14.451 Lecture Notes Economic Growth

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George-Marios Angeletos • Remark: For a more careful discussion on the necessity and sufficiency of the FOCs and the transversality condition, check Stokey and Lucas. 3.2.2 Firms • There is an arbitrary number Mt of firms in period t, indexed by m ∈ [0,Mt]. Firms employ labor and rent capital in competitive labor and capital markets, have access to the same neoclassical technology, and produce a homogeneous good that they sell competitively to the households in the economy. • Let K m t and L m t denote the amount of capital and labor that firm m employs in period t. Then, the profits of that firm in period t are given by Π m t = F (Km t ,Lm t ) − rtK m t − wtL m t . • The firms seeks to maximize profits. The FOCs for an interior solution require FK(K m t ,L m t ) = rt. FL(K m t ,Lm t ) = wt. You can think of the first condition as the firm’s demand for labor and the second condition as the firm’s demand for capital. • As we showed before in the Solow model, under CRS, an interior solution to the firms’ problem to exist if and only if rt and wt imply the same K m t /L m t . This is the case if and only if there is some Xt ∈ (0, ∞) such that rt = f 0 (Xt) wt = f(Xt) − f 0 (Xt)Xt 60
14.451 Lecture Notes where f(k) ≡ F (k, 1). Provided so, firm profits are zero and the FOCs reduce to Π m t =0 K m t = XtL m t . That is, the FOCs pin down the capital labor ratio for each firm (Km t /Lmt ), but not the size of the firm (Lm t ). Moreover, because all firms have access to the same technology, they use exactly the same capital-labor ratio. (See our earlier analysis in the Solow model for more details.) 3.2.3 Market Clearing • There is no exogenous aggregate supply of riskless bonds. Therefore, the bond market clears if and only if 0= • The capital market clears if and only if Equivalently, Z Mt 0 Z Lt 0 b j tdj. K m Z 1 t dm = 0 Z Mt 0 K m t dm = kt k j t dj where kt = Kt ≡ R 1 0 kj t dj is the aggregate and per-head supply of capital in the economy. • The labor market, on the other hand, clears if and only if Z Mt 0 L m t dm = 61 Z Lt 0 l j t dj
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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
Page 19 and 20: Chapter 2 The Solow Growth Model (a
Page 21 and 22: 14.451 Lecture Notes • We say tha
Page 23 and 24: 14.451 Lecture Notes 2.1.3 The Reso
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: 14.451 Lecture Notes The constraint
Page 73 and 74: 14.451 Lecture Notes Proposition 15
Page 75 and 76: 14.451 Lecture Notes individual’s
Page 77 and 78: 14.451 Lecture Notes 3.3 Steady Sta
Page 79 and 80: 3.3.2 Transitional Dynamics 14.451
Page 81 and 82: 14.451 Lecture Notes Proof. The pol
Page 83 and 84: 14.451 Lecture Notes • The ˙c =0
Page 85 and 86: 14.451 Lecture Notes 3.5 Comparativ
Page 87 and 88: 14.451 Lecture Notes • We conclud
Page 89 and 90: where At denotes TFP. Note that 14.
Page 91 and 92: 14.451 Lecture Notes • Note that
Page 93 and 94: 14.451 Lecture Notes 3.6.2 Impulse
Page 95 and 96: Chapter 4 Applications 4.1 Arrow-De
Page 97 and 98: 14.451 Lecture Notes bles. We can t
Page 99 and 100: 14.451 Lecture Notes • Then, the
Page 101 and 102: 14.451 Lecture Notes • More gener
Page 103 and 104: 14.451 Lecture Notes • Consider n
Page 105 and 106: 14.451 Lecture Notes aggregate path
Page 107 and 108: 14.451 Lecture Notes notes to be co
Page 109 and 110: Chapter 5 Overlapping Generations M
Page 111 and 112: 14.451 Lecture Notes Life-cycle con
Page 113 and 114: Note that Recall that ∂m ∂R 14.
Page 115 and 116: where the scalar ζ>0 is given by 1
Page 117 and 118: 14.451 Lecture Notes • Finally, n
Page 119 and 120: 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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