Question

4. A recurring idea in Congress is to move the United States further away from a system of income taxes and towards a system of consumption taxes. A nationwide consumption tax would essentially be a national sales tax, a system that many Western European countries have. It is often referred to as a value-added tax or a VAT Negative consumption is ruled out because it makes no 'economic sense. Zero consumption would be subop timal behavior with either of these utility functions because the marginal utility to be gained from leaving that point would be infinite Consider a representative household in the static consumption-leisure model with a gen- eral utility function u(c, l) that exhibits positive and diminishing marginal utility in each price of P on consumption and earns nominal wages proportional sales tax on argument. The household faces a at rate W on their labor. In addition, the household faces consumption at rate Te and a proportional tax a. wage income of Tn on (a) Write down the budget constraint for the representative household. (b) Express the consumption-leisure optimality condition in terms of u(c, l) (c) Using indifference curve analysis, graphically show the optimal choice (c", l*). Label slopes and intercepts on your graph (d) Suppose under present law that the federal wage tax rate is Tn = 2, while the federal consumption tax rate is Te = 0. Congress wants to lower the wage income tax rate 15, but does not want to alter the aggregate optimal choice of consumption to Tn and leisure (c,l*). Use economic logic based on the households' optimality condition to explain how they can achieve this using the consumption tax. (e) Compute the consumption tax rate that achieves the scenario described in part (d) (f) Suppose Congress only lowers T, without Te: Use your graph from part (c) to show how the optimal choice of aggregate consumption and leisure change, assuming that the substitution effect dominates the income effect on labor supply

Answer 1

S4ucc, e) ) l luure, P Prtce of nominal wage consunptia let ime T Tdteul OcSsime &lakor housalL) T-LR 1=T-L Budget conetraint P. c+ P. TC [wCT- WIT-l]-Tn P[1+ Te1C = WT [I-Tn 1- wl1-Tn]e 9 PrittelC wl1-T1 WT[I-Tn - -(Buolget conatrai TPia pertioal for Tn 8age tan Tc Sale r tax optimatity condition ushere Iudiffsce tangent ゴe to Buoget line Curve hs MRSE,u au/dc /1-Th7 PE1+Te7 Buoget constraint Slope Opei mali ty- onolitiom dulde L-T

Budget eonabuint Prittelc 1-Jl=WT [1-Zn) swpe WTI1- P C1+Te] PEI+TeT MRS=-au Cc, /de Ju cc,e/dc C4 T Cu'sue howes) fueainr (laus) Tn= 2 Price ratio Puaunt M- p P TIto7 New Pouo po sal bmdle must not cumge opeimal Possi ble if pie ato does not chnye Tn=,1S &, C1-S Psuice Ratio =-8.85 New P LI+te .&S Nevo PAice Nati Pruaamt Paice Zc=.85XS- 24 .Tc= 1.0625-1 Te -.062S =2-17 PIit.0625 P1062 At (Te.0625, Tn =. IS) Neua ice ratio =1.85 --.8/4 1Prusut Pruce Ratio

So, If pfa atfo emaiu Unchanged ondle for tc.062s for the ns optimal proposal of Tc = .IS Easuien veutfcal intereupt PE 107 Now after froposal intereupt wiu be =NT [I-.IS]-. PCI+.0627 1062 P And So, Budgel Tmarinun tm horizontal intereept beforu & after Proposad, And frie ato also Aumafn chngcd so s optimal bumelle donstraiut ermafu unchongnd as Tt is Swouon abone computatiom of Tc=.0625 for Tn=IS tan ate for unsnp tion NOkin Napecively hours It is givem ony lowous Tn doe wage tar ds lowered Humee, ineome aftur tanation comparatively Jnizher after Tn loweruol. So, oppontinity warriny Subatitution effects divises that incuasl working houns P oleereaae leisue hows As leiwu hourst of r leisusu inereasess Andl caat that hot Rouns = To tal Time Leisuee & ven effec devfses that And Inesme sump ti'on both noamalgoodl ns,ineuasrin disposable fneome hereases both conounptiona lefsure houes. Alven subotitutim effect overweigh income efets Fhufore,connetiom voiu inerease out lisure OV Nours Ealsas SEIER SE dunsus lusuu hows must be ceereaaed