14.451 Lecture Notes Economic Growth

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George-Marios Angeletos attempt to create a better product that is a close substitute for the product of producer j. Suppose further that, if successful, the innovation will be so “radical” that, not only it will increase productivity and reduce production costs, but it will also permit the outsider to totally displace the incumbent from the market. • Remark: We will later discuss in more detail what is the market structure and how competition between the incumbent and an entrant is resolved. We will then see that the size of the innovation and the type of competition (e.g., Bertrand versus Cournot) will determine what is the fraction of monopoly profits that the entrant can grasp. For the time being, we assume for simplicity that a successful innovator simply becomes the new monopolist in the market. • What is the value of the innovation for this outsider? Being an outsider, he has no share in the market of product j. If his R&D is successful, he expects to displace the incumbent and grasp the whole market of product j. That is, an innovation delivers a dividend equal to total market profits, (1 + γ)Atbπ, in each period of life. Assuming that the outsider also has a probability of death equal to n, the value of innovation for the outsider is given by V out t+1 = ∞X τ=t+1 µ τ 1 − n [(1 + γ)Atbπ] =(1+γ)bvAt 1+R • Now suppose that the incumbent also has the option to innovate is later periods of life. If he does so, he will learn the contemporaneous aggregate level of productivity and improve upon it by a factor 1+γ. The value of innovation in later periods of life is thus the same as in the first period of life: V in t+1 = ∞X τ=t+1 µ 1 − n 1+R 140 τ [γAtbπ] =γbvAt.
14.451 Lecture Notes • Compare now the value of an innovation between the incumbent and the outsider. Ob- viously, V out t+1 >V in t+1. That is because the incumbent values only the potential increase in productivity and profits, while the outsider values in addition the fact that he will be able to “steal the business” of the incumbent. This “business-stealing” effect implies that, ceteris paribus, that innovation will take place mostly in outsiders. • Remark: Things could be reversed if the incumbent has a strong cost advantage in R&D, which could be the case if the incumbent has some private information about the either the technology of the product or the demand of the market. • Using V out t+1/wt =(1+γ)bv, we infer that the optimal level of R&D for an outsider is given by z out t = zt = g ((1 + γ)bv) . Assuming that only outsiders engage in R&D, we conclude that the aggregate level of innovation is and the growth rate of the economy is yt+1 yt λt = q(zt) =λ ((1 + γ)bv) = At+1 At =1+γλ((1 + γ)bv) . • Finally, we can now reinterpret the probability of “death” as simply the probability of being displaced by a successful outside innovator. Under this interpretation, we have and bv solves bv = n = λ ((1 + γ)bv) bπ R + λ ((1 + γ)bv) 141
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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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14.451 Lecture Notes • We conclud
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where At denotes TFP. Note that 14.
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14.451 Lecture Notes • Note that
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14.451 Lecture Notes 3.6.2 Impulse
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Chapter 4 Applications 4.1 Arrow-De
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14.451 Lecture Notes bles. We can t
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