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 Document
Unformatted text preview: (4b)P.1 Overlapping Generations & Fiscal Policy • Focus on Intergenerational Redistribution and other issues excluded in representative agent models. • Assume lumpsum taxes: T 1t = percapita net taxes on the young T 2t+1 = percapita net taxes on the old. If negative, interpret as transfer TR t+1 = T 2t+1 . Government debt = D t+1 (aggregate, at end of period t). Government spending = G t • Individual budget constraints with taxes: C 1 t + a t = W t − T 1 t and C 2 t + 1 = (1 + r t + 1 ) ⋅ a t − T 2 t + 1 => IBC: C 1 t + 1 1 + r t + 1 ⋅ C 2 t + 1 = W t − T 1 t − 1 1 + r t + 1 ⋅ T 2 t + 1 • Consumption depends only on the present value of net taxes: C 1 t = C 1 ( W t − T 1 t − T 2 t + 1 1 + r t + 1 , r t + 1 ) Illustration: Indifference curve diagram. Endowment point ( W t − T 1 t , − T 2 t + 1 ) Consider a marginal change in taxes by ( Δ T 1 t , Δ T 2 t + 1 ) If Δ T 2 t + 1 = − (1 + r t + 1 ) ⋅Δ T 1 t then Δ C 1 t = Δ C 2 t + 1 = and Δ a t = −Δ T 1 t => No consumption effect; tax cut is saved. • Neutrality result: “Timing” of taxes over the life cycle does not influence consumption. (4b)P.2 • Notes about individual behavior from the indifference curve diagram: 1. Consumption is  increasing in current income W t − T 1 t increasing in future net transfers ( − T 2 t + 1 ) influenced by interest rates though two effects:  the substitution effect;  the value of future taxes/transfers: if ( − T 2 t + 1 ) >0, high r reduces ( − T 2 t + 1 ) 1 + r t + 1 2. Individual savings do depend on the timing of taxes: a t = W t − T 1 t − C 1 t = a ( W t − 1 − T 1 t − 1 , T 2 t , r t ) increasing in current income W t − T 1 t decreasing in future net transfers ( − T 2 t + 1 ) , which means increasing in T 2 t + 1 influenced by interest rates like consumption, but in the opposite direction. • Note about derivatives for reference below:  From C 1 t = C 1 ( W t − T 1 t − T 2 t + 1 1 + r t + 1 , r t + 1 ) => ∂ C 1 t ∂ T 2 t + 1 = − 1 1 + r t + 1 ∂ C 1 ∂ ( W − T 1 ) < . Define ∂ C 1 ∂ TR = − ∂ C 1 t ∂ T 2 t + 1 > .  Budget equations imply: a W ≡ ∂ a ∂ ( W − T 1 ) = 1 − ∂ C 1 ∂ ( W − T 1 ) and ∂ a ∂ T 2 t + 1 = − ∂ C 1 ∂ T 2 , so ∂ a ∂ T 2 t + 1 = − ∂ C 1 t ∂ T 2 t + 1 = − 1 1 + r t + 1 ∂ C 1 ∂ ( W − T 1 ) = − 1 1 + r t + 1 (1 − a W ) . (4b)P.3 The Government Budget • Budget equation: D t + 1 = (1 + r t ) ⋅ D t + G t − [ L t ⋅ T 1 t + L t − 1 ⋅ T 2 t ] New element as compared to the representative agent model: Intergenerational redistribution = Transfers from (or taxes on) retirees financed by taxes on (or transfers from) workers in same or other period • Capital market equilibrium condition:  Savings by the young are invested in capital and government bonds: K t + 1 + D t + 1 = L t ⋅ a ( W t − T 1 t , T 2 t + 1 , r t + 1 ) In a growing economy, balanced growth requires restrictions on policy.  In a growing economy, balanced growth requires restrictions on policy....
View
Full Document
 Fall '08
 Staff
 Fiscal Policy, Public Finance, ΔD, WT

Click to edit the document details