Lerner Symmetry Theorem and Lerner Neutrality Theorem



center4500452120Lerner Symmetry Theorem and Lerner Neutrality Theorem11540067000Lerner Symmetry Theorem and Lerner Neutrality Theoremcenter790007945755Midterm Project of Computer ModelingXin Chen, Kwang Jae Sung1154000Midterm Project of Computer ModelingXin Chen, Kwang Jae Sungright23002311402014760098002014IntroductionLerner Symmetry Theorem is a well-known theorem in international trade, which was presented in Lerner’s 1936 article, “The symmetry between import and export taxes”. In this article, Lerner demonstrated that in a perfectly competitive, full employment economy with two outputs and two factor inputs, a tariff on the imported good at a rate t as a percentage of the foreign price of the good is equivalent in its effect on output decisions and resource allocation to a tax on the exported commodity at the same rate t as a percentage of its domestic price. In other words, an across-the-board ad valorem tariff is identical in all respects to an across-the board ad valorem export tax at the same rate. Following the argument, we can also derive the Lerner Neutrality Theorem which states that a tariff on all imports combined with an identical subsidy on all exports will have no economic impact. The Lerner Symmetry Theorem implies that policy makers can protect the import-competing sector as whole by an export tax as by an import duty. Equivalently, exportable sector can be subsidized by subsidizing imports. Because the Lerner Symmetry Theorem is not altogether intuitive but plays an important role in policy making, it will be more convincing to show it by computer modeling. The purpose of this project is to demonstrate the Lerner Symmetry Theorem using Excel simulation. We tested the Lerner Symmetry Theorem under both Keynesian model and Classical Model. It turns out that it holds in both scenarios. ModelWe use Tsiang’s domestic absorption model (Tsiang, 1961).General Assumptions (Tsiang’s assumptions with modifications)Simplified two-country, two-commodity model in which money supply/interest rate variables (Tsiang’s assumption)Keynesian neutral monetary policy: government does not have direct control over imports, exports and domestic expenditure, and that domestic interest rate is maintained constant through infinitely elastic supply of money and credit (Tsiang’s adoption of Meade’s assumption)Modification: Import tariff/export tax is introduced, and money stock is now maintained constant.Trade balance is exogenous (zero trade balance).Prices are perfectly flexible, and so is exchange rate.The outputs of goods are fixed and independent of prices (Cobb-Douglass production function).Tastes for goods are identical.Demand for money is equivalent to money expenditure.Assumptions above satisfy conditions under which Lerner’s Symmetry Theorem holds.Model Setting Consumption FeatureUnder the simplified two-country, two-commodity model, Country A (America) specializes in the production of autos, while Country B (Britain) does in the production of beers. The consumption in this model comprehensively includes the money values from the consumptions of both domestic and import goods. Therefore, the absorption of a country is determined by a fixed proportion of domestic product consumption and import product consumption, indicated by phi parameters. For example, the absorption (specifically, money absorption) in America is equivalent to the product of auto (domestic good) price and auto absorption to the power of auto absorption share multiplied by the product of beer (import good) price and beer absorption (equal to Britain’s exports of beer to America) to the power of beer absorption. This is expressed by the equation 23 in part D, which says absorb=(PA*D)phiA*(PB*Xs)phiB.Variables and ParametersTable 1 and Table 2 summarize the variables and parameters used in the model.For the purpose of the analysis, 9 exogenous variables and 27 endogenous variables are used.Table1: Specification of VariablesVariableDefinitionUnitClassificationAOutput of AutosAutosEndogenousBOutput of BeersBeersEndogenousCPIConsumer Price Index in America$EndogenousCPIsConsumer Price Index in Britain?EndogenousPAPrice of Auto in America$EndogenousPBPrice of Beer in America$EndogenousPAsPrice of Auto in Britain?EndogenousPBsPrice of Beer in Britain?EndogenousDAmerica’s absorption of autos$EndogenousXsBritain’s export of beers?EndogenousDsBritain’s absorption of beers?EndogenousXAmerica’s export of autos$EndogenousrealabMoney absorption/local CPI in AmericaProportionEndogenousabsorbMoney absorption in America ($)$EndogenousrealabsMoney absorption/local CPI in BritainProportionEndogenousabsorbsMoney absorption in Britain (?)?EndogenousRRents in America ($)$EndogenousRsRents in Britain (?)?EndogenousHMoney Supplies in America ($)$EndogenousHsMoney Supplies in Britain (?)?EndogenousrReal interest rate in AmericaProportionEndogenousrsReal interest rate in BritainProportionEndogenousrealincReal Income in AmericaProportionEndogenousRealincsReal Income in BritainProportionEndogenousINCIncome in America$EndogenousINCsIncome in Britain?EndogenousEExchange rateProportionEndogenousTTrade of Balance$/?ExogenousKCapital stock in AmericaMachinesExogenousLLabor in AmericaWorkersExogenousKsCapital stock in BritainMachinesExogenousLsLabor in BritainWorkersExogenousWWage in America$ExogenousWsWage in Britain?ExogenousTAExport tax on AutoProportionExogenousTBImport tax on BeerProportionExogenousTable 2: Parameters / Initial Values of Exogenous VariablesParameterDefinitionInitial ValueAOutput of Auto100BOutput of Beer100phiAShare of absorption on auto in America0.7phiBsShare of absorption on beer in Britain0.7thetaLLabor share in auto production0.7thetaLsLabor share in beer production0.7mSensitivity of demand for money in America1msSensitivity of demand for money in Britain1saveSensitivity of real absorption to interest rate in America1savesSensitivity of real absorption to interest rate in Britain1sigmaUElasticity of substitution in absorption in America1sigmaUsElasticity of substitution in absorption in Britain1sigmaElasticity of substitution in production in America1sigmasElasticity of substitution in production in Britain1CPIConsumer Price Index in America1CPIsConsumer Price Index in Britain1mpcMarginal Propensity to Consume in America0.7mpcsMarginal Propensity to Consume in Britain0.7RRent in America ($)1RsRent in Britain (?)1WWage in America ($)1WsWage in Britain (?)1phiBShare of absorption on beer in America0.3phiAsShare of absorption on auto in Britain0.3thetaKCapital share in auto production0.3thetaKsCapital share in beer production0.3IncomeIncome of America100IncomesIncome of Britain99absorbMoney absorption in America100absorbsMoney absorption in Britain99DAmerica’s absorption of autos70DsBritain’s absorption of beers70XAmerica’s export of autos30XsBritain’s export of beers30TaAmerican export tax on auto0.01TbAmerican import tariff on beer0.01D. System Equations1. A=KthetaKLthetaLAmerica production function2. B=KsthetaKsLsthetaLsBritain production function3. CPI=PAphiAPBphiBAmerican CPI4. CPIs=PAsphiAsPBsphiBsBritain CPI5. DXs= PBPAsigmaUAmerican consumption proportion6. DsX=PAsPBssigmaUsBritain consumption proportion7. PAs = PA*E*(1+TA)Law of one price for auto8. PBs*(1+TB)= PB*ELaw of one price for beer9. D+X=AMaterial balance for autos10. Ds+Xs=BMaterial balance for beer11. realab=absorbCPIDefinition of American real absorption12. realabs=absorbsCPIsDefinition of Britain real absorption13. KL=WRsigmaFactor use ratio in America14. KsLs=WsRssigmasFactor use ratio in Britain15. H=A*PArmMoney market in America16. Hs=B*PBsrsmsMoney market in Britain17. realab=realincmpcrsaveAmerica real absorption function18. realabs=realincsmpcsrssavesBritain real absorption function19. realinc=incomeCPIReal income in America20. realincs=incomesCPIsReal income in Britain21. income=A*PA+X*Ta+Xs*TbIncome in America22. incomes=B*PBsIncome in Britain23. absorb=(PA*D)phiA*(PB*Xs)phiBValue of absorbed goods in America24. absorbs=(PBs*Ds)phiBs*(PAs*X)phiAsValue of absorbed goods in Britain25. PA=WthetaLRthetaKZero profit condition in America26. PBs=WsthetaLsRsthetaKsZero profit condition in Britain27. dT=d(PA*X)-d(PB*Xs)Trade balance (exports-imports)Note that the law of one price equations for auto and beer are modified (equation 7, 8, and 21), as the export tax on auto will increase the auto price in Britain, and the import tax on beer will increase the beer price in America, assuming all the other factors stay constant. Simulation ResultsKeynesian ModelTable 3 Policy Matrix Keynesian ModelWWsTaTbTb-TaA00000B00000cpi100.210.210CPIs010.090.090PA10000PB100.70.70PAs010.30.30PBs0106E-176E-17D00000Ds000.30.30X00000Xs00-0.7-0.70realab00-0.21-0.210absorb10-3E-173E-176E-17realabs000.210.210absorbs010.30.30R10000Rs01000H10-0.0636-0.06360Hs010.2730.2730r000.06360.06360rs00-0.273-0.2730REALINC00-0.2091-0.20910INC100.00090.00096E-17REALINCs00-0.09-0.091E-16INCs01000E-11-0.70.31In Keynesian Model, the nominal wages, W and Ws, are exogenous, so money stock (H, Hs) is endogenously adjusted to maintain full employment. From the policy matrix, we can see that the marginal effect of import tax, Ta, has identical effects on all endogenous variables as the export tax , Tb, except for the exchange rate. This is consistent with Lerner Symmetry Theorem. The blue matrix is the difference between the marginal effects of Ta and Tb. Other than the exchange rate, the difference is zero. So, the Ta-Tb column is consistent with Lerner Neutrality Theorem which states that a tariff on all imports combined with an identical subsidy on all exports will have no economic impact. In our setting, Ta and Tb are both non-negative. So (–Ta) can be seen as a subsidy on export. The aggregate effect of an import tariff and an export subsidy is thus the blue column in the policy matrix. From the column of Ta, there is something interesting to mention. First of all, marginal increasing on the rate of export tax and import tariff has no impact on the productions in both countries. This is because in Keynesian model, although wages in both countries are fixed, money stock is endogenously adjusted to maintain full employment. Besides, interest rate is changing endogenously, so the capital and labor stock in each country are fixed. Given the production technology unchanged and specialization in each country, there should be no change on outputs. Different from an endowment economy, inclusion of production functions in our model allow us to observe the effect of tariff on output prices and factor price. In Keynesian economy, the only flexible factor price is real interest rate r. The change in the real wage is reflected by change in price level, represented by CPI, and exchange rate E.Therefore, one percent increase on export tax Ta has no effect on domestic price of A, PA. It rises PAs as America is specialized to produce autos. So American export X decreases due to the higher price of autos abroad, and domestic absorption of autos increases to absorb the surplus autos from reduced export. On the other hand, PB decreases which might seem counterintuitive at first glance, because if we apply an import tariff on B, the domestic price of B should be increasing. But the constraint of balance of payment and the reduction of auto exports leads to the contraction of trade which decreases the beer export from Britain. We notice that the exchange rate E has same amount of change as PB has with opposite sign. Such results are probably due to the setting of our domestic absorption equation which keeps constant share of value on domestic good A and imported foreign beer. So if American has to absorb more autos, the domestic beer price has to drop by increasing the value of US dollar. Notice that the tariff increases America real income, so American can still have fixed share of value on absorption even if they absorb more autos. We speculate that these should be related to the elasticity of British absorption. If British are more elastic on auto, then the tariff should have smaller effect on American income and other endogenous variables related to consumption.Shown below, an elasticity analysis is conducted under Keynesian model. The results are shown in the following tables. We tested both the elasticity of American absorption, sigmaU, and British absorption, sigmaUs. Given that the marginal effects of Ta and Tb are the same, we only show the elasticity analysis of Ta. The color density represents higher value of coefficients. The denser the color, the more positive the value. Table 4 Elasticity Analysis of SigmaU for Keynesian ModelSigmaU0.010.10.511.5210100TaTaTaTaTaTaTaTaA0.000.000.000.000.000.000.000.00B0.000.000.000.000.000.000.000.00cpi0.680.570.320.210.160.120.030.00CPIs-0.38-0.27-0.020.090.140.180.270.30PA0.000.000.000.000.000.000.000.00PB2.281.891.080.700.520.410.100.01PAs-1.28-0.89-0.080.300.480.590.900.99PBs0.000.000.000.000.000.000.000.00D-0.68-0.51-0.160.000.080.120.260.30Ds0.300.300.300.300.300.300.300.30X1.581.190.380.00-0.18-0.29-0.60-0.69Xs-0.70-0.70-0.70-0.70-0.70-0.70-0.70-0.70realab-0.68-0.57-0.32-0.21-0.16-0.12-0.030.00absorb0.000.000.000.000.000.000.000.00realabs0.680.570.320.210.160.120.030.00absorbs0.300.300.300.300.300.300.300.30R0.000.000.000.000.000.000.000.00Rs0.000.000.000.000.000.000.000.00H-0.21-0.17-0.10-0.06-0.05-0.04-0.010.00Hs0.420.380.310.270.260.250.220.21r0.210.170.100.060.050.040.010.00rs-0.42-0.38-0.31-0.27-0.26-0.25-0.22-0.21REALINC-0.68-0.56-0.32-0.2091-0.16-0.12-0.030.00INC0.010.000.000.00090.000.000.000.00REALINCs0.380.270.02-0.09-0.14-0.18-0.27-0.30INCs0.000.000.0000.000.000.000.00E-2.28-1.89-1.08-0.7-0.52-0.41-0.10-0.01Table 5 Elasticity Analysis of SigmaUs for Keynesian ModelsigmaUs0.010.10.511.5210100TaTaTaTaTaTaTaTaA0.000.000.000.000.000.000.000.00B0.000.000.000.000.000.000.000.00cpi0.010.060.160.210.230.250.290.30CPIs0.290.240.140.090.070.050.010.00PA0.000.000.000.000.000.000.000.00PB0.020.190.540.700.780.820.961.00PAs0.980.810.460.300.220.180.040.00PBs0.000.000.000.000.000.000.000.00D0.000.000.000.000.000.000.000.00Ds0.010.080.230.300.330.350.410.43X0.000.000.000.000.000.000.000.00Xs-0.02-0.19-0.54-0.70-0.78-0.82-0.96-1.00realab-0.01-0.06-0.16-0.21-0.23-0.25-0.29-0.30absorb0.000.000.000.000.000.000.000.00realabs0.010.060.160.210.230.250.290.30absorbs0.300.300.300.300.300.300.300.30R0.000.000.000.000.000.000.000.00Rs0.000.000.000.000.000.000.000.00H0.00-0.02-0.05-0.06-0.07-0.07-0.09-0.09Hs0.210.230.260.270.280.280.300.30r0.000.020.050.060.070.070.090.09rs-0.21-0.23-0.26-0.27-0.28-0.28-0.30-0.30REALINC0.00-0.05-0.16-0.21-0.23267-0.25-0.29-0.30INC0.000.000.000.000.0006670.000.000.00REALINCs-0.29-0.24-0.14-0.09-0.06667-0.05-0.010.00INCs0.000.000.000.0000.000.000.00E-0.02-0.19-0.54-0.70-0.77778-0.82-0.96-1.00So we can see that the elasticity of absorption does affect the magnitudes of most coefficients related to consumption. More elastic of domestic absorption reduces the disturbance of tariff which is shown in column of SigmaU=100 in table 4. On the other hand, if the foreign elasticity of absorption is lower, which means British absorption are inelastic with respect to prices, then the distortion from American tariff is also low. This is consistent with our intuition.Another interesting fact is that the exchange rage in blue column, which is the aggregate effect of a combination of export subsidy and import tariff. A one percent increase on the subsidy and tariff rates causes the value of US dollar increasing by one percent while keeping everything else constant. So the relative prices in both countries are constant. This is again consistent with Lerner Neutrality Theorem.Classical ModelTable 6 Policy Matrix Keynesian Model LINK Excel.Sheet.12 "C:\\Users\\Ivanka\\Dropbox\\2014 Spring\\ECON 567\\Midterm\\ECON567 Midterm Project - Chen, Sung.xlsx" "Sheet1!R1C9:R28C15" \a \f 5 \h \* MERGEFORMAT HHsTaTbTb-TaA00000B00000cpi100.27360.27360CPIs01-0.183-0.1830PA100.06360.06360PB100.76360.76360PAs010.0270.0271E-16PBs01-0.273-0.2730D00000Ds000.30.30X00000Xs00-0.7-0.70realab00-0.21-0.210absorb100.06360.06360realabs000.210.210absorbs010.0270.0276E-17R100.06360.06360Rs01-0.273-0.2730W100.06360.06360Ws01-0.273-0.2730r000.06360.06360rs00-0.273-0.2730REALINC00-0.2091-0.20910INC100.06450.06450REALINCs00-0.09-0.091E-16INCs01-0.273-0.2730E-11-1.0366-0.03661In the classical model, wages become perfectly flexible and money stock is fixed. So we can still have full employment in both country. We can see that the Lerner Symmetry Theorem and Neutrality Theorem also holds in this case. The aggregate effect is the same as Keynesian’s. Table 7 Elasticity Analysis of SigmaU for Classical ModelSigmaU0.010.10.511.5210100TaTaTaTaTaTaTaTaA0.000.000.000.000.000.000.000.00B0.000.000.000.000.000.000.000.00cpi0.890.740.420.270.200.160.040.00CPIs-0.80-0.65-0.33-0.18-0.11-0.070.050.09PA0.210.170.100.060.050.040.010.00PB2.492.071.180.760.570.450.100.01PAs-1.70-1.27-0.380.030.220.340.690.78PBs-0.42-0.38-0.31-0.27-0.26-0.25-0.22-0.21D-0.68-0.51-0.160.000.080.120.260.30Ds0.300.300.300.300.300.300.300.30X1.581.190.380.00-0.18-0.29-0.60-0.69Xs-0.70-0.70-0.70-0.70-0.70-0.70-0.70-0.70realab-0.68-0.57-0.32-0.21-0.16-0.12-0.030.00absorb0.210.170.100.060.050.040.010.00realabs0.680.570.320.210.160.120.030.00absorbs-0.12-0.08-0.010.030.040.050.080.09R0.210.170.100.060.050.040.010.00Rs-0.42-0.38-0.31-0.27-0.26-0.25-0.22-0.21W0.210.170.100.060.050.040.010.00Ws-0.42-0.38-0.31-0.27-0.26-0.25-0.22-0.21r0.210.170.100.060.050.040.010.00rs-0.42-0.38-0.31-0.27-0.26-0.25-0.22-0.21REALINC-0.68-0.56-0.32-0.2091-0.16-0.12-0.030.00INC0.210.180.100.064530.050.040.010.00REALINCs0.380.270.02-0.09-0.14-0.18-0.27-0.30INCs-0.42-0.38-0.31-0.273-0.26-0.25-0.22-0.21E-2.90-2.45-1.48-1.03663-0.82-0.70-0.32-0.22Table 8 Elasticity Analysis of SigmaUs for Classical ModelsigmaUs0.010.10.511.5210100TaTaTaTaTaTaTaTaA0.000.000.000.000.000.000.000.00B0.000.000.000.000.000.000.000.00cpi0.010.080.210.270.300.320.370.39CPIs0.080.02-0.12-0.18-0.21-0.23-0.28-0.30PA0.000.020.050.060.070.070.090.09PB0.030.210.590.760.850.901.051.09PAs0.770.580.200.03-0.06-0.11-0.26-0.30PBs-0.21-0.23-0.26-0.27-0.28-0.28-0.30-0.30D0.000.000.000.000.000.000.000.00Ds0.010.080.230.300.330.350.410.43X0.000.000.000.000.000.000.000.00Xs-0.02-0.19-0.54-0.70-0.78-0.82-0.96-1.00realab-0.01-0.06-0.16-0.21-0.23-0.25-0.29-0.30absorb0.000.020.050.060.070.070.090.09realabs0.010.060.160.210.230.250.290.30absorbs0.090.070.040.030.020.020.000.00R0.000.020.050.060.070.070.090.09Rs-0.21-0.23-0.26-0.27-0.28-0.28-0.30-0.30W0.000.020.050.060.070.070.090.09Ws-0.21-0.23-0.26-0.27-0.28-0.28-0.30-0.30r0.000.020.050.060.070.070.090.09rs-0.21-0.23-0.26-0.27-0.28-0.28-0.30-0.30REALINC0.00-0.05-0.16-0.21-0.23267-0.25-0.29-0.30INC0.010.020.050.060.0711330.080.090.09REALINCs-0.29-0.24-0.14-0.09-0.06667-0.05-0.010.00INCs-0.21-0.23-0.26-0.27-0.28-0.28-0.30-0.30E-0.24-0.43-0.85-1.04-1.12824-1.18-1.34-1.38In the above two tables, green means that with sigmaU or sigmaUs changing, those coefficients changes only in classical model. So more endogenous variables, such as incomes, absorption and rental rates are sensitive to elasticity of absorption in classical model. Interestingly, according to paper “The Balance of Payments Approach to Trade Tax Symmetry Theorems,” Lerner’s symmetry that is observed above will still hold under the imperfect competition. It is important to note that any equilibrium attained by a monopolist (or monopsonist) under one set of tax and subsidy can be reached with different combination of tax and subsidy, as long as the border tax adjustment factor (product of net debit tax factor and net credit tax factor) is maintained. As the prices and incomes are consistent in all equilibria, a particular level of production that maximizes one system would be the optimal decision, with no alternative system necessary, and therefore the symmetry is conserved. Moreover, the validity of the symmetry can be extended to N imperfect competitors, under the combinations of taxes and subsidies that lead to the same adjustment factors.ConclusionWe have demonstrated the validation of Lerner Symmetry Theorem and Lerner Neutrality Theorem in a modification of Tsiang’s model under Keynesian economy. In addition, we also show its validation in a similar setting under classical economy. A computer simulation model thus has more explanatory power as it not only provides a complement of theoretical analysis, but also reveals some interesting details which sometimes might seem counter-intuitive at first glance.ReferenceLerner, A. P. (1936). The symmetry between import and export taxes. Economica, 306-313.Kaempfer, W. H., & Tower, E. (1982). The balance of payments approach to trade tax symmetry theorems.?Weltwirtschaftliches Archiv,?118(1), 148-165.Tsiang, S. C. (1961). The role of money in trade-balance stability: Synthesis of the elasticity and absorption approaches.?The American Economic Review, 912-936. ................
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