lecture4 - Economics 202A Lecture Outline #4 (version 1.3)...

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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 Ramsey-Cass-Koopmans (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 lump-sum taxes t to the government each period, then we may write the private asset-accumulation 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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lecture4 - Economics 202A Lecture Outline #4 (version 1.3)...

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