14.451 Lecture Notes Economic Growth

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• Technology in intensive form: Let Then, by CRS where George-Marios Angeletos y = Y L By definition of f and the properties of F, Also, • Example: Cobb-Douglas technology In this case, and and k = K L . y = f(k) (2.2) f(k) ≡ F (k, 1). f(0) = 0, f 0 (k) > 0 >f 00 (k) lim k→0 f 0 (k) = ∞, lim f k→∞ 0 (k) =0 FK(K, L) = f 0 (k) FL(K, L) = f(k) − f 0 (k)k F (K, L) =K α L 1−α εK = α, εL =1− α f(k) =k α . 12
14.451 Lecture Notes 2.1.3 The Resource Constraint, and the Law of Motions for Cap- ital and Labor • Remember that there is a single good, which can be either consumed or invested. Of course, the sum of aggregate consumption and aggregate investment can not exceed aggregate output. That is, the social planner faces the following resource constraint: Equivalently, in per-capita terms: Ct + It ≤ Yt ct + it ≤ yt (2.3) (2.4) • Suppose that population growth is n ≥ 0 per period. The size of the labor force then evolves over time as follows: We normalize L0 =1. Lt =(1+n)Lt−1 =(1+n) t L0 (2.5) • Suppose that existing capital depreciates over time at a fixed rate δ ∈ [0, 1]. The capital stock in the beginning of next period is given by the non-depreciated part of current-period capital, plus contemporaneous investment. That is, the law of motion for capital is Equivalently, in per-capita terms: Kt+1 =(1− δ)Kt + It. (2.6) (1 + n)kt+1 =(1− δ)kt + it 13
Page 1 and 2: 14.451 Lecture Notes Economic Growt
Page 3 and 4: Contents Preface ix 1 Introduction
Page 5 and 6: 14.451 Lecture Notes 3.1.4 OptimalC
Page 7 and 8: 14.451 Lecture Notes 5.2 SomeExampl
Page 9 and 10: Preface This is the set of lecture
Page 11 and 12: Chapter 1 IntroductionandGrowthFact
Page 13 and 14: 14.451 Lecture Notes 1.2 The World
Page 15 and 16: 14.451 Lecture Notes • Figure 4 3
Page 17 and 18: 14.451 Lecture Notes 9. Openness: I
Page 19 and 20: Chapter 2 The Solow Growth Model (a
Page 21: 14.451 Lecture Notes • We say tha
Page 25 and 26: whereas consumption is given by 14.
Page 27 and 28: 14.451 Lecture Notes where the latt
Page 29 and 30: 14.451 Lecture Notes 2.2 Decentrali
Page 31 and 32: 14.451 Lecture Notes • Let K m t
Page 33 and 34: Equivalently, 14.451 Lecture Notes
Page 35 and 36: 14.451 Lecture Notes where Kt ≡ R
Page 37 and 38: 14.451 Lecture Notes Proof. Follows
Page 39 and 40: 14.451 Lecture Notes • Combining
Page 41 and 42: 14.451 Lecture Notes We would expec
Page 43 and 44: • Straightforward algebra gives W
Page 45 and 46: 14.451 Lecture Notes • Suppose th
Page 47 and 48: 2.6 Miscellaneous 14.451 Lecture No
Page 49 and 50: 14.451 Lecture Notes 2.6.3 Introduc
Page 51 and 52: Chapter 3 The Neoclassical Growth M
Page 53 and 54: 14.451 Lecture Notes ut+1 : There i
Page 55 and 56: 14.451 Lecture Notes • Combining
Page 57 and 58: Equivalently, taking (kt,kt+2) as g
Page 59 and 60: equivalently 14.451 Lecture Notes
Page 61 and 62: 14.451 Lecture Notes • Let B be t
Page 63 and 64: 14.451 Lecture Notes 3.2 Decentrali
Page 65 and 66: 14.451 Lecture Notes only the total
Page 67 and 68: 14.451 Lecture Notes • Finally, i
Page 69 and 70: 14.451 Lecture Notes The constraint
Page 71 and 72: 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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14.451 Lecture Notes Proof. The pol
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14.451 Lecture Notes • The ˙c =0
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14.451 Lecture Notes 3.5 Comparativ
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14.451 Lecture Notes • We conclud
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where At denotes TFP. Note that 14.
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14.451 Lecture Notes • Note that
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14.451 Lecture Notes 3.6.2 Impulse
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Chapter 4 Applications 4.1 Arrow-De
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14.451 Lecture Notes bles. We can t
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14.451 Lecture Notes • Then, the
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14.451 Lecture Notes • More gener
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14.451 Lecture Notes • Consider n
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14.451 Lecture Notes aggregate path
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14.451 Lecture Notes notes to be co
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Chapter 5 Overlapping Generations M
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14.451 Lecture Notes Life-cycle con
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Note that Recall that ∂m ∂R 14.
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where the scalar ζ>0 is given by 1
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14.451 Lecture Notes • Finally, n
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Chapter 6 Endogenous Growth I: AK,
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14.451 Lecture Notes so that consum
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14.451 Lecture Notes • Finally, t
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14.451 Lecture Notes • Combining
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14.451 Lecture Notes Like in the si
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14.451 Lecture Notes Combining the
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14.451 Lecture Notes • Households
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14.451 Lecture Notes Proposition 25
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Chapter 7 Endogenous Growth II: R&D
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14.451 Lecture Notes More generally
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14.451 Lecture Notes you can think
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14.451 Lecture Notes Free entry in
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14.451 Lecture Notes 7.1.8 Pareto A
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14.451 Lecture Notes 7.1.9 Introduc
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7.2.2 The Value of Innovation 14.45
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14.451 Lecture Notes It follows tha
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14.451 Lecture Notes • Compare no
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