14.451 Lecture Notes Economic Growth

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George-Marios Angeletos for all t ≥ 0. Evaluating this at t =0, we infer µ = u 0 (c j 0). It follows that q(s t ) q0 = βt π(s t )u 0 (c j (s t )) u 0 (c j 0) = β t π(s t ) µ c j (s t ) c j 0 −1/θ That is, the price of a consumable in period t relative to period 0 equals the marginal rate of intertemporal substitution between 0 and t. • Solving qt/q0 = β t π(st ) £ cj (st )/c j¤−1/θ j t 0 for c (s ) gives c j (s t )=c j £ ¤ t t θ 0 β π(s ) · q(s t ) q0 ¸ −θ It follows that the present value of consumption is given by X X t s t q(s t )c j (s t )=q −θ 0 cj 0 ∞X £ ¤ t t θ t 1−θ β π(s ) q(s ) Substituting into the resource constraint, and solving for c0, we conclude where m0 ≡ P ∞ t=0 t=0 c j 0 = m0 · x j 0 1 £ ¤ . t β π(st θ ) [q(st 1−θ )/q0] Consumption is thus linear in effective wealth. m0 represent the MPC out of effective wealth as of period 0. 4.1.4 Intertemporal Consumption Smoothing, with No Uncertainty • Consider for a moment the case that there is no uncertainty, so that cj (st )=c j t and q(st )=qt for all st . 88 . .
14.451 Lecture Notes • Then, the riskless bond and the Arrow securities satisfy the following arbitrage condi- tion Alternatively, qt = q0 (1 + R0)(1 + R1)...(1 + Rt) . qt = q0 h 1+ e i−t R0,t where e R0,t represents the “average” interest rate between 0 and t. Next, note that m0 is decreasing (increasing) in qt if and only if θ>1 (θ 1 (θ 1 (θ
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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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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
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Page 63 and 64: 14.451 Lecture Notes 3.2 Decentrali
Page 65 and 66: 14.451 Lecture Notes only the total
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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
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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
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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
Page 117 and 118: 14.451 Lecture Notes • Finally, n
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 127 and 128: 14.451 Lecture Notes Like in the si
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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Page 147 and 148: 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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