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Economic Modelling: Lecture 5 Fiscal Policy and Golden Rules to Fine-Tune the Economy http://www.hmrc.gov.uk/stats/index.htm http://www.hm-treasury.gov.uk/economic_data_and_tools/ forecast_for_the_uk_economy/data_forecasts_index.cfm 1 Government Budget Deficit Percent of GDP 8 A3: CYCLICALLY ADJUSTED BUDGET BALANCES Projections 6 4 2 -4 -6 Public sector net borrowing Surplus on current budget Contents http://www.hm-treasury.gov.uk/economic_data_and_tools/finance_spending_statistics/finexp_index.cfm 2 2011-12 2010-11 2008-09 2009-10 2007-08 2006-07 2005-06 2003-04 2004-05 2002-03 2001-02 2000-01 1999-00 1997-98 1998-99 1996-97 1995-96 1994-95 1992-93 1993-94 1991-92 1990-91 1989-90 1988-89 1986-87 1987-88 1985-86 1984-85 1983-84 1981-82 1982-83 1980-81 -2 1979-80 0 C3: GOVERNMENT RECEIPTS BY FUNCTION 2006-2007 (PROJECTIONS) Council tax, 22.54609297, 4.354% Income tax, 146.0614237, 28.204% Other*, 75.41787888, 14.563% Business rates, 21.48164123, 4.148% National Insurance 17% VAT, 76.153, 14.705% Corporation tax, 48.04208195, 9.277% Excise duties, 39.662, 7.659% *Other receipts include capital taxes, stamp duties, vechile excise duties, and some other tax and non-tax receipts- for example interest and dividends 3 Contents http://www.hm-treasury.gov.uk/economic_data_and_tools/finance_spending_statistics/finexp_index.cfm http://www.hm-treasury.gov.uk/economic_data_and_tools/finance_spending_statistics/finexp_index.cfm 4 2007-08 2006-07 2005-06 2004-05 2003-04 2002-03 2001-02 2000-01 1999-00 1998-99 1997-98 1996-97 1995-96 1994-95 1993-94 1992-93 1991-92 1990-91 1989-90 1988-89 1987-88 1986-87 1985-86 1984-85 1983-84 1982-83 1981-82 1980-81 Ratio of Government Spending to GDP in UK 49 B3: TME (% GDP) 47 45 43 41 39 37 Contents B4: GOVERNMENT SPENDING BY FUNCTION 2006-07 (Projections) Social protection** 27% Personal social services 5% Other* 10% Health 16% Debt interest 5% Public order and safety 6% Housing and environment Defence 4% Industry, agriculture, 6% employment and training 4% Education 13% Transport 4% *Includes spending on general public services; recreation, culture and religion; international cooperation and development; public service pensions; plus spe yet to be allocated and some accounting adjustments. **Includes tax credit payments in excess of an individual's tax liability, which are now counted in AME, in line with OECD guidelines Conten 5 http://www.hm-treasury.gov.uk/economic_data_and_tools/finance_spending_statistics/finexp_index.cfm What is a golden rule of fiscal policy? Why is this necessary? Golden rule of Fiscal Policy: Borrow only to invest Balance budget over the business cycle Theory on economic policy: Rules are better than discretion Scope for discretion provides opportunity to cheat public Tools: Inflation Unemployment GAME Nash Bargaining: non-cooperative solution Cooperative Solution is Pareto Optimal Cooperation generates credibility Backward Induction: Cooperative Solution of a dynamic Game 6 Objectives of Fiscal Policy • • • • • • • • • • • • Macroeconomic stabilisation Higher growth rate of output Full employment Stable prices: low rate of inflation stable interest and exchange rates Equity: horizontal and vertical (tax/transfer) Efficiency in resource allocation Provision of public goods Externality: max positive externality, min neg. ext. Market failure Public private partnership (education, health, R&D) 7 Instruments of Fiscal Policy • Taxes Direct: income, profit, wealth Indirect: VAT, tariff, excise, business Subsidies: goods/services and for use of inputs • Spending Public goods: defence, law / order, national parks Semi-public goods: education, health, R&D • Debt Borrowing from the private sector : Crowding out From the central banks : infaltion8 Theory of Ricardian equivalence 8 Who bears the burden of taxes and who benefit from the public spending? • Producers Labour supply (work hours, leaves, retirement) Taxed sectors vs. subsidised sector Domestic vs. foreign goods Excise duties • Consumers VAT and market prices Sin goods (tobacco, alcohol, • Traders: imports and exports, custom unions 9 Microeconomic Tools To Evaluate the Impact of Taxes 10 Impact of Increase in Taxes in Demand for a commodity Income and Price Effects: Hicksian and Slutsky Decomposition X2 I2 Compensating Variation B I1 Compensating variation c Reduction in Welfare due to increase in taxes MU 2 P2 = c MU 1 P1 (1 + t ) MU 2 aMU 1 = P2 P1 b B BT 0 x2 x1 Substitution effect c x0 X1 Income effect 11 Impact of Increase in Taxes in Demand for a commodity Income and Price Effects: Hicksian and Slutsky Decomposition Equivalent Variation X2 C I2 Equivalent variation I1 B Reduction in Welfare due to increase in taxes c b MU 2 P2 = MU 1 P1 MU 2 P2 = MU 1 P1 (1 + t ) a B BT 0 x2 Income effect x1 c x0 X1 Substitution effect 12 Compensating Variation 1 2 1 1 2 2 Base utility u 0 = x x , with budget ( p1 , p 2 ) = (1,1) m = p1 x1 + p 2 x 2 if m x = m demand functions x1 = 2 p , 2 2 p , given 2 1 (x1 , x 2 ) = (50,50 ) . Tax on good one rises to 2, m =100 ( p1 , p 2 ) = (2,1) , income m 100 x = = = 25 , remains the same m =100, 1 2 p1 2 × 2 x2 = m 100 = = 50 . 2 p 2 2 ×1 How much income need to be compensated to this consumer to maintain at the old level of utility, 1 1 1 2 1 2 2 2 ⎛ m ' ⎞ ⎛ m' ⎞ u 0 = 50 1 50 1 = ⎜ ⎟ ⎜ ⎟ = 50 Î ⎝4⎠ ⎝2⎠ m ’=141, Therefore compensating variation is 141-100=41. Compensating variation is positive for a price rise. 13 Equivalent Variation How much money should be taken away from the consumer in the original prices to make him/her achieve the utility level after the price change. 1 1 2 1 2 1 1 2 1 2 ⎛ m' ⎞ ⎛ m' ⎞ u n = 25 50 = ⎜ ⎟ ⎜ ⎟ = 5 × 5 × 2 ⎝2⎠ ⎝2⎠ m' = 2 × 5 × 5 × 2 = 70.7 EV = 70.7-100 = -29.3. Equivalent variation in negative for a rise in price level 14 Money Metric Measure of Changes in Welfare Due to Tax Reforms Equivalent Variation Compensating Variation Rise in Fall in tax tax Negative Positive Positive Negative Why General equilibrium models to evaluate tax reforms: Need to consider income and substitution effects in individual markets and take account of multiple rounds of knock on effects to measure the Impacts of tax changes more accurately. 15 Measuring the Impact of Taxes in the Economy S’ S PD CL t P PL PS D 0 q’ q 16 Take regular demand and supply functions D =a-bP S = -c+dP equilibrium price and quantity P= a+c ad + bc q = b+d ; b+d . A tax on the commodity creates a wedge between the price received by suppliers and price paid by consumers. This distorts the market equilibrium and allocation. D = a − bP D S = −c + dP S Price that consumers pay is higher with taxes PD = PS +t 17 Demand equals supply in equilibrium: a − bP D = −c + dP S ( ) a − b P S + t = −c + dP S a − bP S − bt = −c + dP S a + c − bt = bP S + dP S S Price received by suppliers: P = a + c − bt b+d Price paid by consumers: PD = PS +t = a + c − bt a + c + dt +t = b+d b+d The equilibrium quantity in the distorted market : ⎛ a + c + dt ⎞ ad − bc + bdt D = a − bP D = a − b⎜ ⎟= b+d ⎝ b+d ⎠ 18 When supply is perfectly elastic all burden of tax falls on to the consumers. S’ P+t t S P D q’ q 19 When Demand is Perfectly Inelastic All Burden taken by Suppliers S P t P-t D q 20 First Round Impact of Taxes: Partial Equilibrium Analysis S’ S Burden to consumers Pc P Burden to producers Ps D 0 Q’ Q Equilibrium in a Single Market 21 Tax Credit Promotes Investment Why Manufacturers Lobby for a Tax Credit? [r + δ − π ] K (1 − τ )[r + δ − π K ] MPK = 0 K1 αk K2 22 α −1 Impact of Taxes and Transfer on Labour Supply of Individuals Why one should work more if entitled for benefit? u Consumption b No benefit equilibrium B_T a Benefit equilibrium u Benefit 0 Leisure Labour L 23 Higher taxes reduce saving and investment and growth ST Saving b r+t r=i-π a Investment 0 Stx S*, I* Saving and Investment 24 Macroeconomic Tools to Evaluate the Impacts of Taxes 25 Macroeconomic Stabilisation Role of Tax and Spending T = tY G=T Tax and G Spending T>G Surplus in boom G T<G Deficit in recession 0 YF Income T 26 How High Should be Public Spending? Costs of public spending Cost and Benefit Of spending C=B c a b Benefits of spendin 0 G* Size of spending 27 How much should be the tax rate to maximise the government revenue ? Tax compliance R-max Tax avoidance Tax evasion Revenue R-low Revenue=F(t) t-Low t-Rmax tH Tax rate 28 Balanced Budget Multiplier with Lump-Sum Taxes The real national income is given by the IS Curve: 1 [ Y= c0 + I + G − c1T ] 1 − c1 . Positive Government expenditure multiplier: Negative tax multiplier: The balanced budget multiplier: 1 ∂Y = ∂G 1 − c1 c1 ∂Y =− ∂T 1 − c1 ∂Y ∂Y =1/(1-c1) - c1/(1- c1) = 1 + ∂G ∂T A change of 100 in both G and T also raised income by 100. Balanced change in G and T is not macro economically neutral.29 Automatic Stabiliser with Proportional Taxes C = c0 + c1YD Consumption: Disposable income: Tax Revenue Income (IS curve): 0 < c1 < 1 YD = Y − T T = t 0 + t1Y 0 < t1 < 1 Y = c0 + c1YD + I + G 1 Y= * [c 0 - c1 t 0 + I + G ] (1 - c1 + c1 t 1 ) The multiplier = 1/(1-c1+c1t1) <1/(1- c1), so the economy responds less to changes in autonomous spending when t1 is positive. High T when Y is high. Low T when Y is low. 30 Macroeconomic Forecasting and Revenue Projection 1e6 Forecasts C Forecasts 300000 I 250000 800000 200000 600000 150000 2000 2005 Forecasts 2010 2015 2000 800000 T 2005 Forecasts 2010 2015 2010 2015 2010 2015 M 750000 600000 500000 400000 2000 10 2005 Forecasts 2010 2015 2000 10 i 2005 Forecasts Inflation 0 0 -10 -20 -10 2000 2005 2010 2015 2000 2005 31 Results from GiveWin PcGive. Laffer Curve Model:A Numerical Example Rt =50t −2t 2 Where R is revenue in billion of pounds, t is the tax rate. The tax rate that maximises the revenue is given by ∂Rt =50−4t = 0 Î t = 12.5 ∂t There are two tax rates that can raise the same revenue. 200=50t−2t 2 Î 2 −4(100) − ( − 25 ) ± ( − 25 ) t 2 −25t +100= 0 ;t = = 1 2 t = 25±15=5,20 1 2 32 General Equilibrium Analysis on Impact of Taxes 33 Government Finance Tax/subsidy Markets Households Economy (income categories) Trade Markets Firms (Sectors of Production) Communication Transport ROW General Equilibrium Models Assume Clearing of all Markets But has no trade-off between unemployment and inflation. 34 General Equilibrium Impact of Taxes • First round effects: incidence of tax – Reduction (increase) in • • • • • • household income Profit of firms Demand for products by households and foreigners Supply of goods and services by firms Government spending Investment spending • Second round effects: Gradual shifting of the burden of taxes – Increase or decrease in prices of commodities – Collection of revenue • Final impacts – When all shifting burdens works through-out the economy 35 General Equilibrium and Knock on Effects in Different Markets Balance of Payment analysis: Graphical approach Labour Market LD LS Goods and Money Money market IS AS LM MD MS Wage i Domestic bonds BS BD i Foreign Bonds i* Foreign Exchange i Interest rt L Y M/P DB FB exchange rate Output Y Employment Output P Price Real money balance Portfolio allocation e 36 Raw Data (National Accounts, IO, tax, trade, household survey) Adjustments to yield benchmark (micro consistent) data set Model Structure Functional forms Calibration check Parameters and Elasticities Replication check Policy change (tax) specified Compute New Equilibrium Compare to benchmark Equilibrium data Steps for Implementation of a General Equilibrium Model 37 Merrlees’ (1971) Theory of Optimal Taxation • Society has distribution of highly skilled people and nonskilled people • There is an incentive compatible allocation in which highly productive people earn more and pay higher taxes • Highly productive individuals have material incentive to work hard even though their net of tax income may not be proportional to their labour • Incentive compatible consumption maximise the social welfare and tax system can be designed to obtain this 38 Fiscal Policy Affects Growth Rates of Output Growth Rates in the UK, USA and Euro Area 5.0 4.0 3.0 2.0 1.0 United Kingdom United States Euro area 0.0 1979- 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 89 -1.0 -2.0 39 Ratio of General Government Expenditure to GDP 60.0 Percent of GDP 50.0 40.0 30.0 United Kingdom United States Euro area 20.0 10.0 0.0 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 40 General Governmental Tax and Non-tax Receipt 50.0 45.0 40.0 Ratio to GDP 35.0 30.0 25.0 20.0 United Kingdom United States Euro area Total OECD 15.0 10.0 5.0 0.0 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 41 Government Budget Deficit or Surplus 6.0 4.0 Percent of GDP 2.0 0.0 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 -2.0 -4.0 -6.0 -8.0 United Kingdom United States Euro area -10.0 42 Composition of the Public Revenue in the UK 250,000 200,000 150,000 Billions of £ IR+VED+NICS VAT Other C&E 100,000 50,000 1994/95 1995/96 1996/97 1997/98 1998/99 1999/00 2000/01 2001/02 2002/03 2003/04 p 43 National Debt Borrowing = Spending - Revenue Debt = Borrowing +Net Debt Stock How much a government can finance from Inflationary taxes? 44 Ratio of National Debt to GDP in Advance Countries 125 Canada France 60 100 40 75 1980 70 60 50 40 1985 1990 1995 2000 2005 1980 125 Germany 1985 1990 1995 2000 2005 1985 1990 1995 2000 2005 1990 1995 2000 2005 Italy 100 75 1980 1985 1990 1995 2000 2005 Japan 150 1985 United Kingdom 50 45 40 35 100 1980 1980 1990 1995 2000 2005 1990 1995 2000 2005 1980 1985 United States 70 60 50 1980 1985 45 Source: IMF Reasons for Public Debt • No debt if the budget is balanced every time: G - T= 0 Î ΔB =0 • Debt (B) accumulates when G > T. • Change in debt has two components Primary deficit (ΔB = G -T) Debt servicing rB ΔB = (G -T) + r B (1) 46 Debt and Primary Surplus In terms of GDP ΔB (G − T ) rB + = Y Y Y (2) If the primary budget is balanced G - T = 0 Then the debt increases by the rate of interest: ΔB =r B (3) A primary surplus is required to pay the interest if debt is to remain constant ΔB = 0 => (T − G ) = rB (4) 47 Debt Dynamics: Determinants of Debt/GDP Ratio B ⎛ B ⎞ G −T (5) + (r − g ) Δ⎜ ⎟ = Y Y ⎝Y ⎠ • Higher the interest rate causes a rise in B/Y • Lower the growth rate of output causes a rise in B/Y • Higher the current deficit (G -T) leads to higher B/Y • Higher initial B/Y implies higher B/Y in subsequent years Example Debt ratio = 100% r = 3% g = 2% T-G = 1% is required to keep B/Y constant 48 Inflation Tax: Seigniorage Revenue From the R* Inflation tax Ξ* Inflation rate 49 Inflationary Finance of Public Budget Deficit B ΔM ⎛ B ⎞ G −T Δ⎜ ⎟ = + (i − π − g ) − Y PY Y ⎝Y ⎠ • Higher the interest rate causes a rise in B/Y • Higher inflation rate lowers the debt/GDP ratio • Lower the growth rate of output causes a rise in B/Y • Higher the current deficit (G -T) leads to higher B/Y • Higher initial B/Y implies higher B/Y in subsequent years • Higher growth rate of money supply lowers the debt/gdp ratio. Example Debt ratio = 100% i = 5% g = 2% π =2% G-T = 4% then money supply should increase by 3% to keep B/Y constant 50 Inflationary Finance of Public Budget Deficit PB Δ (PB ) ΔM PG PT = − +i + PY PY PY PY PY B ΔM ⎛ B⎞ G −T Δ⎜ ⎟ = + (i − π − g ) − Y PY Y ⎝Y ⎠ G −T B ΔM ⎛ B⎞ Δ⎜ ⎟ = 0 = + (i − π − g ) − Y Y PY ⎝Y ⎠ B T − G ΔM + = (i − π − g ) Y Y PY 51 Seigniorage (Inflation Tax) : A Numerical Example Seigniorage π Si 40 1000 0 0 30 905 0.01 9.05 819 0.02 16.38 607 0.05 30.35 368 0.1 36.8 135 0.2 27 82 0.25 20.5 7 0.5 3.5 20 10 5 0. 25 2 0. Inflation 0. 1 0. 05 0. 02 0. 01 0 0 0. Seigniorage revenue M/P 52 Ricardian Equivalence Theorem: Questions • Should government finance public budget deficit by borrowing or by raising taxes? • is it possible to cut tax rates without a cut in public spending? • David Ricardo. British economist, who wrote about 180 years ago that it is not. • Ricardian Equivalence Theorem states that borrowing more from private sector or taxing more have equivalent outcome. 53 Basic Proposition of the Ricardian Equivalence Tax or Borrowing Does not Make Any Difference Tomorrow C2 Before Borrowing Budget Constraint After borrowing budget constraint C1 + C1 + C2 = 1+ r (w 1 ) + ⎛ w2 ⎞ ⎜ ⎟ ⎝1+ r ⎠ τ ⎞ C2 ⎛ w = (w1 − τ 1 ) + ⎜ 2 − 2 ⎟ 1+ r ⎝1+ r 1+ r ⎠ C1 Today 54 Ricardian Equivalence: Main Proposition • It does not matter whether public deficit is financed by raising tax rates or by borrowing from the private sector. • More Borrowing now means higher rates of tax in the future for repayment of debt. • With higher amount of public debt now private households save more in anticipation of higher taxes in the future that government will impose on them to repay the debt. • Private households optimise intertemporally and completely internalise public policy. • Borrowing now or raising tax now are equivalent strategies if both the government and household honour their own inter temporal budget constraints. 55 Fiscal and Monetary Policy Game in a Diagram M (Nardhaus (1994) Model) Budget Surplus, S + Monetary Bliss (MB) F 0 Interest rate, r Budget Deficit, D Nash equilibrium (N) Fiscal Bliss (FB) M F 56 Inflation-Unemployment Game Between Private and Public Sectors: Normal form Government chooses actual inflation and private sector makes expectation about it. H strategy corresponds to high inflation expectation by the private sector L strategy corresponds to low inflation expectation by the private sector ............................... Pr ivate Sector ⎡ Government Sector ⎢⎢ H ⎢⎣ L H (4,4) (3,6) L ⎤ (6,3)⎥⎥ (5,5)⎥⎦ First element represents payoff to the row-player (Government). Second element represents Payoff to the column-player (private sector). 57 Process of Finding a Nash Equilibrium Private sector H 4 4 Government L 3 6 6 3 5 5 H Government Sector’ choice L Private sector 4 H Government H 4 L Private Sector’ choice L 6 3 5 H 4 H L 3 6 3 5 L 4 6 6 5 3 5 Outcome of the Game 58 Nash solution is not Pareto optimal. (L,L) =(5,5) would have been better for both. Inflation-Unemployment Game Between Private and Public Sectors in a diagram π t = π e , H − b(ut − u n ) πt −π e t C(6,3) D(4,4) (govt, private) (High, high) (high, low) π t = π e , L − b(ut − u n ) (low, high) B(3,6) A(5,5) (low, low) 0 ut = u n PC2 ut − u n PC1 59 Inflation-Unemployment Game Between Private and Public Sectors π t = π e , H − b(ut − u n ) Nash Equilibrium πt −π e t C(6,3) D(4,4) Hated by the government Preferred by government π t = π e , L − b(ut − u n ) B(3,6) A(5,5) PC2 0 Cooperative solution Pareto solution ut = u n ut − u n PC1 60 Extensive Form of Inflation-Unemployment Game: When government moves first H H (4,4) Private Sector L (6,3) (3,6) Government H L Private Sector L (5,5) 61 Dynamic Inflation-Unemployment Game: Solution by Backward Induction H H (4,4) Private Sector, T2 L (6,3) (3,6) Government, T1 H L Private Sector, T2 L (5,5) 62 Credibility Problem, Cheating and Discount Factor of the Game Both gain by playing (C,C) But this solution is not credible. There is incentive to deviate. Trigger Strategy Game returns to Nash path in absence of credibility. If the game is played infinite number of times the optimal discount value ff the game is calculated as 5 PV (C , C ) = 5 + 5δ + 5δ + 5δ + ... + 5δ = 1− δ 2 3 n PV (C , C ) = 5 + 5δ + 5δ 2 + 5δ 3 + ... + 5δ n = Lim n →∞ 5 1− δ PV (cheat ) = 6 + 4δ + 4δ 2 + 4δ 3 + ... + 4δ n 63 Solution for the Discount Factor of the Game PV ( L, L) = 5 + 5δ + 5δ 2 + 5δ 3 + ... + 5δ n = Lim n →∞ 5 1−δ PV (cheat ) = 6 + 4δ + 4δ 2 + 4δ 3 + ... + 4δ n δPV (cheat ) = 6δ + 4δ 2 + 4δ 3 + ... + 4δ n +1 (1 − δ )PV (cheat) = 6 − 6δ + 4δ PV (cheat ) = 6 + 4 lim n →∞ δ (1 − δ ) δ 5 = 6+ 4 (1 − δ ) 1−δ 5 = 6(1 − δ ) + 4δ δ n +1 ≈ 0 6 − 5 = 2δ 1 δ = 2 64 References • • • • http://www.statistics.gov.uk/themes/economy/default.asp http://www.ifs.org.uk/publications.php; http://www.ifs.org.uk/public/bn20.pdf http://www.statistics.gov.uk/themes/economy/Articles/NationalAccounts/dow nloads/1995_UK_Analytical_Input_Output_Tables_article.pdf; www.hmtreasury.gov.uk/Economic Data and Tools • • • Barro, R. J. (19740, "Are Government Bonds Net Wealth?," Journal of Political Economy pp. 1095-1117. Bhattarai K. (2002) Welfare Impacts of Equal-yield Tax Reforms in the UK Economy, mimio, University of Hull. Hutton, J. P.; A. Ruocco (1999) Tax Reform and Employment in Europe International Tax and Public Finance, August, 6:3:263-87. Clark Tom , M Elsby and S Love (2001) Twenty Five Years of Falling Investment? Trends in Capital Spending on Public Services, Institute of Fiscal Studies. Mirlees, J.A. (1971) “An exploration in the theory of optimum income taxation”, Review of Economic Studies, 38:175-208. • • • Pigou A.C. (1947) A Study in Public Finance (3rd edition) McMillan, London. • Chote, Emmerson and Harrison and Miles (2006) The IFS Green Budget: January, Institute of Fiscal Studies, Commentary 87, 7 Ridgemount Street, London WC1E 7AE. Emmerson C. and C Frayne (2002) Challenges for the July Spending Review, http://www.ifs.org.uk/budgetindex.shtml; http://www.ifs.org.uk/public/bn20.pdf. HM Treasury (2002) Reforming Britain’s Economic and Financial Policy, Palgrave. Institute for Fiscal Studies (2002), The IFS Green Budget, Janaury. Shoven, J.B. and J. Whalley (1984) “Applied General-Equilibrium Models of Taxation and International Trade: An Introduction and Survey,” Journal of Economic Literature 22, 1007-1051 Whalley J. (1975) “A General Equilibrium Assessment of the 1973 United Kingdom tax reform”, Economica, 42:166:139-161. Ramsey, F. P. (1927) “A contribution to the theory of taxation”, Economic Journal, 37:47-61. • • • • • • 65