204A-slides04b

# 204A-slides04b - (4b-P.1 Overlapping Generations& Fiscal...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (4b)-P.1 Overlapping Generations & Fiscal Policy • Focus on Intergenerational Redistribution and other issues excluded in representative agent models. • Assume lump-sum taxes: T 1t = per-capita net taxes on the young T 2t+1 = per-capita 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

## This note was uploaded on 12/26/2011 for the course ECON 240a taught by Professor Staff during the Fall '08 term at UCSB.

### Page1 / 15

204A-slides04b - (4b-P.1 Overlapping Generations& Fiscal...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online