{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

204A-slides04c - (4c-P.1 Overlapping Generations Dynamic...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
(4c)-P.1 Overlapping Generations & Dynamic Inefficiency Motivating example : Why inefficiency may be empirically relevant and deserves analysis. • Assume log-utility, Cobb-Douglas production, depreciation δ >0 r t + 1 = f '( k t + 1 ) = α k t + 1 α 1 δ • Steady state: k * = [ β /(1 + β ) (1 + n ) (1 + g ) (1 α )] 1 1 α => r * = α [ β /(1 + β ) (1 + n ) (1 + g ) (1 α )] 1 δ = (1 + n ) (1 + g ) α 1 α 1 + β β δ • Suppose most capital depreciates ( δ≈ 1 ), time preference near zero ( β≈ 1 ): => 1 + r * = (1 + n ) (1 + g ) 2 α 1 α => 1 + r * < (1 + n ) (1 + g ) α < 1 3 • Illustration in capital market diagram: Is the intersection between f 1 ( k ) and a ( w ( k ), r ) above or below (1 + n ) (1 + g ) ? Evidence • Long-run U.S. Data: GDP-growth ~ 3%/p.a (n~1%/p.a., g~2%/p.a.) Real return on T-bills r~1%; return on capital r~(5%-8%). Which return is relevant? • Abel-Mankiw-Summers-Zeckhauser: Dynamic efficiency applies if (Capital income) - (Gross investment) > 0 Evidence: difference is positive.
Image of page 1

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

View Full Document Right Arrow Icon
(4c)-P.2 Why does Pareto-efficiency impose a lower bound on r? • Pareto efficiency : Maximize utility of some cohort s.t. constraint that other cohorts’ utility is not reduced => Lagrangian with cohort utility + sum of other cohort utilities * multipliers => Equivalent to maximizing a weighted average of utilities • Social planning problem : Maximize welfare function s.t. resource constraint. Suppose: - Period t=1 old are endowed with K 1 . - Period t=T young all die at the end of period T. (Finite endpoint to start.) - Planner discounts future generations’ per-capita utility with factor γ (unit weight on t=0) - Abstract from productivity growth (to avoid clutter). • Maximize welfare function: W = L 0 β u ( C 21 ) + γ t L t t = 1 T 1 [ u ( C 1 t ) + β u ( C 2 t + 1 )] + γ T L T u ( C 1 T ) , s.t. L t C 1 t + L t 1 C 2 t + K t + 1 = F ( K t , L t ) + (1 δ ) K t , or equivalently C 1 t + 1 1 + n C 2 t + (1 + n ) k t + 1 = f ( k t ) + k t • Consider Lagrangian with multipliers λ t and take FOC: a. consumption of workers: γ t L t u '( C 1 t ) L t λ t = 0 => λ t = γ t u '( C 1 t ) b. consumption of retirees: γ t 1 L t 1 β u '( C 2 t ) L t 1 λ t = 0 => λ t = γ t 1 β u '( C 2 t ) c. capital accumulation: λ t ( F K ( K
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern