14.451 Lecture Notes Economic Growth

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George-Marios Angeletos 3.5.4 Government Spending (Figure 7 and 8) • We now introduce a government that collects taxes in order to finance some exogenous level of government spending. A. Lump Sum Taxation • Suppose the government finances its expenditure with lump-sum taxes. The household budget is c j t + k j t+1 = wt + rtk j t +(1− δ)k j t − Tt, implying Uc(c j t) Uc(c j t+1) = β[1 + rt+1 − δ] =β[1 + f 0 (kt+1) − δ] That is, taxes do not affect the savings choice. On the other hand, the government budget is Tt = gt, where gt denotes government spending. The resource constraint of the economy be- comes • We conclude ct + gt + kt+1 = f(kt)+(1− δ)kt ˙ct ct = θ[f 0 (kt) − δ − ρ], ˙kt = f(kt) − δkt − ct − gt • In the steady state, k ∗ is independent of g and c ∗ moves one-to-one with −g. Along the transition, a permanent increase in g both decreases c and slows down capital accumulation. See Figure 7. 80
14.451 Lecture Notes • Note that the effect of government spending financed with lump-sum taxes is isomorphic to a negative endowment shock. B. Distortionary Taxation • Suppose the government finances its expenditure with distortionary income taxation. The household budget is implying c j t + k j t+1 =(1− τ)(wt + rtk j t )+(1− δ)k j t , Uc(c j t) Uc(c j t+1) = β[1 + (1 − τ)rt+1 − δ] =β[1 + (1 − τ)f 0 (kt+1) − δ]. That is, taxes now distort the savings choice. On the other hand, the government budget is gt = τf(kt) and the resource constraint of the economy is again • We conclude ct + gt + kt+1 = f(kt)+(1− δ)kt. ˙ct ct = θ[(1 − τ)f 0 (kt) − δ − ρ], ˙kt =(1− τ)f(kt) − δkt − ct. Government spending is now isomorphic to a negative TFP change. • In the steady state, k ∗ is a decreasing function of g (equivalently, τ) and c ∗ decreases more than one-to-one with g. Along the transition, a permanent increase in g (and τ) drastically slows down capital accumulation. The immediate See Figure 7. 81
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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
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 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) ≡
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
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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
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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
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Page 119 and 120: Chapter 6 Endogenous Growth I: AK,
Page 121 and 122: 14.451 Lecture Notes so that consum
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Page 129 and 130: 14.451 Lecture Notes Combining the
Page 131 and 132: 14.451 Lecture Notes • Households
Page 133 and 134: 14.451 Lecture Notes Proposition 25
Page 135 and 136: Chapter 7 Endogenous Growth II: R&D
Page 137 and 138: 14.451 Lecture Notes More generally
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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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