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1、Chapter 1 Overview1.1.WarningThis chapter provides a nontechnical summary of some themes of this book. Wedebated 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 pr
2、esented 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. Buton first reading, this chapter will be difficult, partly because the discussion is mainly literary and
3、 therefore incomplete. Measure what you have learned bycomparing your understandings after those first and second readings. Or just skip this chapter and read it after the others.1.2.A common ancestorClues in our mitochondrial DNA tell biologists that we humans share a com- mon ancestor called Eve w
4、ho lived 200,000 years ago. All of macroeconomics too seems to have descended from a common source, Irving Fisher s and Mil- ton Friedman s consumption Euler equation, the cornerstone of the permanent income theory of consumption. Modern macroeconomics records the fruit andfrustration of a long love
5、-hate affair with the permanent income mechanism. Asa way of summarizing some important themes in our book, we briefly chroniclesome of the high and low points of this long affair. 3 4Overview1.3.The savings problemA consumer wants to maximizeE0?t=0tu(ct)(1. 3. 1)where (0,1), u is a twice continuous
6、ly differentiable, increasing, strictly con- cave utility function, and E0denotes a mathematical expectation conditioned on time 0 information. The consumer faces a sequence of budget constraints1At+1= Rt+1(At+ yt ct)(1. 3. 2)for t 0, where At+1 A is the consumer s holdings of an asset at the beginn
7、ing of period t+1, A is a lower bound on asset holdings, ytis a random endowment sequence, ctis consumption of a single good, and Rt+1is the gross rate of return on the asset between t and t + 1. In the general version of the problem, both Rt+1and ytcan be random, though special cases of the problem
8、 restrict Rt+1further. A first-order necessary condition for this problem isEtRt+1u?(ct+1) u?(ct) 1,= if At+1 A.(1. 3. 3)This Euler inequality recurs as either the cornerstone or the straw man in many theories contained in this book.Different modeling choices put (1. 3. 3) to work in different ways.
9、 One can restrict u, the return process Rt+1, the lower bound on assets A, the in- come process yt, and the consumption process ctin various ways. By making alternative choices about restrictions to impose on subsets of these objects, macroeconomists have constructed theories about consumption, asse
10、t prices, and the distribution of wealth. Alternative versions of equation (1. 3. 3) also underlie Chamley s (1986) and Judd s (1985b) striking results about eventually not taxing capital.1We use a different notation in chapter 17: Athere conforms to btin chapter 17.The savings problem51.3.1. Linear
11、 quadratic permanent income theoryTo obtain a version of the permanent income theory of Friedman (1955) and Hall (1978), set Rt+1= R, impose R = 1, assume the quadratic utility function u(ct) = (ct )2, and allow consumption ctto be negative. We also allow yt to be an arbitrary stationary process, an
12、d dispense with the lower bound A. The Euler inequality (1. 3. 3) then implies that consumption is a martingale:Etct+1= ct.(1. 3. 4)Subject to a boundary condition that2E0? t=0tA2t0 (which occurs whenever taxes are necessary), the objective in the primal version of the Ramsey problem disagrees with
13、the preferences of the household over (c,?) allocations.This conflict is the source of a time-inconsistency problem in the Ramsey problem with capital.The savings problem13implication of the two Euler equations (1. 3. 8) and (1. 3. 12). If the government expenditure sequence converges and if a stead
14、y state exists in which ct,?t,kt,kt all converge, then it must be true that (1. 3. 9) holds in addition to (1. 3. 11). But both of these conditions can prevail only if k= 0. Thus, the steady-state properties of two versions of our consumption Euler equation (1. 3. 3) underlie Chamley and Judd s rema
15、rkable result that asymptotically it is optimal not to tax capital. In stochastic versions of dynamic optimal taxation problems, we shall glean additional insights from (1. 3. 3) as embedded in the asset-pricing equations (1. 3. 16) and (1. 3. 18). In optimal taxation problems, the government has th
16、eability to manipulate asset prices through its influence on the equilibrium con- sumption allocation that contributes to the stochastic discount factor mt+1,tdefined in equation (1. 3. 16) below. The Ramsey government seeks a way wisely to use its power to revalue its existing debt by altering state-history prices. To appreciate what the Ramsey government is doing, it helps to know the theory of asset pricing.1.3.8. Asset pricingThe dynamic asset pricing theor
