14.451 Lecture Notes Economic Growth

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George-Marios Angeletos where wt is the wage rate and pt,j is the price of intermediate good j. • Profits in the final good sector are zero, due to CRS, and the demands for each input aregivenbytheFOCs and for all j ∈ [0,Nt]. wt = ∂Yt ∂Lt pt,j = ∂Yt ∂Xt,j 7.1.3 Intermediate Good Sector =(1− α) Yt Lt µ 1−α Lt = αA Xt,j • The intermediate good sector is monopolistic. Firms understand that they face a downward sloping demand for their output. • The producer of intermediate good j solves subject to the demand curve max Πt,j = pt,jXt,j − κ(Xt,j) Xt,j = Lt µ αA pt,j 1 1−α , where κ(X) represents the cost of producing X in terms of final-good units. • We will let the cost function be linear: κ(X) =X. The implicit assumption behind this linear specification is that technology of producing intermediate goods is identical to the technology of producing final goods. Equivalently, 128
14.451 Lecture Notes you can think of intermediate good producers buying final goods and transforming them to intermediate inputs. What gives them the know-how for this transformation is precisely the blueprint they hold. • The FOCs give for the optimal price, and for the optimal supply, where pt,j = p ≡ 1 α Xt,j = xL > 1 x ≡ A 1 1−α α 2 1−α . • Note that the price is higher than the marginal cost (p =1/α > κ 0 (X) =1),the gap representing the mark-up that intermediate-good firms charge to their customers (the final good firms). Because there are no distortions in the economy other than monopolistic competition in the intermediate-good sector, the price that final-good firms are willing to pay represents the social product of that intermediate input and the cost that intermediate-good firms face represents the social cost of that intermediate input. Therefore, the mark-up 1/α gives the gap between the social product and the social cost of intermediate inputs. (Hint: The social planner would like to correct for this distortion. How?) • The resulting maximal profits are where Πt,j = πL π ≡ (p − 1)x = 1−α α 129 1 1−α x = A 1−α α α 2 1−α .
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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
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Chapter 3 The Neoclassical Growth M
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14.451 Lecture Notes ut+1 : There i
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14.451 Lecture Notes • Combining
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Equivalently, taking (kt,kt+2) as g
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equivalently 14.451 Lecture Notes
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14.451 Lecture Notes • Let B be t
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14.451 Lecture Notes 3.2 Decentrali
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14.451 Lecture Notes only the total
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14.451 Lecture Notes • Finally, i
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14.451 Lecture Notes The constraint
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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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Page 89 and 90: where At denotes TFP. Note that 14.
Page 91 and 92: 14.451 Lecture Notes • Note that
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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
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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
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Page 143 and 144: 14.451 Lecture Notes 7.1.8 Pareto A
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Page 147 and 148: 7.2.2 The Value of Innovation 14.45
Page 149 and 150: 14.451 Lecture Notes It follows tha
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