tailieunhanh - Recursive macroeconomic theory, Thomas Sargent 2nd Ed - Chapter 1

Chapter 1 Overview . Warning This chapter provides a non-technical summary of some themes of this book. We debated whether to put this chapter first or last. A way to use this chapter is to read it twice, once before reading anything else in the book | Part I The imperialism of recursive methods Chapter 1 Overview . Warning This chapter provides a non-technical summary of some themes of this book. We debated whether to put this chapter first or last. A way to use this chapter is to read it twice once before reading anything else in the book then again after having mastered the techniques presented in the rest of the book. That second time this chapter will be easy and enjoyable reading and it will remind you of connections that transcend a variety of apparently disparate topics. But on first reading this chapter will be difficult partly because the discussion is mainly literary and therefore incomplete. Measure what you have learned by comparing your understandings after those first and second readings. Or just skip this chapter and read it after the others. . A common ancestor Clues in our mitochondrial DNA tell biologists that we humans share a common ancestor called Eve who lived 200 000 years ago. All of macroeconomics too seems to have descended from a common source Irving Fisher s and Milton Friedman s consumption Euler equation the cornerstone of the permanent income theory of consumption. Modern macroeconomics records the fruit and frustration of a long love-hate affair with the permanent income mechanism. As a way of summarizing some important themes in our book we briefly chronicle some of the high and low points of this long affair. - 1 - 2 Overview . The savings problem A consumer wants to maximize Eq u Ct t 0 where p G 0 1 u is a twice continuously differentiable increasing strictly concave utility function and E0 denotes a mathematical expectation conditioned on time 0 information. The consumer faces a sequence of budget constraints1 At i Rt i At yt ct for t 0 where At i A is the consumer s holdings of an asset at the beginning of period t 1 A is a lower bound on asset holdings yt is a random endowment sequence ct is consumption of a single good and Rt 1 is the gross rate of .

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