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204A-slides04a - (4a-P.1 Part 4 Overlapping Generations...

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(4a)-P.1 Part 4: Overlapping Generations Models • Basic Version: Each birth-cohort lives for two periods, young and old age. - Individuals are identical except for their date of birth => Each generation has a representative agent. - Young individuals earn labor income, consume, and save. Savings are invested in capital and earn a return. - Old individuals consume their investment earnings (extension: also work) . => Key issue: How much does the young generation save ? • Comparison to representative agent models: - Technical shift: trade easier individual problem for aggregation issues. - New issues: Intergenerational redistribution, dynamic inefficiency… • Flexible framework: OG can be extended to many periods, more choices, more heterogeneity. • Agenda here: 1. Basic model – dynamics of the capital stock. 2. Government policy: Debt, taxation with income effects, social security. [Real spending withdraws resources as in representative agent models—nothing new, hence ignored.] 3. Altruism and bequests: The dynastic model as limiting case. 4. Dynamic inefficiency: excessive savings cannot be ruled out. Phenomena in inefficient economies: Bubbles, Ponzi schemes, fiat money as store of value.
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(4a)-P.2 A. The Basic Model (see Romer ch.2B) Preferences : Individuals born in period t maximize: u ( C 1 t ) + β u ( C 2 t + 1 ) - Preferences u: increasing, declining marginal utility. - Romer’s notation: Time preference ρ , discount factor β =1/(1+ ρ ), power utility. Constraints : Labor income when young & working = W t . [ Exogenous labor supply.] - Savings = Assets a t . Invested at an interest rate r t+1. [Exogenous to the individual.] Intuition: If one period ~ generation ~ 25-30 years, then 1+r~300%. - Budget equation for workers: C 1 t + a t = W t - Budget equation for retirees: C 2 t + 1 = (1 + r t + 1 ) a t => Intertemporal budget constraint: W t = C 1 t + 1 1 + r t + 1 C 2 t + 1 Optimality condition : u '( C 1 t ) = β u '( C 2
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