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Unformatted text preview: Economics 202A Lecture Outline #4 (version 1.3) Maurice Obstfeld Government Debt and Taxes As a result of the events of September 2008, government actions to un derwrite the U.S. &nancial system, coupled with a massive recession and a huge &scal stimulus plan, are sharply increasing the U.S. federal debt. Leav ing aside the fascinating questions raised by the &nancial crisis itself, how do macroeconomists think about government debt and its e/ects? Should government debt matter at all after all, leaving aside the possibility of bor rowing from foreigners, we owe any public debt to ourselves! Because one logical possibility is that government debt somehow a/ects capital accumu lation and growth, it is natural to consider the question in the context of our growth models. The leading breakthrough on the subject is Peter A. Diamonds ( Ameri can Economic Review 1965) adaptation of Paul A. Samuelsons overlapping generations model to incorporate capital, growth, and public debt. (Inci dentally, this paper was written when Diamond was on the faculty here in Berkeley.) We shall study the Diamond model soon, but before doing so we take a look at the debt question within the RamseyCassKoopmans (RCK) dynastic family setup. There the answers are less interesting (and perhaps less intuitive), yet they provide an essential benchmark case for understand ing the Diamond models very di/erent predictions. Within the RCK framework we now wish to distinguish between the pri vate sector and the government, two sectors that add up to be the total economy, of course. As we are now therefore dropping the idea that a gov ernment plannermakes allocation decisions, we need to observe (following basic welfare economics) that the RCK allocation can be decentralized if pri vate agents face the time path of real interest rates corresponding to that optimal allocation, r t = f ( k t ) and earn real wages per unit labor given by the marginal product of labor, w t = f ( k t ) & f ( k t ) k t : 1 [Following Diamond 1965, I assume that the depreciation rate & of capital is 0; otherwise the real interest rate would be r = f ( k ) & & .] A key step in showing this is to contemplate the government and private sectors&budget constraints separately. With respect to the private sector, household assets at the start of period t are the sum of capital K t and debt issued by the government, D t . If we redene these stocks in per capita terms as k t and d t , and also assume that the household pays per capita lumpsum taxes t to the government each period, then we may write the private assetaccumulation equation in terms of real per capital wealth a k + d as a t +1 = 1 1 + n [(1 + r t ) a t + w t & t & c t ] : Above, r t is the interest paid during period t on assets accumulated over t & 1 . It is now easy to see that if consumers invest at the real interest rate r t +1 between dates t and t +1 , then the relevant Euler equation of optimality would be u ( c...
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 Fall '07
 AKERLOF
 Economics

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