Modeling Monetary Economies Third Edition This textbook is designed to be used in an advanced undergraduate course The approach of this text is to teach monetary economics using the classical paradigm of rational agents in a market setting Too often, monetary economics has been taught as a collection of facts about existing institutions for students to memorize By teaching from first principles instead, the authors aim to instruct students not only in the monetary policies and institutions that exist today in the United States and Canada but also in what policies and institutions may or should exist tomorrow and elsewhere The text builds on a simple clear monetary model and applies this framework consistently to a wide variety of monetary questions The authors have added in this third edition new material on money as a means of replacing imperfect social record keeping, the role of currency in banking panics, and a description of the policies implemented to deal with the banking crisis that began in 2007 Bruce Champ is Senior Research Economist at the Federal Reserve Bank of Cleveland Previously, he taught at Virginia Polytechnic Institute, the Universities of Iowa and Western Ontario, and Fordham University Dr Champ’s research interests focus on monetary economics, and his articles have appeared in the American Economic Review; Journal of Monetary Economics; Canadian Journal of Economics; and Journal of Money, Credit, and Banking, among other leading academic publications He co-authored the first and second editions of Modeling Monetary Economies with the late Scott Freeman Scott Freeman (1954–2004) was a Professor of Economics at the University of Texas, Austin He taught previously at Boston College and the University of California, Santa Barbara Professor Freeman died in 2004 after struggling with amyotrophic lateral sclerosis for several years Professor Freeman specialized in monetary theory, and his articles appeared in the Journal of Political Economy; American Economic Review; Journal of Monetary Economics; and Journal of Money, Credit, and Banking, among other eminent academic journals Joseph Haslag is Professor and Kenneth Lay Chair in Economics at the University of Missouri, Columbia He previously worked as an economist at the Federal Reserve Bank of Dallas He also taught at Southern Methodist University and Michigan State University Professor Haslag has focused on monetary economics, and his articles have appeared in the Review of Economics and Statistics, Journal of Monetary Economics, Review of Economic Dynamics, and International Economic Review, among other leading academic journals Modeling Monetary Economies Third Edition BRUCE CHAMP Federal Reserve Bank of Cleveland SCOTT FREEMAN JOSEPH HASLAG University of Missouri, Columbia cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S˜ao Paulo, Delhi, Tokyo, Mexico City Cambridge University Press 32 Avenue of the Americas, New York, NY 10013-2473, USA www.cambridge.org Information on this title: www.cambridge.org/9780521177009 First and Second editions © Bruce Champ and Scott Freeman 1994, 2001 Third edition © Bruce Champ, the Estate of Scott Freeman, and Joseph Haslag 2011 This publication is in copyright Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published 1994 Second edition published 2001 Third edition published 2011 Printed in the United States of America A catalog record for this publication is available from the British Library Library of Congress Cataloging in Publication data Champ, Bruce Modeling monetary economies / Bruce Champ, Scott Freeman, Joseph Haslag – 3rd ed p cm Includes bibliographical references and index ISBN 978-1-107-00349-1 (hardback) – ISBN 978-0-521-17700-9 (paperback) Money – Mathematical models I Freeman, Scott II Haslag, Joseph H III Title HG221.C447 2011 332.401 5118–dc22 2010048090 ISBN 978-1-107-00349-1 Hardback ISBN 978-0-521-17700-9 Paperback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet Web sites referred to in this publication and does not guarantee that any content on such Web sites is, or will remain, accurate or appropriate We dedicate this edition to Scott Freeman, a good friend and a brilliant economist Unfortunately, Scott lost his long battle with ALS He is missed by everyone who had the pleasure of knowing him, and especially by those of us who had the opportunity to work with him We are writing this edition to honor Scott’s contributions to the field of economics and to continue his legacy Contents Preface page xv Part I Money A Simple Model of Money: Building a Model of Money The Environment Preferences Future Generations The Initial Old The Economic Problem Feasible Allocations The Golden Rule Allocation The Initial Old Decentralized Solutions Equilibrium without Money Equilibrium with Money Finding the Demand of Fiat Money An Individual’s Budget Finding Fiat Money’s Rate of Return The Quantity Theory of Money The Neutrality of the Fiat Money Stock The Role of Fiat Money Is This Monetary Equilibrium the Golden Rule? A Monetary Equilibrium with a Growing Economy The Feasible Set with a Growing Population The Budget Set with a Growing Population A Record-Keeping Device Summary vii 6 10 10 10 11 13 13 14 15 15 16 18 21 21 22 22 23 24 25 26 28 viii Contents Exercises Appendix: Using Calculus An Example Appendix Exercise Barter and Commodity Money A Model of Barter Direct Barter Monetary Exchange What Should Be Used as Money? Exchange Costs A Model of Commodity Money The Consumption of Gold The Inefficiency of Commodity Money Summary Exercises Inflation A Growing Supply of Fiat Money The Budget Set with Monetary Growth The Inefficiency of Inflation The Golden Rule Monetary Policy in a Growing Economy A Government Policy to Fix the Price Level Financing Government Purchases Is Inflation an Efficient Tax? A Nondistorting Tax The Limits to Seigniorage Summary Exercises Appendix: Equilibrium Consumption Is at the Edge of the Feasible Set International Monetary Systems A Model of International Exchange Foreign Currency Controls Fixed Exchange Rates The Costs of Foreign Currency Controls The Indeterminacy of the Exchange Rate Exchange Rate Fluctuations International Currency Traders Fixing the Exchange Rate Cooperative Stabilization Unilateral Defense of the Exchange Rate Speculative Attacks on Currencies Inflationary Incentives 28 30 32 33 34 34 36 37 38 39 40 42 43 44 45 47 47 49 51 54 56 58 60 61 64 68 68 71 73 73 75 77 78 78 80 82 84 84 86 91 92 References 325 Miron, J A 1986 “Financial Panics, the Seasonality of the Nominal Interest Rate, and the Founding of the Fed.” American Economic Review 76(March): 125–40 Muth, J F 1961 “Rational Expectations and the Theory of Price Movements.” Econometrica 29(July): 315–35 Persson, R., and L E O Svensson 1989 “Why a Stubborn Conservative Would Run a Deficit: Policy with Time Inconsistent Preferences.” Quarterly Journal of Economics 104(May): 325–45 Porter, R., and R Judson 1996 “The Location of US Currency: How Much Is Abroad?” Federal Reserve Bulletin 82(10): 245–74 Prescott, E C 1987 “ A Multiple Means-of-Payment Model.” In New Approaches to Monetary Economics, W Barnett and K Singleton, eds Cambridge, MA: Cambridge University Press *Radford, R A 1945 “The Economics Organization of a P.O.W Camp.” Economica 12(November): 189–201 *Rolnick, A J., and W E Weber 1989 “A Case for Fixing Exchange Rates.” Federal Reserve Bank of Minneapolis 1989 Annual Report: 3–14 *Rolnick, A J., B D Smith, and W E Weber 1998 “Lessons from a Laissez-Faire Payments System: The Suffolk Banking System (1825–58).” Federal Reserve Bank of St Louis Review 80(May/June): 105–16 Romer, D 1985 “Financial Intermediation, Reserve Requirements, and Inside Money.” Journal of Monetary Economics 16(September): 175–94 Salant, S W., and D W Henderson 1978 “Market Anticipation of Government Policy and the Price of Gold.” Journal of Political Economy 86(August): 627–48 Samuelson, P A 1958 “An Exact Consumption-Loan Model of Interest With and Without the Social Contrivance of Money.” Journal of Political Economy 66(December): 467–82 *Sargent, T J 1986a “The Ends of Four Big Inflations.” In Rational Expectations and Inflation New York: Harper & Row: 40–109 *Sargent, T J 1986b “Interpreting the Reagan Deficits.” Federal Reserve Bank of San Francisco Quarterly Review (Fall): 5–12 *Sargent, T J., and N Wallace 1981 “Some Unpleasant Monetarist Arithmetic.” Federal Reserve Bank of Minneapolis Quarterly Review (Fall): 1–17 Sargent, T J., and N Wallace 1982 “The Real-Bills Doctrine vs The Quantity Theory: A Reconciliation.” Journal of Political Economy 90(December): 1212–36 Sargent, T J., and N Wallace 1983 “A Model of Commodity Money.” Journal of Monetary Economics 12(July): 163–87 Schreft, S 1992 “Transactions Costs and the Use of Cash and Credit.” Economic Theory 2(April): 283–96 Sims, C 1972 “Money, Income and Causality.” American Economic Review 62(September): 540–52 Sims, C 1980 “Comparison of Interwar and Postwar Cycles: Monetarism Reconsidered.” American Economic Review 70(May): 250–75 *Smith, B D 1985 “American Colonial Monetary Regimes: The Failure of the Quantity Theory and Some Evidence in Favour of an Alternate View.” Canadian Journal of Economics 18(3)(August): 531–64 *Smith, B D 1988 “The Relationship Between Money and Prices: Some Historical Evidence Reconsidered.” Federal Reserve Bank of Minneapolis Quarterly Review 12(Summer): 18–32 Smith, B D., 1991 “Interest on Reserves and Sunspot Equilibria: Friedman’s Proposal Reconsidered.” Review of Economic Studies 58(January): 93–105 Sprague, O M W 1910 A History of Crises Under the National Banking System, Washington, DC: U.S Government Printing Office 326 References Tallman, E W., and J R Moen 1990 “The Panic of 1907: How Trusts Tipped the Scales.” Federal Reserve Bank of Atlanta Economic Review 75(May/June): 2–13 Tobin, J 1965 “Money and Economic Growth.” Econometrica 33(October): 671–84 Tobin, J 1970 “Money and Income: Post Hoc Ergo Propter Hoc?” Quarterly Journal of Economics 84(May): 301–17 Tolley, G 1957 “Providing for the Growth of the Money Supply.” Journal of Political Economy 65(January): 447–84 Townsend, R M 1979 “Optimal Contracts and Competitive Markets with Costly State Verification.” Journal of Economic Theory 21(October): 265–93 Townsend, R M 1980 “Models of Money with Spatially Separated Agents.” In Models of Monetary Economies, J Kareken and N Wallace, eds., 265–303 Minneapolis: Federal Reserve Bank of Minneapolis *Wallace, N 1979 “Why Markets in Foreign Exchange Are Different from Other Markets.” Federal Reserve Bank of Minneapolis Quarterly Review 3(Fall): 1–7 *Wallace, N 1980 “The Overlapping Generations Model of Fiat Money.” In Models of Monetary Economies, J Kareken and N Wallace, eds., 49–82 Minneapolis: Federal Reserve Bank of Minneapolis Wallace, N 1981 “A Modigliani-Miller Theorem for Open Market Operations.” American Economic Review 71(June): 267–74 Wallace, N 1983 “A Legal Restrictions Theory of the Demand for ‘Money’ and the Role of Monetary Policy.” Federal Reserve Bank of Minneapolis Quarterly Review 7(Winter): 1–7 *Wallace, N 1984 “Some of the Choice for Monetary Policy.” Federal Reserve Bank of Minneapolis Quarterly Review 8(Winter): 15–24 White, L J 1991 The S&L Debacle: Public Policy Lessons for Bank and Thrift Regulation New York: Oxford University Press *Williamson, S D 1987 “Recent Developments in Modeling Financial Intermediation.” Federal Reserve Bank of Minneapolis Quarterly Review 11(Summer): 19–28 Williamson, S D 1989 “Restrictions on Financial Intermediaries and Implications for Aggregate Fluctuations: Canada and United States, 1870–1913.” In NBER Macroeconomics Annual 1989, O Blanchard and S Fisher, eds Cambridge, MA: Cambridge University Press Young, J P 1925 European Currency and Finance, vols and 2, Commission of Gold and Silver Inquiry, United States Senate, Serial Washington, DC: U.S Government Printing Office Author Index Abel, Andrew, 54n Aiyagari, S Rao, 62n, 297n Alesina, Alberto, 313, 314 Auernheimer, Leonardo, 291, 292n, 315n Avery, Robert B., 62n Bacchetta, Phillipe, 292n Bade, Robin, 313 Bailey, Martin J, 54n, 66n Barro, Robert J, 63n 64n, 260n, 296, 297, 310n Bernanke, Ben, 194 Bhattacharya, Joydeep, 144n, 233n Boyd, John H., 144n Bryant, John, 211n, 248n Cagan, Phillip, 167n, 168n Calvo, Guillermo, 310n, 315n Caminal, Ramon, 292n Canzoneri, Matthew, 95n Carr, Jack, 219n Cass, David, 115n Champ, Bruce, 206n, 226n, 238n, 306n Cooley, Thomas, 174n Darby, Michael R., 257n Diamond, Douglas W., 144n, 211n, 213n Diamond, Peter A., 115n, 131n, 285n Dybvig, Phillip H., 144n, 211n, 213n Elliehausen, G G., 62n Fama, Eugene, 148n Feinman, Joshua, 181n Fischer, Stanley, 63, 95n Fisher, Irving, 97, 123 Freeman, Scott, 35n, 47n, 123n, 137n, 148n, 168n, 172n, 181n, 195n, 206n, 211n, 292n, 296n, 306n Friedman, Milton, 43n, 56n, 167n, 181n, 216n, 217n, 237n, 241 Gordon, David B., 310n Greenwood, Jeremy, 144n Grilli, Vittorio, 313 Hammond, Bray, 194 Haslag, Joseph, 181n, 233n, 237n, 292n Haubrich, Joe, 240n Henderson, Dale, 91 Herodotus, 40n Huffman, Gregory W., 168n, 172n Jevons, W S., 14 Johnson, J F., 203n Jones, Larry, 293n Jovanovic, Boyan, 144n Judson, Ruth, 86n Kahn, Charles, M, 198n Kareken, John, H., 78n, 219n Kennickell, A B., 62n King, Robert, 82, 167n, 168n Kiyotaki, Nobuhiro, 35n Krugman, Paul, 91, 91n Kydland, Finn, 302n Lacker, Jeffrey, 168n Laffer, Arthur, 68n Laidler, David, 203n Leamer, Edward, 174n LeRoy, Stephen, 174n Litterman, Robert, 167n Loewy, Michael, 213n Lucas, Robert E Jr., 98, 100, 100n, 101n, 103n, 104, 109, 110, 309n, 318n Maeda, Yasuo, 35n Manuelli, Rodolpho, 293n Martin, Antoine, 233n, 237n Masciandaro, Donato, 313 Metzler, Lloyd, 181n Miller, Preston J., 257n Miron, Jeffrey A., 206n, 241 327 328 Author Index Moen, John R., 204n Muth, John, 100 Nixon, Richard, 80, 94n Parkin, Michael, 313 Persson, Torsten, 263n Phillips, A W., 97, 97n Plosser, Charles, 167n, 168n Porter, Richard, 86n Prescott, Edward, 144n, 168n, 302n Quigley, Neil, 219n Radford, R A., 39n Ricardo, David, 287 Roberds, William, 198n Rogers, Carol Ann, 95n Rolnick, Arthur J., 84n, 202n Romer, David, 148n Rotemberg, Julio, 91n Salant, Stephen, 91 Samuelson, Paul, Sargent, Thomas J., 65, 168n, 254n, 257n, 261n, 266n, 312n Schreft, Stacey L., 168n Schwartz, Anna J., 167n, 217n, 241 Sims, Christopher, 167n Smith, Bruce, 180n, 181n, 187n, 202n, 206n, 226n, 227n, 232n, 238n Spindt, P A., 62n Sprague, O M W., 216n Stokey, Nancy, 318n Summers, Lawrence, 313 Svensson, Lars E O., 263n Tabellini, Guido, 195n, 313 Tallman, Ellis W., 204n Tobin, James, 119, 167n Tolley, George, 181n Townsend, Robert, 144n, 226n Wallace, Neil, 52n, 78n, 82, 100n, 115n, 127n, 168n, 185n, 248n, 254n, 257n, 261n, 266n Weber, Warren E., 82, 84n, 202n, 206n Weiss, Laurence, 167n White, Lawrence, 222 Williamson, Stephen D., 144n, 206n, 226n, 238n, 240n Wright, Randall, 35n Yaari, Menahem, 115n Young, J P., 66, 67, 312 Subject Index administered rate, 163 altruism, 299 arbitrage, 136 defined, 141 and equilibrium, 141–142 government debt and, 247–248 incentive to borrow, 163, 169, 205 reserve requirements and, 148 Argentina currency board, 189–191 exchange rate, 189, 190, 191 inflation rate, 191 seigniorage revenue, 63 assets interest-bearing, 86, 149, 158, 159, 189, 191, 218, 262–263, 278, 293–295 risky, 136, 144, 219, 220, 223, 224 separated markets model, 248–250 velocity of, 140 Austria, hyperinflation, 66 autarkic equilibrium, 14, 15, 23, 199 balance sheets, 149 central bank, 181, 183, 262 clearinghouse, 200 positive net worth, 218, 221 banknotes clearinghouse issue of, 200, 201, 202 defined, 148 fully backed, 201–202 and inflation, 202–203 overissue of, 202–203 privately issued, 169, 201, 248 Suffolk system, 202 Bank of Canada, see also open market operations bank rate, 162, 163, 208 lending policies, 163 reserves, 147 bank runs defined, 211 government deposit insurance and, 216–217 interbank lending and, 215 model of, 213–214 prevention of, 214–215 and suspension of withdrawals, 215 unnecessary withdrawals and, 215 banking/banks, see also central banking, financial intermediation arbitrage, 141, 169 balance sheets, 149, 159, 208, 218, 231 capital requirements, 220–223 clearinghouse note, 200 defined, 140 demand deposit, 153,210–213 deposits, 150, 168, 171, 177 exercises, 224–225 failures, 210, 217–219 insolvent, 221–222 interest rates, 142 monitor role, 143–46 net worth, 149, 218 panics, see bank runs; panics regulation of, 239–241 reserve requirements, 148–149 barter defined, 34 double coincidence of wants, 35 exchange costs, 39–40 exercises, 45 fiat money compared, 38–39 model of, 35–37 search costs, 37, 40 versus monetary exchange, 35, 37–40, 44 bequests, 296–299 bonds, government 306, 316–318; see also government debt Brazil, seigniorage revenue, 63 Bretton Woods agreement, 94 budget constraints of borrowers, 127 capital and, 116 central bank, 183 commodity money and, 41 defined, 16 329 330 Subject Index budget constraints (cont.) fiat money demand and, 19, 49 golden rule and, 22–23 government, 48, 237, 253, 258–259, 265, 284, 301, 305 in model of illiquidity, 138–140 of infinitely lived person, 292–299 of lenders, 127 lifetime, 17 for savings decisions, 269 and seigniorage, 59 taxation and, 275–277 wealth and, 270 budget line, 17, 18, 20, 22, 32, 48, 52, 53, 55, 60, 116, 127, 129, 269 budget set, 17 in bequest model, 298 capital and, 116 commodity money vs fiat money, 44 fixed price level and, 57 with inflation, 49 lifetime, 17, 27, 49 with population growth, 25 with seigniorage, 61 bullion, 40 Canada banknote redemption, 243 central bank lending policies, 162–164 debt/GNP ratio, 256 deposit insurance in, 219 n.9 exchange rates, 81 reserve requirements, 148; see also Bank of Canada seigniorage revenue, 63 social insurance, 278 capital crowding out of, 283–285, 287, 289–292, 305, 309, 316 exercises, 288 feasible set for economies with, 132, 133, 134 with fiat money and loans as assets, 129–131 fixed private, 120, 151 and government debt, 283 illiquid, 137–140, 148–14, 182–183 importance of, 220–221 in infinitely lived agents model, 293–294 intergenerational transfers, 4, 26, 134, 279 intermediation and, 140 marginal product of , 117, 119–120, 123, 131–135, 161, 285, 287–288, 306–307 model of, 115–117 motive for holding, 136 nominal interest rates, 121–122 optimal level of, 120 overaccumulation, 133 and population growth, 132 with private debt as assets, 129–131 private saving through, 134 productive, 176, 180, 191 rate of return on, 115–117, 118–119 and real output, 119, 150–151, 157, 180, 291, 306, 309 risk, 124–126 in stationary allocation, 132 tax cuts and accumulation of, 285–287 Tobin effect, 119–121, 123, 177, 296 total product of, 117 underaccumulation, 133 velocity of, 140 and wealth, 284–285 capital formation, inflation and, 120 capital requirements defined, 220 importance of, 220–223 for insured banks, 221 risk-based, 221 for savings and loans, 223 U.S laws regarding, 221, 223 capital stock central bank interest rates and, 161 and GDP, 162 golden rule (optimal), 131–134 measure of, 120, 151 in United States, 120, 151 central bank, see also Bank of Canada; Federal Reserve; financial intermediation, open market operations, reserve requirements balance sheets, 159, 181, 183, 262 budget constraint, 183, 184, 186, 187, 188, 189 debt clearing arrangements, 194, 195–197, 197–199 defined, 147 deposits, 149 economic independence of, 313 exercises, 164 measures of money, 152–157 net worth, 149 political independence of, 313 central bank lending Canadian policies, 162–164 and capital stock, 159–160 and government revenue, 158 interest on loans, 160–161 and intermediated investment, 159–160 limited, 158–161 and money stock, 160 and price level, 160 and rate of return to depositors, 160–161 and reserve requirement, 159, 160, 161 unlimited, 161–162 U.S policies, 162–164 central bank money, fully backed currency boards, 189–191 deflation, 187–189 exercises, 191 expansion of, 186, 187 interest payments on reserves, 181–184 open market operations, 181, 182, 185, 199, 262–263, 292 and price level, 184, 186, 187, 191 quantity theory and, 184–187 rate of return on, 181, 182, 183, 184, 185, 187, 188, 191 in stationary equilibrium, 182 value of, 182, 184, 185, 187 Chile, seigniorage revenue, 63 Subject Index CHIPS, 194, 207 coins, face value of, 40 commodity money budget set, 41 bullion, 40 cigarettes in P.O.W camps, 39 consumption versus trade, 42, 43 defined, 34 equilibrium, 40 exchange costs, 39–40 exercises, 45 fiat money compared, 44 inefficiency of, 43–44 intrinsic value of, 39, 41, 42, 43, 44 model of, 40–44 price of, 42 quantity theory of money and, 42–43 rate of return on, 43–44 competitive equilibrium monetary, 15 nonmonetary, 14 properties of, 14 rate of return in, 141–142 consumption and saving, 268–270 taxes and, 275–277 wealth and, 272–273 consumption good, endowment of, correlation, causality distinguished from, 173–174 covariance, 316–319 defined, 317 cross-country comparisons, 63, 98–100 cross-sectional comparisons, 104 currency, see also deposit-to-currency ratio; foreign currency controls boards, 189–191, 315 destruction of, 80, 187 face value, 79 international traders, 82–84 money supply with, 168–171 perfect substitutes, 80, 92, 95 rate of return, 169, 172, 174 as risky assets, 84 shortage of, 85, 199, 240, 242 speculative attacks on, 85, 91–92, 94 U.S dollar as international money, 94 value of, 37, 87 data correlations cross-country comparisons, 98–100 economic policy and, 110, 302, 309 Phillips curve, 97–98, 103, 104, 106, 110 reduced–form, 108 debt, see also government debt; private debt discounted value of, 204 par value of, 204 debt clearing creditor-debtor island economy, 197 direct repayment, 198 fiat money stock expansion and, 202, 259 institutions for, 198–199 model of, 195–197 decentralized solutions monetary equilibrium, 15 331 nonmonetary equilibrium, 14–15 in overlapping generations models, 10, 13–15 default on debt central bank independence and, 313 commitment to repayment, 303 defined, 124 and rate of return on risky debt, 304 and reputation for repayment, 303–304 time inconsistency of, 314, 315 unanticipated inflation and, 305–306, 310 deficit financing central bank independence of, 313 interest payments, 260, 265 perpetual, 253, 255, 257, 265 population growth and, 254–256 separated asset markets, 248–250 tax cuts, 293 deflation, 187–189, 296, 315 demand for goods, for money, 3, 15–22 demand deposits defined, 213 model of, 211–213 deposit insurance moral hazard of, 219–220 premiums, 220 prevention of bank runs, 216 Depository Institutions Deregulation and Monetary Control Act of 1980, 223 deposit-to-currency ratio defined, 170 determinants of, 178 fluctuations in, 167 inflation and, 176–177 money multiplier and, 171 deposits, see also demand deposits central bank, 148 checkable, 148 demand for, 152, 156, 157, 162, 179 Eurodollar, 154, 155 Notice, 155, n.8 rate of return on, 141, 142 depreciation rate, 115 diminishing marginal product of capital, 117, 119, 123, 131, 285, 288, 306, 318 diminishing marginal rate of substitution, 7, 8, 31 diminishing marginal utility, 318 discount factor, 271, 293, 297 discount rate, 162, 163, 199 discount window, 158, 199, 200, 202, 205, 208 dissaving, 274 double coincidence of wants, 35, 36, 37, 44 absence of, 14, 22 econometric policy evaluation, Lucas critique of, 107–109 economic growth golden rule policy and, 131–134 monetary equilibrium with, 23–26 endowment of goods, in overlapping generations model, 5–6, 13, 14, 15, 16, 17, 18 332 Subject Index equilibrium, see also competitive equilibrium; stationary monetary equilibrium arbitrage and, 141–142 autarkic, 14, 15, 23 commodity money, 40, 41, 43 without fiat money, 14–15 with inelastic money supply, 199 equity, 208, 218 European Economic Community currency, 73, 94 exchange rates, 85 European Monetary Union, 85, n.8 exchange costs of barter, 40 of money, 39 exchange rates, see also currency appreciation, 76 cooperative stabilization of, 84–86 by country, 81 defined, 73 fixed/fixing, 77–78, 84–93 flexible, 75, 77 fluctuations, 80–82, 83, 94, 95 foreign currency controls and, 75–78, 79, 84, 85, 86, 87, 90 indeterminacy of, 78–84 inflation and, 85, 86, 92–93, 94 international currency traders and, 82–84 population growth and, 76 rates of change in, 76, 77 and seigniorage revenue, 77, 93, 95 speculative attacks on, 85, 91–92 taxation and, 91 time path of, 77 two-country model of, 78, 87 unilateral stabilization of, 86–91 expectations, see also rational expectations formation of, 100 and neutrality of money, 98–100 self-fulfilling, 310–311 expected value, 124, 239, 316, 317 feasible allocations golden rule, 11–13, 22, 26, 28, 51 inflation tax and, 51, 58 and initial old, 13 in overlapping generations models, 11–13 stationary, 11 feasible set for capital-based economies, 132 inflation with, 52, 57, 71–72 with population growth, 24–25 stationary monetary equilibrium with, 22, 25 feasible set line, 11, 22, 23, 52, 53, 55, 61, 64 Federal Deposit Insurance Corporation, 217, 221, 223 too big to fail policy, 223 federal funds market, 158 n.12, 215 n.5 federal funds rate, 162, 208 Federal Reserve 84; see also central bank; open market operations discount rate, 162, 163, 199 and interest rate fluctuations, 206 lending policies, 162–163 monetary aggregates, 152, 153, 154, 173, 176 nonmember reserve balances, 148 n.2 payments clearinghouse, 194, 195, 198, 199, 200 Federal Savings and Loan Insurance Corporation (FSLIC), 222 Fedwire, 194, 207 fiat money, see also money barter compared, 34, 36–38, 44–45 budget constraints, 16, 25–26, 48 with capital and loans, 128–130, 139 commodity money compared, 43–44 costs, 37, 39, 136 and crowding-out effect, 283–285, 289–292 defined, 15 equality with supply and demand for, 19, 102, 105, 179, 192, 197 as individually held currency, 153 inefficiency of, 180 inside money as replacement for, 140, 142, 147, 180 liquidity, 136–140 motive for holding, 136 in overlapping generations model, 4, 14–15, 22, 47, 48 population growth and, 23, 25, 54 public balances of, 201 role of, 22 Tobin effect, 119–120, 123 velocity of, 140 fiat money demand, 19 budget constraints, 16–17 derivation, 30–33 finding, 15–22 inflation and, 65, 66, 67 in Lucas model, 102 lump-sum taxation and, 62, 65 population growth and, 26 quantity theory of money and, 21 seigniorage tax base and, 65, 66, 67, 314 rate of return and, 18–21 reserve requirement and, 147, 148, 158 fiat money rate of return arbitrage and, 141 capital compared, 139, 140 defined, 18 deflation and, 187–188 determination of, 18–21 exchange rate and, 76 inflation and, 49, 55, 59, 121 population growth and, 25, 119 reserve requirements and, 151 stock of money and, 62, 119 in two-country model, 76 fiat money stock elastic, 199, 200–203, 206, 207, 208, 240, 242–243 and employment, 104, 105 fixed, 26, 139, 232, 239, 290 golden rule, 22, 25, 51 measured in goods, 19 neutrality of, 21–22 price level and, 49, 56–58, 121, 149 in reserve requirements economy, 148, 152, 156, see also monetary base in United States, 119 value of, 16, 21, 25, 27, 56, 64 Subject Index fiat money stock expansion, see also money stock fluctuations anticipated rate of, 119, 120, 177 constitutional prohibition of, 303 and debt clearance, 195–196 effects of, 47–57, 97, 121, 187, 304 and exchange rates, 76 and inflation, 48–58, 65–68, 119–121, 200, 305 lump-sum subsidies and, 48, 54, 68, 100, 226 once-and-for-all increase, 21, 103, 174–175 output as a function of, 103, 308 and price level, 21, 26, 49, 122, 156, 172, 174, 184, 191 random rate of, 104, 106, 108, 109 reserve requirement and, 150 and seigniorage revenue, 150 stock market crash and, 195 and taxation, 51, 253, 262 temporary, 194, 200, 205 in two-asset model, 249 fiat money value, see also rate of return expectations and, 18 inside money and, 140 intrinsic value of, 18, 39, 41 in overlapping generations model, 22, 285 population growth and, 26, 29, 249 price level and, 16, 21, 49 reserve requirements an, 149 stationary equilibrium and, 20, 21, 49, 55, 62, 88, 138, 188, 290 supply of money and, 54 and wealth transfers, 291–292 Financial Crisis of 2007, 206–209 Financial Institutions Reform, Recovery and Enforcement Act of 1989, 221, 223 financial intermediation, see also banks/banking; central banking arbitrage, 141, 148, 162, 169, 242, 247 and capital/output relationship, 150, 171, 173 costs of, 142, 143, 248 deregulation of, 223 economies of scale, 144 n.4 monitoring role, 143, 144–145 regulation of, 220 n.11, 223 n.12, 239–241 services, 144 two-period model of, 168 zero-profit, 142, 183, 191 fiscal policy, monetary policy linked to, 237 Fisher effect, 123 floating penalty rate, 163 foreign currency controls, 75–78 costs of, 78, 93 defined, 75 fixed exchange rates, 77–78, 84 and value of fiat money, 75 France exchange rates, 81, 82 seigniorage revenue, 63 future generations in autarkic equilibrium, 14 defined, preferences of, 6–10 utility maximization for, 12, 13 welfare maximization for, 12, 22, 23, 26, 44 333 future value, 270, 271 Garn-St Germain Act of 1982, 223 geometric distribution, 36 n.3 Germany exchange rates, 81, 82 hyperinflation, 64 seigniorage revenue, 63 gold consumption in commodity money model, 41 intrinsic value, 41, 42, 43 reserves, 86 n.10 golden rule allocation, 11–13, 51 of consumption, 134 fiat money stock and, 52 inflation and, 52, 54–56 population growth and, 23, 54 golden rule capital stock, 131–134 government bonds, 241, 247, 250, 251, 252, 255, 258, 262, 268, 283 government budget constraint, 48, 237, 253, 258–259, 260, 261, 263, 264, 278, 301, 305 government debt anticipated inflation and, 304, 306–307 and arbitrage, 247 bond issuance, 251, 252, 253, 256, 260, 283, 291 crowding-out effect, 283–285, 287, 289–292, 305, 209, 316 default on, 301, 302–303 deficit financing, 257 exercises, 266–267, 288–289 fiscal-monetary policy linkages, 237 forms of, 247 GNP/debt ratio, 256 high-denomination, 247–250 indexed to price level, 313 infinitely lived agents model, 292–299 inflation and, 304–313 as interest-bearing asset , 289, 293–295 and interest rates, 250, 251, 255, 265, 285, 286, 289, 293–295, 316 intertemporal choices, 259–262 model of, 248–250 monetization of, 253, 262, 263 neutral, 262, 263 open market operations, 181 n.3, 262–263, 292 perpetual, 252–255 political ramifications, 263–265 population growth and, 249, 252 random return on, 317 rational expectations, 307–308 real rate of return on, 251, 258, 264, 306 Ricardian equivalence theorem, 287 separated asset markets, 248–250 time path of, 253, 254, 255 unanticipated inflation and, 305–306, 310 and wealth transfers, 291–292 government purchases financing, 58–64 Great Depression, 207, 217 n.7 gross domestic product (GDP), 119, 120 reserve requirements and, 150 gross national product (GNP), see also output, 63, 64 government debt and, 256 334 Subject Index hyperinflation defined, 63 government debt and, 311–312 postwar episodes, 64, 65, 312 illiquidity, model of, 137–140 income defined, 270 effect, 101 and saving, 274–275 taxes, 275–277 wealth and, 270, 272–273 indifference curves of borrowers, 129 budget constraints and, 12, 49 defined, features of, 6–10 in golden rule allocation, 12 inflation and, 49 for savings decisions, 269 indifference maps, Indonesia seigniorage revenue, 63 speculative attacks on currency, 91 inferior good, defined, 272 infinitely-lived agents bequests, 296–299 model of, 292–299 parents, 297–299 inflation, see also hyperinflation anticipated, 103, 119, 120, 121, 123–124, 176–177, 304, 306–307, 310 banknote overissuance and, 202–203 and budget set, 51, 56 and capital formation, 120 central bank independence and, 313 commitment in monetary policy, 303 exchange rates and, 76, 77, 92–93 exercises, 68–71 with feasible set, 71–72 fiat money creation and, 56, 60, 63, 67, 307 Fisher effect, 123 fixed price levels and, 56–58 and GNP (output), 99, 103, 304, 305, 309 and golden rule allocation, 54–56, 61 and government debt, 304–313 gross rate of, 48 inefficiency of, 51–54 leisure-labor model, 54 net rate of, 49 and nominal interest rates, 121–124, 306, 310 nonrandom, 101–104 Phillips curve, 104, 110 and private debt, 315 and rate of return, 49, 50, 51, 53, 56, 60, 119 and real interest rate, 121, 122, 123–124 in representative agent model, 296 seigniorage and, 59, 60, 61, 62, 64–68 self-fulfilling expectations, 310–311 systematic, 110, 308, 309, 310, 315 and taxation, 51, 64, 87 Tobin effect, 119–121, 123, 177, 296 unanticipated, 97, 304–306 and employment, 97, 98, 104, 106 inflation tax, 61, 262, 314 inefficiency of, 51–54 initial old in autarkic equilibrium, 14 in commodity money economy, 42, 44 defined, feasible allocations for, 13 in monetary equilibrium, 23 preferences of, 10 utility of, 23 innovations, money, 167 inside money central bank money and, 168 defined, 140 elastic supply of, 200–201 fiat money replaced for, 147, 180 intermediation and, 140, 142 model of, 168–171 and output, 172, 175 rate of return, 147 interest payments on reserves, 183, 186 interest rates, see also nominal interest rates; real interest rates on central bank loans, 160, 161 discounted, 204, 290 free market and, 133 government deficits and, 285 innovations in, 167 and savings decisions, 268–275 short-term, 140, 203–206 intergenerational transfers, 4, 26, 134, 279 international currency traders, 82–84 international monetary systems, see also exchange rates exercises, 95–96 fixing exchange rates, 77–78, 84–93 foreign currency controls, 75–78 indeterminacy of exchanges rate, 78–84 model of, 74–75 optimal, 93–94 investment direct, 150, 173 intermediated, 146, 150, 151, 159, 177, 186 risky, 146 unintermediated, 145–146 IOUs, 127, 137, 138, 140, 141, 198, 211, 257 Italy, 63, 82, 314 Japan exchange rates, 74, 81, 86 seigniorage revenue, 63 labor endowment, Laffer curve, 68 leisure–labor model of inflation, 54, 100 lender problem, 127 lending, see also central bank lending; private debt interbank, 215 of reserves, 215 n.5 lifetime budget set, 17, 27, 49 lifetime budget set line, 17 Subject Index liquidity, 136, 199–202 defined, 136 exercises, 143 of liabilities, see demand deposits, 211 of fiat money, 136 payment systems model of, 199–202 loans, see also private debt, 117, 118, 127 default on, 124, 202, 219 demand for, 129 discount window, 200 duration of, 271 equilibrium quantity of, 130 fiat money with, 118 future value of, 270 monitoring repayment of, 144 present value of, 270 real interest rates, 130 supply of, 129 Lucas critique of econometric policy evaluation, 106–109 Lucas model, 100–101 lump-sum subsidies, 151 n.5 taxation, 61, 226, 237, 260, 275, 283, 293, 302, 314 M1, 153, 155, 156, 160, 171, 175, 178 M2, 155 M3, 155 many-goods model, 34–38 marginal product of capital, 117, 119, 123, 132, 161, 285, 287 diminishing, 117, 285, 288 marginal rate of substitution, 7, 31 diminishing, 7, 31 foreign currency controls and, 78 n.2 market clearing conditions, 14, 71, 79, 88, 92, 102, 179, 192, 196, 202, 229, 232 for money balances, 19, 87, 179, 193 for currency, 197 medium of exchange, see also monetary exchange, 3, 22, 28, 35, 37, 38, 41, 42, 140, 153, 195, 226 and distribution of wealth, 43 monetary aggregates, see also M1; M2; M3 defined, 152 total money stock and, 156, 165, 168, 172, 176 monetary base defined, 155 money supply and, 156, 164, 167, 172, 174 and rate of return on deposits, 151 and seigniorage revenue, 150 Monetary Control Act of 1980, 223 monetary economies, essential features, monetary equilibrium, see also equilibrium budget constraints in, 17 defined, 15 with economic growth, 23–28 and feasible set, 24 golden rule allocation, 22–23 neutrality of money in, 21 with population growth, 25 in separated assets market, 248 stationary, 11 monetary exchange, see also international monetary systems, 37 335 commodity money, 34 costs, 39–40 fiat money, 37 monetary policy activist, 316–319 econometric policy evaluation, 107–109 fiscal policy linked to, 237 optimal, 237–238 random, 104–106 stabilization, 175–176 monetization of government debt, 253, 263 money, see also central bank money; commodity money; currency; fiat money; inside money; outside money; quantity theory of money; money supply demand for, 3, 25, 30 53, 64, 75, 80, 156, 237, 238, 263, 291 high-powered, 156 Lucas model of, 100–101, 110 as medium of exchange, 3; see also monetary exchange, 22, 37, 38, 41, 44, 153, 195, 226, 242 and memory, 4, 27 neutrality of, 21 and output, 97, 165, 166–172, 174 in overlapping generations, usefulness, 10, 38, 136 willingness to hold, 115 money market mutual funds, 155, 217 n.8 money multiplier defined, 156 deposit-to-currency ratio, 167, 170, 174 determinants of, 168 fluctuations in, 165 innovations in, 165, 167 model of, 156, 168 output linked to, 167 random, 165 U.S., 166 money stock defined, 165 innovations in, 165, 167 and price level, 150 total nominal, 91, 152, 155, 160, 171, 178 money stock fluctuations anticipated inflation, 176–177 central bank lending and, 158–163 exercises, 179 inside money (bank deposits) and, 168–171 monetary aggregates and, 173, 176 monetary stabilization policy, 175–176 money multiplier, 165, 168, 171–176 once-and-for-all change, 174–175 and output, 166–167, 171–176 with reserves, 178–179 money supply defined, 155 elastic, 199–200 inelastic, 199 and monetary base, 155 monitors, banks as, 144 moral hazard, 219, 224 multinational institutions, and exchange rates, 81 336 Subject Index national debt, see also government debt nominal, 304–313 real, 305–307 national product, see gross national product; net national product net domestic product, defined, 132 net transactions accounts, 148 neutrality of fiat money, 21–22, 98–106 of government debt, 285–287 risk, 124, 168, 308 New York Clearinghouse Association, 194 nominal interest rates defined, 121 Fisher effect, 123 fluctuations, 206, 248 gross, 205 inflation and, 123, 124, 248, 305, 306, 310, 315, 316 net, 122, 307 real interest rate and, 121–122 nonmonetary equilibrium, 14–15 nonstationary equilibria, 21 normal good, defined, 272 once-and-for all increase, 21, 174–175 open market operations central bank money and, 181, 185 debt clearance, 199 defined, 181 effects of, 184–187 government debt purchase, 262–263, 292 mechanics of, 182 two-period model, 181 output, see also gross domestic product; gross national product aggregate, 54, 103 from capital, 117, 132, 173, 310 inflation and, 98, 103, 110, 176–177 innovations in, 167 interest rates and, 175 intermediation and, 142 monetary base and, 150 money multiplier linked to, 171–176 money stock and, 174–175 real, 157, 165, 166 welfare distinguished from, 120 outside money defined, 172 model of, 168–171 overlapping generations models capital in, 115–117, 137–140, 150–151, 226, 257, 268 commodity money in, 40–44 debt-clearing model, 195–197 decentralized solutions, 13–15 demand for money in, 15–22 of demand deposit banking, 211–213 desirable features, economic problem, 10 endowment patterns, 5, 14, 274 environment, 5–6 exchange rates in, 73 exercises, 28–30, 33 feasible allocations, 10–13 fiat money in, 3, 15, 47–58 government debt in, 283–285 inflation in, 47–58 linear capital production technology in, 115 n.1 Lucas model, 100–101, 110 preferences, 6–10 quantity theory of money in, 21 of savings decisions, 268–275 two-country model, 78, 87 panic, see also bank runs defined, 210 of 1893, 216 of 1907, 204 n.8 prevention, 214–217 par value, 204 parents no bequests from, 299 simple model of, 297–299 payments system, see also debt clearing clearinghouses, 194 defined, 197 liquidity provided for, 199–202 overissue of banknotes, 202–203 short-term interest rates, 203–206 pension plans, fully backed, 278–279 perfect foresight, 18 perfect substitutes, 80, 92, 118, 119, 124, 136, 200, 202, 263 perfectly competitive markets, 19 Phillips curve, 97–98, 103, 106, 308 population growth budget set with, 25–28 capital and, 132, 141 economic growth modeled as, 23 and exchange rates, 73 feasible set with, 24 and fiat money, 25, 54–56, 249 golden rule allocation with and government debt financing, 249, 252 gross rate, 23 net rate, 23 and social security plans, 281 preferences diminishing marginal rate of substitution, of future generations, 6–10 of initial old, 10 in overlapping generations models, 6–10, 18 present value and crowding out of capital, 283–285 defined, 270 and saving, 270–272 of lifetime taxes, 276 price level central bank lending and, 158–159 central bank money and, 171, 184–187, 192 defined, 16 fiat money stock and, 21, 49, 56–58, 105, 109, 156, 171, 202, 305 fixed by government, 56–58 government debt indexed to, 313, 315 indeterminacy of, 192–193 and output, 309 payments system and, 197, 201 Subject Index population and, 21, 102, 105, 107–108 quantity theory of money and, 21, 49, 156 reserve requirement and, 149–150 value of money and, 21 price surprises contradictory correlations and, 98 econometric policy evaluation and, 106–109 exercises, 110–111 expectations and neutrality of money, 98–106 optimal policy, 109 principle of rate-of-return equality, 117–118 private debt borrower problem, 127–129 and capital as assets, 129–131 exercises, 131 inflation and, 315 IOU model of, 126–127 lender problem, 127 rate of return on, 118 private saving, capital accumulation and, 134 production technology, 115 quantity theory of money for central bank money, 156, 184–187 for commodity money, 42–43 for fiat money, 21 interest on money and, 201 price level and, 21, 49, 156 random relocation model, 227, 229–233 rate of return, see also arbitrage; fiat money rate of return on backed central bank money, 180, 181–184 on capital, 115–117, 199, 121, 123, 136, 138, 148, 151, 168, 188, 211–212, 237, 251 on commodity money, 41 in competitive equilibrium, 141–142 on currency, 170, 187, 247 defined, 18 on deposits, 141, 151 expected, 124–125, 306 fixed, 116, 161 on government bonds, 250, 304 gross, 119, 122, 125 inflation and, 49 on inside money, 147 on loans, 118, 124 net, 125, 251–252, 307 random, 124 on real estate, 137 on risky debt, 304 seigniorage and, 59 on storage assets, 211–213 to work, 103 rate-of-return equality, principle of, 117–118 rational expectations defined, 18 self-fulfilling inflationary, 310–311 real interest rates anticipated inflation and, 123–124 budget line, 127 on central bank loans, 160 337 defined, 121 equilibrium, 130 and government debt, 255, 285, 311 gross, 122 net, 270, 274 nominal interest rate and, 121 and output, 173–174, 255 and supply of loans, 127 real money balances, 21, 66, 87, 185, 195, 231, 290, 295–296 recession, 98, 165, 260 reduced-form correlation, 108 representative agent models, 296 see also infinitely lived agents defined, 293 repurchase agreements, 155 reserve requirements banks with, 148–149 Canadian, 148 central bank measures of money, 152–157 defined, 147, 148 and demand for money, 148, 156 deposits and, 151 form of, 148 and GDP (output), 150–151 lump-sum, 289, 295 model of, 148–152 and price levels, 149–150 and seigniorage, 150 U.S., 148 and value of money, 149, 193 and wealth transfers, 291 welfare effects, 152 reserves for banknotes, 193 and exchange rates, 80 n.4 interest payments on, 181–183, 186 measure of, 151 n.4 nonborrowed, 158 in U.S commercial banks, 151 Resolution Trust Corporation, 217 Ricardian equivalence theorem, 287 risk aversion, 125, 136, 145, 219, 220,229, 235, 238, 304, 316 default, 304 in lending, 129 neutrality, 124, 174 n.11, 308 premium, 125, 136, 316, 318 saving, 118 see also dissaving; private saving; social security budget constraints, 268–269, 272, 274 consumption and, 272–273 determinants of, 268–275 exercises, 278 income and, 274 interest rate and, 270–271 present value and, 270–272 and seigniorage revenue, 66 social security plan and, 279 taxes and, 275–277 utility-maximizing choice of, 273 wealth and, 270, 272–273 338 Subject Index savings and loans core capital requirements, 221 failures, 219 n.9 regulation of asset holdings, 223 n.12 Savings Association Insurance Fund, 222 seigniorage revenue banknote overissuance and, 202–203 and budget set, 64 by country, 63 defined, 58 exchanges rates and, 77, 93, 94, 190 fiat money creation and, 65, 67, 77, 250, 314 and fiat money value, 305 inflation and, 60–61, 314 limits to, 64–68 lump-sum taxation compared to, 61–63 monetary base and, 150 from open market operations, 262–263 real value of, 65 reserve requirements and, 150, 152, 157, 158 saving and, 68 tax base, 64 tax rate, 64 time consistency problem of, 302 welfare effects of, 58, 60–61 self-fulfilling expectations, 310–311 separate-markets model, 248–250 shocks, 19, 174, 175, 238, 318 silver as commodity money, 40 n.6, 46 social security exercises, 281–282 fully funded pension plan, 278–279 pay-as-you-go system, 279–281 wealth and, 281 South Korea speculative attacks on currency, 91 speculation attacks on currency, 91–92 static models, stationary allocations capital in, 132 fiat money in, 11–13, 17, 21, 26, 60 stationary monetary equilibrium, 20, 22, 25, 57, 71 backed central bank money in, 180, 182, 184–187 budget set, 20, 57 commodity money in, 41 feasible set, 22, 57, 71 government debt in, 250, 290 inflation in, 50, 55, 57 with population growth, 24, 55, 290 properties, 20 value of fiat money in, 87, 290 stock market crash, 195 stocks, 137 storage assets, 211–214, 215, 217 subsidies, see lump-sum subsidies; taxation substitution diminishing marginal rate of, 7, 31 effect, 101, 103 marginal rate of, 32, 78 n.2 supply-side economics, 68 n 12 Sweden, speculative attacks on currency, 91 taxation/taxes bank insolvency, 217, 220 budget constraints, 228, 259 and capital accumulation, 133, 293 and consumption, 275–277 cuts, 287, 293 default on government debt and, 301–304 deficit financing and, 247, 258–259, 264–265, 286, 287, 293 and exchange rates, 86–87, 89–90, 91–92, 93, 94, 189 government’s willingness to use, 91 income, 62, 68, 260, 302 inflation and, 51, 60–61, 61–64, 262 lump-sum, 61–64, 65, 226, 275, 283, 293, 302, 314 present value of, 275, 276 rate-revenue relationship, 68 revenue from, 264 and savings, 275–277, 287, 294 seigniorage as, 62 wealth-neutral changes, 275–277 Term Auction Facility, 208 thrifts FSLIC-insured, 222 tangible-insolvent, 222 time consistency problem, 302, 314 time-series comparisons, 104, 106, 206 Tobin effect, 119–120, 123, 177, 296 defined, 119 trading, in debt-clearing model, 194, 196–197 transaction costs, 93, 136–137, 147, 169, 176–177, 180, 289 transitivity, Treasury bills, 247, 304 unemployment, inflation and, 97, 103 United Kingdom exchanges rates, 81, 86 inflation-unemployment relationship, 97 seigniorage revenue, 63 speculative attacks, 91 United States bank failures, 217, 221 budget deficits, 260 debt/GNP ratio, 256 capital stock, 120, 150 central bank, see Federal Reserve, 84, 153, 162, 206 currency stock held abroad, 63, 86 n.11 exchange rates, 74, 78, 80 fiat money stock, 153 inflation, 92, 97 money cleared daily, 194 money multiplier, 165 reserves, 148 seigniorage revenue, 63 social security, 134, 278–281 Uruguay, seigniorage revenue, 63 utility in autarkic equilibrium, 14 defined, 14 diminishing marginal, 318 functions, 13, 30 of initial old, 13 Subject Index instantaneous, 292, 293 lifetime, 12, 228, 232, 292 maximization, 32, 52, 269 velocity of assets, 140 Vietnam War, 94 n 15 wealth capital and, 290, 293–295 and consumption, 272–274 defined, 270 distribution of, 43 effect, 103, 237, 277 fixed exchange rates and, 87–88 government debt and, 293–295 income and, 270, 273, 293–294 in infinitely lived agents model, 281, 283 and lifetime budget constraint, 273 measure of, 276 and real money balances, 290, 295–296 reserve requirements and, 295–296 and saving, 270, 272–273, 278–279 and social security plan, 279–281 taxation and, 275–277 transfers, 291–292, 296 welfare effects fiat money replaced by inside money, 141–142 of inflation, 51–54 of reserve requirements, 152 welfare maximization, 120 for future generations, 12, 22 339