lecture19 - Economics 202A Lecture Outline, November 29,...

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Economics 202A Lecture Outline, November 29, 2007 (Version 2.0) Maurice Obstfeld Issues in Monetary Policy In this lecture I survey several issues important in the design and imple- mentation of monetary policy in practice. Some of these are related to the government’s revenue needs, as discussed in the last lecture, but we also go beyond that question to consider other problems. Money and welfare: Milton Friedman’s \optimum quantity of money" A useful dynamic framework for thinking about monetary policy in a world of flexible prices was provided by Miguel Sidrauski and William Brock. 1 The representative consumer maximizes Z 1 t u [ c ( s ) ; m ( s )] e ( s t ) d s; where c is consumption and m M=P the stock of real balances held. Above, interest rate. We are motivating a demand for money by assuming that the individual derives a ±ow of utility from his/her holdings of real balances | implicitly, these help the person economize on transaction costs, provide liquidity, etc. Total real ²nancial assets a are the sum of real money m and real bonds b , which pay a real rate of interest r ( t ) at time t : a = m + b: 1 See Miguel Sidrauski, \Rational Choice and Patterns of growth in a Monetary Econ- omy," American Economic Review 57 (May 1967): 534-44; and William A. Brock, \Money and Growth: The Case of Long Run perfect Foresight," International Economic Review 15 (October 1974): 750-77. 1
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Let ( t ) be a transfer that the individual receives from the government each instant. 2 Then if we assume an endowment economy with output y ( t ), the _ a = y + rb + c ±m = y + ra + c ( r + ± ) m: Since this last constraint incorporates the portfolio constraint that a = m + b , we need no longer worry about it. Under an assumption that we have perfect foresight, so that actual ± = _ P=P equals expected in±ation, the Fisher equation tells us that the nominal interest rate is i = r + ±; so the last constraint becomes _ a = y + ra + c im: We can analyze the individual optimum using the Maximum Principle. If ² denotes the costate variable, the (current-value) Hamiltonian is H = u ( c; m ) + ² ( y + ra + im ) : In the maximization problem starting at time t , a ( t ) is predetermined at the level of the individual, who chooses optimal paths for c and m . The Pontryagin necessary conditions are @H @c = u c ² = 0 ; @H @m = u m ²i = 0 ; _ ² ³² = @H @a = ²r: 2 Beware: in the last lecture the same symbol denoted taxes, or negative transfers, so all signs preceding are reversed in this lecture compared to the last.
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lecture19 - Economics 202A Lecture Outline, November 29,...

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