This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Comparative Dynamics Prof. Lutz Hendricks October 7, 2009 L. Hendricks () Comparative Dynamics October 7, 2009 1 / 31 Comparative Dynamics We use phase diagrams to uncover the dynamic response to shocks. We study tax changes in a growth model. L. Hendricks () Comparative Dynamics October 7, 2009 2 / 31 Model The household solves max Z e & t u ( c t ) dt (1) subject to k t = r t k t + w t & c t & t (2) and k given. Firms produce output using F ( K , L ) . The government uses the tax revenue to &nance goverment spending: G t = t . L. Hendricks () Comparative Dynamics October 7, 2009 3 / 31 Competitive Equilibrium A competitive equilibrium consists of functions c ( t ) , k ( t ) , ( t ) , w ( t ) , r ( t ) that satisfy: 1 Household: Budget constraint and g ( c ) = r & (3) 2 Firms: r = f ( k ) & (4) w = f ( k ) & f ( k ) k (5) 3 Government: = G (6) 4 Market clearing: k = f ( k ) & k & c & G (7) L. Hendricks () Comparative Dynamics October 7, 2009 4 / 31 Phase Diagram The only change relative to the model without government: G shifts the k = locus down. k c B A L. Hendricks () Comparative Dynamics October 7, 2009 5 / 31 Permanent Tax Increase Consider a permanent, unannounced increase in G . In the phase diagram k = locus shifts down by G . k ss remains unchanged because the c = locus does not shift. Dynamics: c ss drops to the new saddle path, then moves along it. An interesting longrun result: full crowding out of consumption ( c ss = & G ) . L. Hendricks () Comparative Dynamics October 7, 2009 6 / 31 Temporary Tax Increase Consider a temporary , unannounced increase in G . G t = G & + G for t T , but G t = G & for t > T . To &nd the dynamics, we work backwards. Start from t = T : the economy looks like one without taxes (on saddle path). Consider < t < T : The phase diagram with taxes applies. But the economy is not on the saddle path (why not?). Key point: consumption cannot jump, except when new info arrives. We need to construct a path that follows the withtax phase diagram and connects with the no tax saddle path at t = T ....
View Full
Document
 '09
 LUTZHENDRICKS

Click to edit the document details