14.451 Lecture Notes Economic Growth

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• We conclude that George-Marios Angeletos Proposition 22 Consider the social planner’s problem with linear technology f(k) =Ak and CEIS preferences. Suppose (β,θ,A,δ) satisfy β (1 + A − δ) > 1 >β θ (1 + A − δ) θ−1 . Then, the economy exhibits a balanced growth path. Capital, output, and consumption all grow at a constant rate given by kt+1 kt = yt+1 yt = ct+1 ct =[β (1 + A − δ)] θ > 1. while the investment rate out of total resources is given by s = β θ (1 + A − δ) θ−1 . The growth rate is increasing in the net return to capital, increasing in the elasticity of intertemporal substitution, and decreasing in the discount rate. 6.1.2 The Frictionless Competitive Economy • Consider now how the social planner’s allocation is decentralized in a competitive market economy. • Suppose that the same technology that is available to the social planner is available to each single firm in the economy. Then, the equilibrium rental rate of capital and the equilibrium wage rate will be given simply r = A and w =0. • The arbitrage condition between bonds and capital will imply that the interest rate is R = r − δ = A − δ. 112
14.451 Lecture Notes • Finally, the Euler condition for the household will give ct+1 ct =[β (1 + R)] θ . • We conclude that the competitive market allocations coincide with the Pareto optimal plan. Note that this is true only because the private and the social return to capital coincide. 6.2 A Simple Model of Human Capital 6.2.1 Pareto Allocations • Total output in the economy is given by Yt = F (Kt,Ht) =F (Kt,htLt), where F is a neoclassical production function, Kt is aggregate capital in period t, ht is human capital per worker, and Ht = htLt is effective labor. • Note that, due to CRS, we can rewrite output per capita as or equivalently yt = F (kt,ht) =F µ kt , 1 ht ht [kt + ht] = kt + ht yt = F (kt,ht) =A (κt)[kt + ht], where κt = kt/ht = Kt/Ht is the ratio of physical to human capital, kt + ht measures total capital, and A (κ) ≡ represents the return to total capital. F (κ, 1) 1+κ 113 ≡ f(κ) 1+κ
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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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Page 83 and 84: 14.451 Lecture Notes • The ˙c =0
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Page 89 and 90: where At denotes TFP. Note that 14.
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Page 119 and 120: Chapter 6 Endogenous Growth I: AK,
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Page 135 and 136: Chapter 7 Endogenous Growth II: R&D
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