Analysis of tax effects on consolidated household/government debts of a nation in a monetary union under classical dichotomy


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1 MPRA Munich Personal RePEc Archive Analysis of ax effecs on consolidaed household/governmen debs of a naion in a moneary union under classical dichoomy Minseong Kim 8 April 016 Online a hps://mpra.ub.unimuenchen.de/71016/ MPRA Paper No , posed 30 April :5 UTC
2 Analysis of ax effecs on consolidaed household/governmen debs of a naion in a moneary union under classical dichoomy Minseong Kim 016/04/8 Absrac Unlike many analysis of ax effecs on consolidaed household/governmen debs in a moneary union, his paper builds up analysis from a consolidaed budge consrain, insead of saring from a model. By a moneary union, i is assumed ha all naions in he union share same currency. if axes are assumed o be in real values, or if one assumes ha governmen arges real value of axes T/P, hen i is also possible o produce he size of fiscal muliplier on real value of consolidaed debs, if relaxed version of classical dichoomy  ha agens decisions are only affeced by real variables  is assumed. This paper argues ha size is db/d r = 1 where r is real value of axes or real axes and b = B/(P R) where B = D wih D nominal deb, P price and R 1 nominal ineres rae, or in erms of real debs, dd/d r = 1. 1 Budge Consrain Analysis A naion being analyzed is in a moneary union wih some oher naions. inside hese naions, here is no exchange rae mechanism. For simplificaion, here are only consumpion goods in an economy, wihou any capial goods. The naion faces he following consolidaed households/governmen budge consrain, assuming such an emergen budge consrain exiss: C + T + B R W N + Π + B 1 (1) where P is price level, C is consumpion, T is ne axes, W is nominal wage, R 1 is nominal ineres rae, Π is firms profis all disribued as dividends, X is ne expor. B is ne oneime bond holding, wih B < 0 implying ne indebedness. I will be assumed ha he agens in he economy do no hold any bond for simplificaion purposes. I will be assumed for res of analysis ha T 0 wih assumpion of zero governmen spending. for simplificaion, 1
3 Analysis of ax effecs on household/governmen debs in a moneary union impor M will be assumed o be zero, and all naions are assumed o be in a moneary union. P > 0 for an obvious reason. B 1 is assumed o be given. Assuming ha he markes clear, W N + Π = (C + X ). Equaion 1 becomes wih equaliy: C + T + B R = (C + X ) + B 1 () T + B R = X + B 1 (3) Le us define b = B R. b = X + B 1 Define relaionships as in he Figure: T + B = X + B 1 (4) R T (5) b X P T The above diagram shows ha b = b(x, P, T ), X = X(P ), P = P (T ). The underlying idea is ha increase or decrease in axes affec P, expors are assumed o only depend on price of goods  which is a reasonable assumpion given ha all expor demands are honored, ha all naions are in a moneary union, and ha qualiy of goods or echnology does no suddenly improve solely by increasing axes, and inverse ne indebedness obviously depends on X, P, T. = X + + (6) X Recall Equaion 5: b = X + B 1 T
4 Analysis of ax effecs on household/governmen debs in a moneary union 3 = 1 (7) X = 1 (8) = B 1 P P + T (9) = B 1 dt P + T P + X P 1 (10) I is assumed ha X < 0 and for our ineress, T 0. < 0, > X 0. Real value of debs increase when axes are raised. If P < 0, P < 0, P a iniial X,, T, B, B 1. Then, db < < X a iniial X,, T, B, B 1. < 1. Then sill db < X a iniial X,, T, B, B 1. = 0, hen db > 1. Then, db > > 0, < X a iniial X,, T, B, B 1. Then, db < > 0, P > 0, P > X a iniial X,, T, B, B 1. < 1. Then sill db > X a iniial X,, T, B, B 1. Now, le us change Equaion 5 ino: > 1. Then, db > 0. b = X + B 1 r, (11) where r, = T /, real axes. b = b(x, P, r ), X = X(P ), P = P ( r ). = X + + (1) d r, X = 1 (13) X = 1 (14)
5 Analysis of ax effecs on household/governmen debs in a moneary union 4 = B 1 = B 1 d r, P + X (15) P 1 (16) Now I will inroduce a relaxed version of classical dichoomy. Even under many sickyprice models, price level iself is irrelevan, as long as some real variables remain adjused. Le new P n, = k. Then, one needs o adjus B 1, B and T o reflec he change. B n, 1 = kb 1, B n, = kb, T n, = kt, wih iniial equilibria adjused appropriaely. Bu r, does no change under price level ransformaion, and similarly b does no change. Le k. Then, Bn, 1 P n, Bu X 0. is invarian relaive o price level ransformaion. Then he problem appears: oo, hen db d r, hree choices: = X 1 (17) d r, is nonzero and finie whenever k 0,. If is finie no longer remains invarian relaive o price level ransformaion. P = all he ime = 0 all he ime X = all he ime If he second choice is made, d r, = 1 (18) The firs choice brings an ineresing conclusion: ha raising real axes explodes nominal value, and if he governmen cares also abou moneary/nominal sabiliy, hen real axes canno be se exogenously and hus are endogenous. The hird choice implies ha expors are exremely sensiive o price change. This can be expeced in an economy where every good is homogeneous and marke is perfecly compeiive. However, if any form of monopolisic compeiion exiss, hen he hird choice is likely no rue.
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