Theorems Market failure Welfare theorems IE If either of the welfare theorems hold, government has no role in allocation of resources (efficiency) Does not apply to distribution Departure from pure principle of consumer sovereignty Social welfare function (SWF) needed If market and/or technical assumptions do not hold: market failure, possible government intervention More recently: Distinction less clear due to private information Freeriding, moral hazard, adverse selection Problem with government-as-agent model Justification for fiscal federalism 19 / 54

20 Ingredients Problem setup FONCs IE 1 2 Government expenditure : Overview 3 Samuelson General Equilibrium Model Model ingredients Problem setup FONCs 4 5 Inter-personal equity 20 / 54

21 Model for gov. economic policy Necessary characteristics Ingredients Problem setup FONCs IE General equilibrium (GE) model GE effects crucial for public policy Must capture broad range of problems Externalities, decreasing cost production, private information etc. Tradeoff btw. equity and efficiency Must be comparable to market economy 21 / 54

22 General equilibrium modeling Ingredients Problem setup FONCs Base ingredients Consumer preferences Technology Market clearance Equity: Social welfare function IE Types of GE models Quantities Social planner chooses quantities; prices adjust. Prices Market economy. Assumptions about market behavior / structure and behavior of government; quantities adjust. 22 / 54

23 Base model Ingredients Problem setup FONCs IE Start with quantities model by Samuelson Assume that market and technical assumptions satisfied Relate solution to market economy 23 / 54

24 Individual preferences Ingredients Problem setup FONCs IE H individuals or households G goods and services F factors X hg := consumption of good g by person h h=1,...,h g=1,...,g V hf := supply of factor f by person h h=1,...,h f=1,...,f U h := U h (X h1,..., X hg ; V h1,..., V hf ) or simply U h = U h (X hg ; V hf ) 24 / 54

25 Production technologies Ingredients Problem setup FONCs r gf := factor f used in production of good g g=1,...,g f=1,...,f X g := aggregate amount of g produced g=1,...,g IE X g = φ g (r g1,..., r gf ) or X g = φ g (r gf ) g = 1,..., G 25 / 54

26 Market clearance Ingredients Problem setup FONCs IE Goods markets: H X hg = X g h=1 g = 1,..., G Factor markets: H V hf = G h=1 g=1 r gf f = 1,..., F 26 / 54

27 Social welfare function Ingredients Problem setup FONCs IE Individualistic Samuelson-Bergson SWF: W = W [ U 1 (X 1g ; V 1f ),..., U H (X Hg ; V Hf ) ] or W = W [ U h (X hg ; V hf ) ] 27 / 54

28 Maximizing social welfare Ingredients Problem setup FONCs IE Maximize efficiency: "Size of pie" Equity: Optimize distribution according to SW function First-best environment: Efficiency and equity independent 28 / 54

29 Social planner s optimization problem Ingredients Problem setup FONCs IE max W [ U h (X hg ; V hf ) ] X hg ;V hf ;X g ;r gf s.t. φ g (r gf ) X g g = 1,..., G H X g g = 1,..., G h=1 H V hf h=1 X hg G g=1 r gf f = 1,..., F 29 / 54

30 Lagrangian Ingredients Problem setup FONCs IE max L =W [ U h (X hg ; V hf ) ] X hg ;V hf ;X g ;r gf G [ µ g φ g (r gf ) X g] g=1 G δ g [X g g=1 H ] X hg h=1 F [ H π f V hf f =1 h=1 G ] r gf g=1 30 / 54

31 First-order necessary Choice variables Ingredients Problem setup FONCs IE L = W U h X hg U h δ g = 0 X hg L = W U h V hf U h + π V f = 0 hf L X g = δ g µ g = 0 h = 1,..., H g = 1,..., G h = 1,..., H f = 1,..., F g = 1,..., G L φ g = µ g π r gf r f = 0 gf g = 1,..., G f = 1,..., F 31 / 54

32 First-order necessary Shadow prices Ingredients Problem setup FONCs IE L µ g : ( φ g (r gf ) X g) µ g = 0 g = 1,..., G L δ g : ( X g H h=1 X hg ) δ g = 0 g = 1,..., G L π f : ( H V hf h=1 G g=1 r gf ) π f = 0 f = 1,..., F 32 / 54

33 Balance of FONCs and variables Ingredients Problem setup FONCs IE HG+HF+GF+3G+F of which 2G+F HG+HF+GF+G equations and variables shadow prices economic variables 33 / 54

34 Efficiency-equity dichotomy Ingredients Problem setup FONCs IE Equations for economic variables can be combined into (PO) Interpersonal equity (IE) First-best: PO contain no welfare terms! 34 / 54

35 MRS MRTS MRS=MRT Market economy IE Optimal consumption Pairing of FONCs P1 Any two goods demanded by same person P2 Any two factors supplied by same person P3 Any good demanded and any factor supplied by same person Optimal production P4 Any one factor used in production of any two goods P5 Any two factors used in the production of same good 35 / 54

36 MRS MRTS MRS=MRT Market economy IE Pairing of FONCs (cont.) Optimal relationship between consumption and production P6 Rate at which any one person is willing to trade two goods (P1) combined with their efficient rate of exchange in production (P4) P7 Rate at which any one person is willing to substitute any two factors (P2) with their efficient rate of exchange in production (P5) P8 Rate at which any one person is willing to substitute any one good for any one factor (P3) with their efficient rate of exchange in production (P4) 36 / 54

37 Interpersonal equity Pairing of FONCs MRS MRTS MRS=MRT Market economy IE E1 Any one good demanded by two different people E2 Any one factor supplied by two different people 37 / 54

38 MRS MRTS MRS=MRT Market economy IE If factor supply is fixed: Factors are not choice variables Conditions P1, P5 and P6 (incl. P4) sufficient Derivation in discussion section Next: Review and interpret these 38 / 54

39 MRS MRTS MRS=MRT Market economy IE P1: Marginal rate of substitution "Bottom-up efficiency" U h X hg U h X hg = MRS g,g = δ g δ g all h = 1,..., H ( ) = dg dg any g, g = 1,..., G Interpretation: Nr. of units of g consumer h is willing to give up to obtain an additional unit of g, or vice versa. g : Numeraire good (negative of) slope of indifference curve MRS between two goods the same for all consumers 39 / 54

40 X 2 g X 1 g* Edgeworth-Bowley Box I h : Indifference curve of person h Person 2 MRS MRTS MRS=MRT Market economy IE I 2 2 I 2 3 D A I 2 1 B I 1 2 C I 1 3 I / 54 Person 1 X 2 g* X 1 g

41 Mapping to UPF MRS X 2 g X 1 g* I 2 2 I 2 3 D I 2 1 B A I 1 2 C I 1 3 Person 2 MRTS MRS=MRT I 1 1 Market economy IE Person 1 X 2 g* X 1 g U 2 A B C Utility possibilities frontier (UPF) 41 / 54 U 1

42 MRS MRTS MRS=MRT Market economy φ g r gf φ g r gf P5: Marginal rate of technical substitution (MRTS) "Top-down efficiency" = MRTS f,f = π f π f ( = MP ) f (g) MP f (g) = dr gf dr gf IE all g = 1,..., G; any f, f = 1,..., F 42 / 54 Interpretation: Nr. of units of r gf needed to replace one unit of r gf in the production of g ratio of marginal products (MP) of f and f for g (negative of) slope of iso-production curve MRTS between two factors the same for all goods

43 L g Mapping to PPF K g* X g* MRS q g* 3 q g* 2 D q g* 1 B A q g 2 C q g 3 MRTS MRS=MRT q g 1 Market economy IE X g L g* K g X g* A B C Production possibilities frontier (PPF) 43 / 54 X g

44 MRS MRTS MRS=MRT Market economy IE φ g r g f φ g r gf = µ g µ g all f = 1,..., F; P4: Marginal rate of transformation (MRT) = MRT g,g ( any g, g = 1,..., G = MP f (g ) ) MP f (g) = dr g f dr gf Interpretation: Nr. of units of g that can be produced if one less unit of g is produced by reallocating factor f ratio of marginal products for f in g and g (negative of) slope of PPF MRT between two goods the same for all factors 44 / 54

45 P6: MRS=MRT "Overall efficiency" MRS MRTS MRS=MRT Market economy IE MRT g,g = φ g r g f φ g r gf = µ g µ g = δ g δ g =MRS g,g all f = 1,..., F any g, g = 1,..., G Interpretation: Rate of exchange in production between two goods has to equal rate of exchange in consumption "Correct" production mix 45 / 54

46 MRT=MRS X g* MRS MRTS MRS=MRT Market economy IE A Person 2 A MRT g*,g X 1g* MRS g*,g 46 / 54 Person 1 X 1g X g

47 MRS MRTS MRS=MRT Market economy IE Correspondence to competitive market economy P1: MRS equalized across consumers Utility-maximizing, price taking consumers equalize MRS to price ratio max U h (X hg, V hf ) X hg,v hf s.t. p g X hg F G w f V hf U h X hg U h X hg MRS g,g = p g p g 47 / 54

48 MRS MRTS MRS=MRT Market economy IE P5: MRTS equalized across firms Cost-minimizing, price taking firms equalize MRTS to input price ratio min r gf w f r gf s.t. φ g (r gf ) X g F φ g r gf φ g r gf MRTS f,f = w f w f 48 / 54

49 MRS MRTS MRS=MRT Market economy IE P6: MRS=MRT Price taking firms equalize marginal costs to output price p g p g = MC(g) MC(g ) 1 Consumers equate MRS to price ratio 2 Efficient production: Ratio of MC equals MRT MRS g,g = pg p g = MC(g) MC(g ) = MRT g,g 49 / 54

50 Competitive market economy and social welfare MRS MRTS MRS=MRT Market economy IE Perfectly competitive markets generate full set of PO (P1-P8) But: They do not generate IE Equilibrium from free market is somewhere on utility-possibilities frontier To reach "Bliss Point", need social welfare function 50 / 54

51 E1: Demand of same good by two people IE W U h U h = W U h X hg U h X h g all g = 1,..., G; any h, h = 1,..., H 51 / 54

52 How many goods to redistribute? IE G+F interpersonal equity Not independent If one holds, all of them hold! 52 / 54

53 Suppose E1 holds for good g: IE Restore welfare terms in P1: W U h U h = W U h X hg U h X h g MRS h g,g = W U h U h X hg W U h U h X hg = W U h U h X h g W U h U h X h g = MRS h g,g Numerators equal from E1 denominators equal too! Only holds if P1-P8 apply (no distortions) 53 / 54

54 How to achieve E1 IE Lump-sum redistribution of one good not affected Moves equilibrium along utility-possibilities frontier to social optimum Demand, supply, prices, MRTs, MRTS s, MRS s change, in general 54 / 54