204A-slides04b

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

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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 ( T 1 t , T 2 t + 1 ) If T 2 t + 1 = (1 + r t + 1 ) T 1 t then C 1 t = C 2 t + 1 = and a t = 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....
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204A-slides04b - (4b)-P.1 Overlapping Generations...

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