Figures and Tables
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Figures and Tables Chapter 2 Equilibrium and Efficiency Figures and Tables An Edgeworth Box x12 12 22 x12 2 x x22 1 x11 11 12 Preferences and Demand 2 x 2 x1 1 Relative Price Change 2 x2 x1 1 Equilibrium 2 x2 x1 1 Equilibrium and Excess Demand Z 2 1, p2 p2 A Typical Production Set Good 2 3 Yj -2 Good 1 Profit Maximization Good 2 y* p2 p1 0 Good 1 Utility Maximization Good 2 ~ x* 1 p1 Good 1 Efficient Equilibrium Good 2 ~ x* y * 1 p1 Good 1 Constant Returns to Scale 0 Good 2 ~ x* y * 1 p1 Good 1 Pareto Efficiency 2 c d b a 1 The First Theorem 2 e 1 Contract Curve The Second Theorem 2 e' 1 ' Proof of the Second Theorem Z x̂ W Price Line x̂1 x̂ 2 Feasible Set A Lump-Sum Transfer 2 e ' 1 ~ x11 Chapter 3 Public Sector Statistics Figures Total Expenditure 1870 – 1996 (% of GDP) 60 50 US 40 UK Germany 30 France 20 Japan 10 0 1870 1890 1910 1930 1950 1970 1990 Total Expenditure 1970 - 2002 (% of GDP) 60 55 50 France 45 Germany 40 United Kingdom 35 United States 30 Japan 25 Australia 20 15 1970 1980 1990 2000 Individual Expenditure Items (% of GDP) 10 7 9 8 6 7 6 Japan 5 4 US 3 2 1 0 1890 UK 5 4 UK Germany 3 Germany France 2 France 1 1910 1930 1950 1970 0 1870 1890 1910 1930 1950 1970 1990 b. Education 1990 a. Defence 8 14 7 12 6 Japan 5 UK 4 US 3 Germany 2 France Japan 10 UK 8 US 6 Germany 4 France 2 1 0 1900 Japan 1920 1940 1960 c. Health 1980 2000 0 1910 1930 1950 1970 d. Pensions 1990 Government Expenditure 1998 (% of GDP) Belgium Canada France Germany Hungary Italy Japan Korea Netherlands New Zealand Poland Sweden UK United States 0 10 20 30 40 50 60 Share of Expenditure by Levels of Government 100% 90% 80% 70% 60% Local 50% 40% State Central 30% 20% 10% 0% US 1996 UK 1998 Germany 1996 Composition of Consolidated General Spending a. US 1996 c. UK 1998 b. Germany 1996 Composition of Central Spending a. US 1996 c. UK 1998 b. Germany 1996 Composition of State Spending a. US 1996 b. Germany 1996 Composition of Local Spending a. US 1996 c. UK 1998 b. Germany 1996 Tax Revenues 1965 - 2000 (% of GDP) 50 45 Canada 40 United States 35 Australia 30 Japan 25 France 20 Turkey United Kingdom 15 10 1965 1975 1985 1995 Tax Revenue for Category of Taxation, 2000 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Other Goods and Services Property Payroll Social Security St at e Au s str ali a Ja pa n Fr an c Ge e rm an y Un Tu rk ite ey d Ki ng do m Un i ted Ca na da Income and Profits Tax Revenue by Level of Government, Federal Countries, 2000 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Social Security Local State Federal or Central Supranational Australia Belgium Canada Germany United States Tax Revenue by Level of Government, Unitary Countries, 2000 100% 90% 80% 70% Social Security 60% 50% 40% Local Federal or Central Supranational 30% 20% 10% 0% France Italy Japan Spain Turkey Tax Shares at each Level of Government, United States, 2000 100% 90% Taxes on Use 80% 70% Other Taxes 60% 50% 40% Specific Goods and Services General Taxes 30% 20% Property 10% 0% Income and Profits Central State Local Tax Shares at each Level of Government, Germany, 2000 100% 90% Taxes on Use 80% 70% Other Taxes 60% 50% 40% Specific Goods and Services General Taxation 30% 20% Property 10% 0% Income and Profits Central State Local Tax Shares at each Level of Government, Japan, 2000 100% Taxes on Use 80% Other Taxes 60% Specific Goods and Services 40% General Taxes 20% Property Income and Profits 0% Central Local Tax Shares at each Level of Government, United Kingdom, 2000 100% 90% Taxes on Use 80% 70% Other Taxes 60% 50% 40% Specific Goods and Services General Taxes 30% 20% Property 10% 0% Income and Profits Central Local Chapter 4 Theories of the Public Sector Figures Excessive Government Marginal Budget and Marginal Cost C' y B' y a b y* yb Output Government Agency Benefit and Cost bG ch G c G Gh ch c Gh G Public Good Chapter 5 Public Goods Figures and Tables Typology of Goods Rivalrous NonRivalrous Excludable Private Good Club Good NonExcludable Common Property Resource Public Good Preferences and Choice Budget Constraint g2 g2 ĝ 1 g1 Best Reaction for 2 g2 Budget Constraint ĝ 2 g 1 g1 Nash Equilibrium g2 ĝ 2 ĝ 1 g1 Inefficiency of Equilibrium Locus of Pareto Efficient Allocations g2 ĝ 2 Set of ParetoImprovements ĝ 1 g1 Allocation through Voting Private good Public good Utility G1 Gm GH Public good Price and Quantities Private good Public good Price Same Different Quantity Different Same The Lindahl Equilibrium G1 G2 G* G* Reaction of 1 Reaction of 2 1 2 Gaining by False Announcement G G2 1 eL eM 1 2 Announcements and Payoffs Player 2 0 0 Player 1 1 1 0 0 0 1 1 0 1 1 2 2 Payoffs and Overstatement 0 0 Announcement of Player 1 Announcement of Player 2 1 1 0 1 1 1 0 1 2 4 4 2 1 1 2 4 Clarke-Groves Mechanism Player 2 -1 -1 Player 1 +1 v 1 2 0 v 1 0 1 v 1 v 1 2 +1 v1 1 2 v1 1 Payoffs for Player 1 Player 2 -1 Player 2 -1 +1 0 0 Player 1 -1 +1 -1 0 2 +1 0 2 Player 1 +1 2 0 v1 1 v1 1 Effect of Income Transfer g2 ĝ 2 ĝ 2 ĝ 1 ĝ 1 g1 New Equilibrium g2 ĝ 2 ĝ 2 ĝ 1 ĝ 1 g1 Additional Consumers G H 3 H 2 ParetoEfficient Reaction Function g Public Good Experiment Private Good Public Good Private Benefit 5 1 Social Benefit 5 10 A Contribution Campaign Total Contributions C xT yT 1 xT 2 yT 3 xT 4 ... T Time Chapter 6 Club Goods and Local Public Goods Figures Utility and Club Size Utility U n 0 N 2 n* N Optimum with Unequally-Sized Clubs W n Optimum with Equally-Sized Clubs W n Non-Unique Club Size U 2 3 n Achieving Efficiency U U1 n ' n' ' U 2 U3 n Stability of the Symmetric Equilibrium U1 1 U h2 Uh U2 c d a h1 b e H 2 h2 Inefficient Stable Equilibria U1 U h2 U h1 U2 b c a h1 H 2 h2 Chapter 7 Externalities Figures Deviation of Private from Social Benefits Marginal Benefit and Cost SMB (vh~ ' 0) PMB MC SMB (vh~ ' 0) zh Equilibrium with River Pollution Revenue Cost u Upstream w 0u L u , Ld d Cost Revenue w 0d Downstream Choice of Commuting Mode Minutes Commuting Maximum Time Saving 40 Car Train 20 0 20 40 % of Car Users Job Choice Income of Lawyers Income of Economists Lawyer Economist 0 E % of Economists 100 The Rat Race Player 2 low high 1/2 low Player 1 1/2 0 0 high 1-c 1-c 1/2 - c 1/2 - c Tragedy of the Commons Revenue per Boat tax Total Cost per Boat cw AR MR Bo B* Number of Boats Equilibrium Keyboard Choice 1 % of Qwerty p* users at time t 0 p* % of Qwerty users at time t 1 Pigouvian Taxation PMC ' Value t PMC PMB SMB xo xm Quantity Uncertain Costs Value PMCH PMCE PMCL t* SMB zH z* zL Quantity Non-Convexity Output Output Externality Externality Chapter 8 Imperfect Competition Figures and Tables Market concentration in US Manufacturing, 1987 Source: Concentration ratios in manufacturing, 1992, U.S. Bureau of the Census) Industry Number of firms 4-firm concentration ratio Herfindahl index Cereal breakfast foods 33 0.87 0.221 Pet food 130 0.61 0.151 Book publishing 2182 0.24 0.026 Soap and detergents 683 0.65 0.170 Petroleum refining 200 0.32 0.044 Electronic computers 914 0.43 0.069 Refrigerators / freezers 40 0.85 0.226 Laundry machines 11 0.93 0.286 147 0.85 0.283 Greeting cards Monopoly Pricing Price p * Price p* “Inverse” Demand Marginal Revenue c Quantity Monopoly with Uniform Pricing “Expected” Demand 1 F p Marginal Revenue c Prob.(Trade) Monopoly with Incomplete Information Deadweight Loss with Monopoly Price A pm B c E D MR ym yc AR Quantity Monopoly Welfare Loss Author Sector Welfare loss (%) Harberger US Manufacturing 0.08 Gisser US Manufacturing 0.11 – 1.82 Peterson and Connor US Food Manufacturing 0.16 – 5.15 Masson and Shaanan 37 US Industries 3 16 McCorriston UK Agricultural Inputs 1.6 – 2.5 20 – 40 Cowling and Mueller US 4 – 13 UK 3.9 – 7.2 Tax Incidence with Perfectly Elastic Supply Price q=c+t t p=c Quantity Tax Incidence in the General Case Price q t p Quantity Tax Under-Shifting Price q p c+t b t c a MR yt yo AR Quantity Tax Over-Shifting Price q p c+t b AR t a c MR yt yo Quantity Calculations of Tax Shifting Baker and Brechling UK Beer 0.696 UK Tobacco 0.568 Delipalla and O’Connell, Tobacco “Northern” EU 0.92 “Southern” EU 2.16 Tasarika, Beer UK 0.665 Possibility of a Profit Increase y2 r1 y2 m2 c b r 2 y1 m1 y1 Contrasting Taxes Price Price q p q p ct c MR AR MR 1 c AR 1 Quantity Quantity Specific Tax AR Ad Valorem Tax Natural Monopoly Price p MR 2 y2 MR1 , AR 2 y1 AC MC AR1 Quantity Estimating the Effect of Merger in the Bath Tissue Market Source: Data from Tables 1 and 2 in Hausman and Leonard (1997) Bath Tissue Brand Market share Own-price (%) elasticity Price change [cost change] (%) Kleenex 7.5 -3.38 +1.0 [-2.4] Cottonelle 6.7 -4.52 -0.3 [-2.4] Scot Tissue 16.7 -2.94 -2.6 [-4.0] Charmin 30.9 -2.75 Northern 12.4 -4.21 Angel Soft 8.8 -4.08 Private Label 7.6 -2.02 Other 9.4 -1.98 Market demand -1.17 Monopsony in the Labor Market Wage Marginal Cost Labor Supply w(L) wc wm Labor Demand MRL Lm Lc Quantity of Labor Chapter 9 Asymmetric Information Figures and Tables Equilibrium in the Insurance Market Expected Risk E : 45o 0 1 2 1 Multiple Equilibria Expected Risk E3 E2 E1 45o 0 1 Perfect Information Equilibrium S h* p h S * Vh p V 0 d Separating Contracts Sh p h Vh V 0 p S d Separating and Pooling Contracts Sh p h Vh V 0 So p S d Non-Existence of Pooling Equilibrium S Vh V 0 d Market Intervention S ph t h V p t Vh t Vh 0 0 d The Single-Crossing Property Wage Utility Increase V Vh Education Separating Equilibrium V w Vh w* e h E e* e* h Maximal education low type is willing to acquire to get w h e Unreasonable Beliefs V w Vh h Unreasonable beliefs w* e E e* Maximal education low type is willing to acquire to get w h e First-Best Contract Utility Increase * , * I pe d Switching Line Switching Line * Effort V , No Effort d Second-Best Contract Switching Line E0 Effort No Effort E1 d Categorization of Outcomes Cost of effort c2 c1 1st best Effort, full coverage No effort, full coverage 2nd best Effort, partial coverage No effort, full coverage Chapter 10 Political Economy Figures and Tables Stability Alil Alice Bob Beth Carl Carol Beth Alil Beth Carl Alice Bob Alice Carl Alice Alil Beth Carl Carol Bob Carol Bob Carol Alil Condorcet Paradox Voter 1 Voter 2 Voter 3 a c b b a c c b a Location of Households 1 2 3 4 ................. n–3 n–2 n–1 n Single-Peaked Preferences U U U1 U1 U3 U2 U2 G a. Not single-peaked G b. Single-peaked Single-Crossing without SinglePeakedness Utility level U1 U2 U3 Policy spectrum Single-Peakedness in MultiDimensions Time 1 x1 x2 3 x3 2 Location Rankings Voter 1 Voter 2 Voter 3 x1 x2 x3 x2 x3 x1 x3 x1 x2 Binary Agenda [b] a b [b] [c] a c c b Borda Voting (3) (2) (2) a c b b a c c b a Top Cycle Voter 1 Voter 2 Voter 3 a c b b d c c a d d b a Independence of Irrelevant Alternatives (3) (2) (2) d c b a d c b a d c b a Plurality Voting (2) (3) (4) a b c b a a c c b Approval Voting (3) (1) (1) a b c b a b c c a Runoff Voting (6) (5) (4) (2) a c b b b a c a c b a c Probabilities of Election Outcomes X2 0 X2 1 X2 2 X1 0 1 8 2 8 1 8 X1 1 1 8 2 8 1 8 Participation and the Probability of being Pivotal P p 0.2 p 0.5 p 0.9 N Closeness and the Probability of being Pivotal P N 1 0.25 2 0.75 1 0.5 2 0.5 N Testing the Paradox of Voting (*) all coefficients are significantly different from zero at the 1-per cent level. (Source: Shachar and Nalebuff, 1999, Table 6) Variable Coefficient (*) Standard Error Constant 0.4033 0.0256 Closeness 0.1656 0.0527 Voting population -0.0161 0.0036 Blacks (%) -0.4829 0.0357 Rain on election day -0.0349 0.0129 New residents (%) -0.0127 0.0027 The Apportionment of Seats Party Vote share Exact Hamilton apportionment apportionment Left 0.45 11.25 11 Right 0.41 10.25 10 Center 0.14 3.5 4 Total 1 25 25 The Paradox Party Vote share Exact Hamilton apportionmen apportionment t Left 0.45 11.7 12 (+1 seat) Right 0.41 10.66 11 (+1 seat) Center 0.14 3.64 3 (-1 seat) Total 1 26 26 Chapter 11 Rent-Seeking Figures Monopoly Deadweight Loss Price pm d c MR ym AR yc Quantity Competitive and Monopoly Equilibria Good 2 pc ppf a b pm Good 1 Monopoly and Lobbying Good 2 pc ppf ppf L a b c pm Good 1 The Threat of Lobbying Good 2 pc Good 2 a pc a d d b b pm pm a. Monopoly Worse Good 1 b. Lobbying Worse Good 1 Chapter 12 Optimality and Comparability Figures and Tables The Utility Possibility Frontier U2 2 a b c a 1 c b U1 Social Optimality U2 o U1 Optimal Lump-Sum Taxes and Incentive Compatibility Good 2 e 2 e* p e1 Good 1 Efficiency and Inequity 2 1 Incompleteness of Pareto Ranking 2 s2 s1 s3 1 Allocations and Utility x1 y1 U1 x2 x2 U2 A 4 9 6 3 2 5 B 16 1 4 2 5 7 Non-Comparability and Level Comparability Non-Comparability ~1 U f 1 U 1 3U 1 ~2 U f 2 U 2 2U 2 ~h W min U A 18 B 12 10 14 10 12 Level Comparability ~1 U f U 1 (U 1)2 ~2 U f U 2 (U 2)2 ~ W min U h A 36 B 16 25 49 25 16 Cardinal Utility Non-Comparability ~1 U f 1 U 1 2 2U 1 ~2 U f 2 U 2 5 6U 2 ~1 ~ 2 W 2U U Level Comparability ~1 U f U 1 (U 1)2 ~2 U f U 2 (U 2)2 ~ ~ W 2U 1 U 2 A 14 B 10 35 47 63 67 A 20 B 14 20 26 60 54 Full Comparability Non-Comparability ~1 U f 1 U 1 7 3U 1 ~2 U f 2 U 2 1 3U 2 A 25 B 19 16 22 1 ~h W U min U U 2 Level Comparability ~1 U f U 1 1 3U 1 ~2 U f U 2 1 3U 2 1 ~h W U min U U 2 18.25 19.75 A 19 B 13 16 22 16.75 15.25 Chapter 13 Inequality and Poverty Figures and Tables Minimum Needs Equivalence Scales Sources: B.S. Rowntree (1901) Poverty: A Study of Town Life, (Macmillan) W. H. Beveridge (1942) Social Insurance and Allied Services, (HMSO) US Bureau of the Census (2003) www. census.gov/hhes/poverty/threshld/thresh03.html Rowntree Beveridge US Poverty (1901) (1942) Scale (2003) Single person 60 59 78 Couple 100 100 100 +1 child 124 122 120 +2 children 161 166 178 +3 children 186 166 178 +4 children 223 188 199 Construction of Engel Scale Expenditure share of food s d2 d1 M1 M2 Income Adult Good Equivalence Scale Demand for adult good d1 d2 x M1 M2 Income General Equivalence Scale Budget Line with Income M 2 Good 2 Budget Line with Income M 1 U * |d 2 U * |d 1 Good 1 Construction of a Lorenz Curve 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Lorenz Curves as an Incomplete Ranking A B A B A more equal than B A and B incomparable Relating Gini to Lorenz Lorenz Curve The Gini Social Welfare Function M2 M1 The Equally Distributed Equivalent Income Income of Household 2 M2 M EDE Social Indifference Curve M1 M EDE Income of Household 1 Inequality Before and After Taxes and Transfers Source: OECD ECO/WKP(98) Notes: 1. The Squared Coefficient of Variation (SCV) is defined by SCV = [H-1]C. 2. For the Atkinson measure, e = 0.5. Measure SCV GIni Atkinson Before After Before After Before After Denmark 1994 .671 .229 .420 .217 .209 .041 % change 1983-1994 4.9 2.0 11.2 -4.9 25.3 -11.1 Italy 1993 1.19 .584 .570 .345 .299 .105 % change 1984-1993 59.6 44.7 20.8 12.8 43.8 33.1 Japan 1994 .536 .296 .340 .265 .124 .059 % change 1984-1994 33.7 21.7 14.0 4.9 47.3 10.9 Sweden .894 .217 .487 .230 .262 .049 % change 1975-1995 49.1 36.9 17.2 -1.0 28.7 3.2 United States .811 .441 .455 .344 .205 .100 % change 1974-1995 32.0 25.4 13.1 10.0 19.6 18.6 Poverty using the FGT P2 Measure Source: Foster, Greer and Thorbecke (1985) Years in Nairobi Level of poverty % Contribution to total poverty 0 .4267 5.6 .01 – 1 .1237 6.5 2 .1264 6.6 3–5 .0257 5.1 6 – 10 .0343 12.1 11 – 15 .0291 9.4 16 – 20 .0260 6.6 21 – 70 .0555 23.8 Permanent resident .1659 8.7 Don’t know .2461 15.5 Total .0558 99.9 Evolution of Poverty (% Change in Poverty Measure) Source: OECD ECO/WKP(98)2 Poverty line (% of median income) Measure 40% 50% 50% Head- Head- Income count count gap 50% 60% Sen index Headcount Australia 1984 - 1993/4 0.0 -2.7 5.0 -4.2 -1.4 Belgium 1983 - 1995 -1.4 -2.8 1.1 -27.1 -2.3 Germany 1984 – 1994 1.8 2.9 2.5 20.8 3.8 Japan 1984 – 1994 0.6 0.8 2.5 23.1 0.4 Sweden 1983 - 1995 0.9 0.4 7.9 23.7 0.4 United States 1985 - 1995 -1.2 -1.2 0.2 -4.9 -0.1 Chapter 14 Commodity Taxation Figures and Tables Deadweight Loss Price a f e p c d q pt X1 DWL b X0 Quantity Income and Substitution Effects Good 2 c a U0 b d U1 U2 Good 1 Absence of Deadweight Loss Good 2 a U0 b U1 Good 1 Revenue and Production Possibilities Good 2 (Consumption) Y p 1 R Good 1 (Labor) Consumer Choice Good 2 (Consumption) Offer Curve q p 1 Good 1 (Labor) Optimal Commodity Taxation Good 2 (Consumption) I1 e* e Y -R q I0 t* p 1 Good 1 (Labor) Production Efficiency Good 2 (Consumption) e f -R q I0 p 1 Good 1 (Labor) Tax Reform Source: Madden (1995) Good Other goods e=2 2.316 e=5 4.349 Services Petrol Food Alcohol 2.258 1.785 1.633 1.566 5.064 3.763 3.291 3.153 Transport and equipment Fuel and power Clothing and footwear 1.509 1.379 1.341 3.291 2.221 2.837 Durables Tobacco 1.234 0.420 2.514 0.683 Tax Reform Source: Madden (1995) Item Cereals =2 -0.015 =5 -0.089 Milk and milk products Edible oils Meat, fish and eggs -0.042 0.359 0.071 -0.011 0.342 0.083 Sugar and tea Other food Clothing Fuel and light 0.013 0.226 0.038 0.038 0.003 0.231 0.014 0.014 Other non-food 0.083 0.014 Redistribution of Indian commodity taxes Source: Ray (1986b) Rural T h Urban T h Expenditure level h h Rs. 20 0.105 0.220 Rs. 50 0.004 0.037 Optimal Redistribution Source: Ray (1986b) T n = 0.1 n = 1.5 n=5 0.07 0.343 0.447 Chapter 15 Income Taxation Figures and Tables Labor Supply Decision Consumption Consumption px 1 t z 1 t wT x* x* T * a. Leisure T Leisure z* Pre-Tax Income b. Pre-Tax Income Effect of a Wage Increase Consumption Consumption c c a b a Leisure a. Leisure Pre-Tax Income b. Pre-Tax Income A Tax Threshold Consumption Consumption c c b b a T z* w a. Leisure a Leisure z* Pre-Tax Income b. Pre-Tax Income Several Thresholds Consumption Consumption Leisure a. Leisure Pre-Tax Income b. Pre-Tax Income Taxation and the Participation Decision Consumption Consumption T m T a. Leisure Leisure w m Pre-Tax Income b. Pre-Tax Income Labor Supply Elasticities Source: Blundell (1992) Married Women Married Men Lone Mothers US UK US UK US UK Uncompensated wage 0.45 0.43 0.03 -0.23 0.53 0.76 Compensated wage 0.90 0.65 0.95 0.13 0.65 1.28 Income -0.45 -0.22 -0.98 -0.36 -0.18 -0.52 Taxation and the Consumption Function x T zˆ x̂ c z T 45o ẑ z Agent Monotonicity x High-skill Low-skill x̂ ẑ z Income and Skill x Low-skill High-skill a z Upper Limit on Tax Rate x z Lower Limit on Tax Rate x c1 h1 h2 c2 l2 l1 z Zero Marginal Rate of Tax x D b C B A 45 o z Allocations and the Consumption Function x High-skill Low-skill ah al z The Utilitarian Case (e = 0) Income Consumption Average tax (%) Marginal tax (%) 0 0.03 - 23 0.055 0.07 -34 26 0.10 0.10 -5 24 0.20 0.18 9 21 0.30 0.26 13 19 0.40 0.34 14 18 0.50 0.43 15 16 Some Equity Considerations (e = 1) Income Consumption Average tax (%) Marginal tax (%) 0 0.05 - 30 0.05 0.08 -66 34 0.10 0.12 -34 32 0.20 0.19 7 28 0.30 0.26 13 25 0.40 0.34 16 22 0.50 0.41 17 20 Differential Taxation and NonSeparability x2 I h2 I h1 I p p' x1 Chapter 16 Tax Evasion Figures and Tables Hidden Economy as % of GDP, Average Over 1990-93 Source: Schneider and Enste (2000) Developing Transition OECD Egypt 68-76% Georgia 28-43% Italy 24-30% Thailand 70% Ukraine 28-43% Spain 24-30% Mexico 40-60% Hungary 20-28% Denmark 13-23% Malaysia 38-50% Russia 20-27% France 13-23% Tunisia 39-45% Latvia 20-27% Japan 8-10% Singapore 13% Slovakia 9-16% Austria 8-10% Interior Choice: 0 < X* < Y Yc 1 t Y X Y X* 1 t 1 F Y X 0 1 t Y Y Y nc Corner solutions Yc Yc 1 t Y 1 t Y X* Y 1 t 1 F Y 1 t 1 F Y 1 t Y a: X* Y Y Y nc X* 0 1 t Y b: X* 0 Y Y nc Increase in Detection Probability Yc 1 t Y new 1 t 1 F Y old 1 t Y Y Y nc Increase in the Fine Rate Yc 1 t Y 1 t 1 F Y 1 t 1 Fˆ Y X new 1 t Y X old Y Y nc Income Increase Yc 1 t Yˆ 1 t Y X old X new 1 t 1 F Yˆ 1 t 1 F Y 1 t Y 1 t Yˆ Y Yˆ Y nc Tax Rate Increase Yc 1 t Y 1 tˆY 1 t 1 F Y X new X old 1 tˆ1 F Y 1 tˆY 1 t Y Y Y nc Declaration and Income Source: Mork (1975) Income interval Midpoint 17-20 20-25 25-30 30-35 35-40 18.5 22.5 27.5 32.5 37.5 Assessed income 17.5 20.6 24.2 28.7 31.7 Percentage 91.5 88.0 88.3 84.5 94.6 Explanatory Factors Source: Spicer and Lundstedt (1976) Variable Propensity to evade Extent of evasion Inequity 0.34 0.24 Number of evaders known 0.16 0.18 Probability of detection -0.17 Age -0.29 Experience of adults 0.22 Income level -0.27 Income from wages and salaries 0.20 0.29 The Audit Game Revenue Service Taxpayer Audit No Audit Evasion Y T F, T F C Y, 0 No Evasion Y T, T C Y T, T Equilibrium Compliance Compliance Payoff Non-compliance Payoff 0 Non-compliance Rate 1 Chapter 17 Fiscal Federalism Figures and Tables The Costs of Uniformity Utility Level UB UA G A G0 GB Public Good Level Centralization and Decentralization [ ] 0 Centralized Region L 1 Region R [ ][ ] 0 Decentralized 1 Political Accountability and Voter Welfare State a State b Policy A 0, 3 r, 0 Policy B r, 1 0, 1 Regional Distribution of Income State a State b Region a ya ya Region b yb yb Share of Central Government Expenditure in Total Expenditures Source: Vernon Henderson's dataset, 1975-1995, Brown University Countries 1975 1985 1995 Developed 0.57 0.49 0.46 Russia n.a. 0.61 0.63 Latin America 0.76 0.71 0.70 Asia 0.79 0.74 0.72 Africa 0.88 0.86 0.82 World 0.76 0.68 0.64 Local Expenditures as a % of Total Government Expenditure by Function (1995-1999) Source: IMF Government Finance Statistics Yearbook, 2001 Country Education Health Social Welfare Housing Transport Total Australia 72 48 10 77 85 50 Canada 94 96 31 74 90 60 Denmark 45 95 55 29 51 56 France 37 2 9 82 42 19 Germany 96 28 21 93 57 38 Ireland 22 48 6 70 43 25 Netherlands 33 5 14 79 35 26 Norway 63 78 19 87 31 38 Russia 83 90 10 96 68 39 Spain 71 63 6 93 62 36 UK 68 0 20 40 61 26 US 95 43 31 32 75 49 Average 64 64 18 71 56 38 Chapter 18 Fiscal Competition Figures and Tables Allocation of Capital f ' k1 f ' k 2 t1 t 2 01 k1 k1 t1 , t 2 02 k2 Symmetric Nash Equilibrium t2 r1 t 2 t1 t 2 r2 t1 t1 The Advantage of Smallness f ' k 2 f ' k1 c1 g1 t1 t2 R 01 k1 k1* , k 2* c2 g2 R 02 k2 Tax Overlap Price D p1 p0 t0 T0 q1 q0 S Quantity Matching Versus Lump-Sum Grant Private Good Lump-Sum Grant Matching Grant Public Good Statutory Corporate Income Tax Source: Devereux et al. (2002) 1982 2001 Austria 61 34 Belgium 45 40 Canada 45 35 Finland 60 28 France 50 35 UK 53 30 Germany 62 38 Greece 42 38 Ireland 10 10 Italy 38 40 Japan 52 41 Netherlands 48 35 Portugal 55 36 Sweden 61 28 USA 50 49 Statutory and Effective Corporate Income Tax Rates Source: Devereux et al. (2002) 82 84 86 88 90 92 94 96 98 01 Median statutory 50 48 46 43 39 38 37 36 37 35 Average effective 43 42 41 38 36 37 36 36 34 32 Chapter 19 Intertemporal Efficiency Figures and Tables Generational Structure Generation t Generation t+1 Generation t+2 Generation t+3 t t 1 t 2 t 3 t 4 time Consumer Choice Consumption when Old wt 1 rt 1 xtt 1 xtt wt Consumption when Young Consumption Possibilities x2 k large k increases k 0 x1 Steady-State Equilibrium x2 Equilibrium a Gradient 1 r 1 f ' ( k ) b x1 Golden Rule and Competitive Equilibrium x2 Golden Rule Allocation x 2* Gradient – [1+n] x 1* x1 Gross Profit minus Investment as a Proportion of GDP Abel, Mankiw, Summers and Zeckhauser (1989) Year England France Germany Italy Japan US 1964 9.4 13.6 8.5 22.9 15.2 6.9 1970 7.5 11.8 7.8 18.9 11.6 5.6 1975 6.0 10.9 12.4 16.6 6.8 14.4 1980 10.1 8.3 8.4 12.9 7.5 10.2 1984 13.9 12.9 13.8 17.3 9.4 6.7 Chapter 20 Social Security Figures and Tables Dependency Ratio (Population over 65 as a proportion of population 15 - 64) Source: OECD (www.oecd.org/dataoecd/40/27/2492139.xls) 1980 1990 2000 2010 2020 2030 2040 Australia 14.7 16.7 18.2 19.9 25.9 32.3 36.1 France 21.9 21.3 24.5 25.4 32.7 39.8 45.4 Japan 13.4 17.2 25.2 34.8 46.9 51.7 63.6 UK 23.5 24.1 24.1 25.3 31.1 40.4 47.2 US 16.9 18.9 18.6 19.0 25.0 32.9 34.6 Annual Income and Cost Forecast for OASI Source: www.ssa.gov/OACT/TR/TR04 Cost Rate 18 16 14 12 10 8 6 4 2 0 90 9 1 Income Rate 00 0 2 10 0 2 20 0 2 30 0 2 40 0 2 50 0 2 60 0 2 70 0 2 80 0 2 Forecasts for UK Basic State Pension Source: UK Department of Work and Pensions (www.dwp.gov.uk/asd/asd1/abstract/Abstrat2003.pdf) Date Rate as a % of average earnings 1975 39.3 1980 39.4 1985 35.8 1990 29.1 1995 28.3 2000 25.7 Pareto-Improvement and Social Security Consumption when Old 1 1/ 2 x 1/ 2 1* , x 2* 1 Consumption when Young Population Growth and Consumption Possibilities x2 Frontier after Increase in n Gradient 1 n Initial Frontier x1 Population Growth and Consumption Possibilities x2 e1 e0 x1 Population Growth and Social Security x2 New Frontier New Golden Rule Allocation Initial Golden Rule Allocation Initial Frontier x1 Social Security Game Player 1 Contribute Contribute Don’t contribute 5, 5 0, 10 Player 2 Don’t contribute 10, 0 2, 2 Gains and Losses in transition Source: Miles (1998) Age in 1997 UK Europe 57 0 0 50 – 57 -0.09 -0.6 50 – 50 -1.1 -2.3 30 – 40 -3.0 -5.7 20 – 30 -3.8 -7.2 10 – 20 -2.3 -4.2 0 – 10 0.7 1.7 -10 – 0 3.95 9.2 -20 - -10 6.5 15.7 -40 - -30 7.4 18.7 < -40 7.2 18.9 Age of the Median Voter Source: Galasso and Profeta (2004) Country France Germany Italy Spain UK US Year Age of median voter 2000 43 2050 53 2000 46 2050 55 1992 44 2050 57 2000 44 2050 57 2000 45 2050 53 2000 47 2050 53 Chapter 21 Economic Growth Figures and Tables Dynamics of the Capital Stock kt 4 3.5 3 2.5 2 1.5 1 0.5 49 46 43 40 37 34 31 28 25 22 19 16 13 10 7 4 1 0 t The Steady State Output f k Consumption n k sf k k Capital The Golden Rule Output f k Consumption k* n k Capital Consumption and the Saving Rate c s Welfare Cost of Taxation Source: Chamley (1981) Initial tax rate (%) Increase in consumption (%) Welfare cost (% of tax revenue) 30 3.30 11 50 8.38 26 Tax Rate and Consumption Growth Ct 1 Ct Ct Level and Growth Effects Output 3 2 d c e 1 b a t0 t1 Time Growth Effects of Tax Reform Author Features Utility Parameters Initial Tax Rates and Growth Rate Final Position Additional Observations Lucas (1990) Production of human capital did not require physical capital =2 = 0.5 Capital 36% Labor 40% Growth 1.50% Capital 0% Labor 46% Growth 1.47% 33% increase in capital stock 6% increase in consumption King and Rebelo (1990) Production of human capital requires physical capital (proportion = 1/3) =2 =0 Capital 20% Labor 20% Growth 1.02% Capital 30% Labor 20% Growth 0.50% Labor supply is inelastic Jones, Manuelli and Rossi (1993) Time and physical capital produce human capital =2 = 4.99 calibrated given Capital 21% Labor 31% Growth 2.00% Capital 0% Labor 0% Growth 4.00% 10% increase in capital stock 29% increase in consumption Pecorino (1993) Production of human capital requires physical capital =2 = 0.5 Capital 42% Labor 20% Growth 1.51% Capital 0% Labor 0% Growth 2.74% Capital and consumption different goods, consumption tax replaces income taxes US Tax and Growth Rates Source: US Department of Commerce: www.bea.doc.gov 30 25 20 15 10 5 0 -51950 -10 -15 1960 1970 1980 1990 2000 / UK Tax and Growth Rates Source: Feinstein (1972), UK Revenue Statistics, Economic Trends 25 20 15 10 5 0 1910 -5 -10 -15 1920 1930 1940 1950 1960 1970 1980 Average and Marginal Tax Rates Post-Tax Income Y1 Y2 Ŷ Pre-Tax Income
