14.451 Lecture Notes Economic Growth

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George-Marios Angeletos Proposition 24 Let A ≡ f 0 (1/η) and ω ≡ f(1/η)η − f 0 (1/η), and suppose β (1 + A − δ) > 1 >β θ (1 + A − δ) θ−1 . Then, the market economy exhibits a balanced growth path. Physical capital, knowledge, output, wages, and consumption all grow at a constant rate given by yt+1 yt = ct+1 ct =[β (1 + A − δ)] θ > 1. The wage rate is given by wt = ωkt, while the investment rate out of total resources is given by s = β θ (1 + A − δ) θ−1 . 6.4.2 Pareto Allocations and Policy Implications • Consider now the Pareto optimal allocations. The social planner recognizes that knowledge in the economy is proportional to physical capital and internalizes the effect of learning-by-doing. He thus understands that output is given by yt = F (kt,ht) =A ∗ kt where A ∗ ≡ f(1/η)η = A + ω represents the social return on capital. It is therefore as if the social planner had access to a linear technology like in the simple Ak model, and therefore the Euler condition for the social planner is given by u 0 (ct) u 0 (ct+1) = β (1 + A∗ − δ) . • Note that the social return to capital is higher than the private (market) return to capital: A ∗ >A= rt The difference is actually ω, the fraction of the social return on savings that is “wasted” as labor income. 122
14.451 Lecture Notes Proposition 25 Let A ∗ ≡ A+ω ≡ f(1/η)η and suppose β (1 + A ∗ − δ) > 1 >β θ (1 + A ∗ − δ) θ−1 . Then, the Pareto optimal plan exhibits a balanced growth path. Physical capital, knowledge, output, wages, and consumption all grow at a constant rate given by yt+1 yt = ct+1 ct =[β (1 + A ∗ − δ)] θ > 1. Note that A
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14.451 Lecture Notes Economic Growt
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Contents Preface ix 1 Introduction
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14.451 Lecture Notes 3.1.4 OptimalC
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14.451 Lecture Notes 5.2 SomeExampl
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Preface This is the set of lecture
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Chapter 1 IntroductionandGrowthFact
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14.451 Lecture Notes 1.2 The World
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14.451 Lecture Notes • Figure 4 3
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14.451 Lecture Notes 9. Openness: I
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Chapter 2 The Solow Growth Model (a
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14.451 Lecture Notes • We say tha
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14.451 Lecture Notes 2.1.3 The Reso
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whereas consumption is given by 14.
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14.451 Lecture Notes where the latt
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14.451 Lecture Notes 2.2 Decentrali
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14.451 Lecture Notes • Let K m t
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Equivalently, 14.451 Lecture Notes
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14.451 Lecture Notes where Kt ≡ R
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14.451 Lecture Notes Proof. Follows
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14.451 Lecture Notes • Combining
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14.451 Lecture Notes We would expec
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• Straightforward algebra gives W
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14.451 Lecture Notes • Suppose th
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2.6 Miscellaneous 14.451 Lecture No
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14.451 Lecture Notes 2.6.3 Introduc
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Chapter 3 The Neoclassical Growth M
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14.451 Lecture Notes ut+1 : There i
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14.451 Lecture Notes • Combining
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Equivalently, taking (kt,kt+2) as g
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equivalently 14.451 Lecture Notes
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14.451 Lecture Notes • Let B be t
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14.451 Lecture Notes 3.2 Decentrali
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14.451 Lecture Notes only the total
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14.451 Lecture Notes • Finally, i
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14.451 Lecture Notes The constraint
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14.451 Lecture Notes where f(k) ≡
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14.451 Lecture Notes Proposition 15
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14.451 Lecture Notes individual’s
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14.451 Lecture Notes 3.3 Steady Sta
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3.3.2 Transitional Dynamics 14.451
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