14.451 Lecture Notes Economic Growth

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George-Marios Angeletos • Following the analysis of the previous section, consumption for individual j is given by c j t = mt · x j t. Note that individuals share the same MPC out of effective wealth because they have identical θ. • Adding up across households, we infer that aggregate consumption is given by where mt ≡ ct = mt · xt xt ≡ (1 + Rt)at + ht, ∞X qτ [wτlτ − Tτ], ht ≡ τ=t qt 1 P∞ τ=t βθ(τ−t) . (qτ/qt) 1−θ • Next, recall that individual consumption growth satisfies qt q0 = βt u 0 (c j t) u 0 (c j 0) = βt Ã c j t c j ! −1/θ 0 for every j. But if all agents share the same consumption growth rate, this should be the aggregate one. Therefore, equilibrium prices and aggregate consumption growth satisfy Equivalently, qt q0 qt q0 = β t µ −1/θ ct c0 = βt u 0 (ct) u 0 (c0) . 92 ,
14.451 Lecture Notes • Consider now an economy that has a single consumer, who is endowed with wealth xt and has preferences U(c) = c1−1/θ 1 − 1/θ The Euler condition for this consumer will be qt q0 = βt u 0 (ct) u 0 (c0) . Moreover, this consumer will find it optimal to choose consumption ct = mt · xt. But these are exactly the aggregative conditions we found in the economy with many agents. • That is, the two economies share exactly the same equilibrium prices and allocations. It is in this sense that we can think of the single agent of the second economy as the “representative” agent of the first multi-agent economy. • Note that here we got a stronger result than just the existence of a representative agent. Not only a representative agent existed, but he also had exactly the same preferences as each of the agents of the economy. This was true only because agents had identical preference to start with and their preferences were homothetic. If either condition fails, the preferences of the representative agent will be “weighted average” of the population preferences, with the weights depending on the wealth distribution. • Finally, note that these aggregation results extend easily to the case of uncertainty as long as markets are complete. 93
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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
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) ≡
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
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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
Page 123 and 124: 14.451 Lecture Notes • Finally, t
Page 125 and 126: 14.451 Lecture Notes • Combining
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
Page 139 and 140: 14.451 Lecture Notes you can think
Page 141 and 142: 14.451 Lecture Notes Free entry in
Page 143 and 144: 14.451 Lecture Notes 7.1.8 Pareto A
Page 145 and 146: 14.451 Lecture Notes 7.1.9 Introduc
Page 147 and 148: 7.2.2 The Value of Innovation 14.45
Page 149 and 150: 14.451 Lecture Notes It follows tha
Page 151 and 152: 14.451 Lecture Notes • Compare no
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