Lecture Notes in Macroeconomics
                                                     John C. Driscoll
                                             Brown University and NBER1
                                                    December 21, 2003
                           1Department of Economics, Brown University, Box B, Providence RI 02912. Phone
                        (401) 863-1584, Fax (401)c863-1970, email:John Driscoll@brown.edu, web:http:\\
                        econ.pstc.brown.edu\ ∼jd. °Copyright John C. Driscoll, 1999, 2000, 2001. All rights
                        reserved. Do not reproduce without permission. Comments welcome. I especially
                        thank David Weil, on whose notes substantial parts of the chapters on Money and
                        Prices and Investment are based. Kyung Mook Lim and Wataru Miyanaga provided
                        detailed corrections to typographical errors. Several classes of Brown students have
                        provided suggestions and corrections. All remaining errors are mine.
                 ii
                            Contents
                            1 Money and Prices                                                                   1
                               1.1   De¯nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    2
                                     1.1.1   Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    2
                                     1.1.2   Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     2
                               1.2   The History of Money . . . . . . . . . . . . . . . . . . . . . . . .        3
                               1.3   The Demand for Money . . . . . . . . . . . . . . . . . . . . . . .          4
                                     1.3.1   The Baumol-Tobin Model of Money Demand . . . . . . .                4
                               1.4   Money in Dynamic General Equilibrium . . . . . . . . . . . . . .            6
                                     1.4.1   Discrete Time . . . . . . . . . . . . . . . . . . . . . . . . .     7
                                     1.4.2   Continuous Time . . . . . . . . . . . . . . . . . . . . . . .      10
                                     1.4.3   Solving the Model . . . . . . . . . . . . . . . . . . . . . .      13
                               1.5   The optimum quantity of money . . . . . . . . . . . . . . . . . .          14
                                     1.5.1   The Quantity Theory of Money . . . . . . . . . . . . . . .         14
                               1.6   Seigniorage, Hyperin°ation and the Cost of In°ation . . . . . . .          16
                               1.7   Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     21
                            2 Nominal Rigidities and Economic Fluctuations                                      27
                               2.1   Old Keynesian Economics: The Neoclassical Synthesis . . . . . .            28
                                     2.1.1   Open Economy . . . . . . . . . . . . . . . . . . . . . . . .       31
                                     2.1.2   Aggregate Supply      . . . . . . . . . . . . . . . . . . . . . .  33
                               2.2   Disequilibrium Economics . . . . . . . . . . . . . . . . . . . . . .       36
                                     2.2.1   Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    36
                                     2.2.2   The Walrasian Benchmark Case . . . . . . . . . . . . . .           37
                                     2.2.3   Exogenously Fixed Price . . . . . . . . . . . . . . . . . . .      38
                                     2.2.4   Exogenously Fixed Nominal Wage . . . . . . . . . . . . .           39
                                     2.2.5   Both prices and wages in°exible       . . . . . . . . . . . . . .  39
                                     2.2.6   Analysis of this model . . . . . . . . . . . . . . . . . . . .     40
                               2.3   Imperfect Information Models . . . . . . . . . . . . . . . . . . . .       41
                               2.4   New Keynesian Models . . . . . . . . . . . . . . . . . . . . . . . .       43
                                     2.4.1   Contracting Models . . . . . . . . . . . . . . . . . . . . .       43
                                     2.4.2   Predetermined Wages . . . . . . . . . . . . . . . . . . . .        44
                                     2.4.3   Fixed Wages . . . . . . . . . . . . . . . . . . . . . . . . .      47
                               2.5   Imperfect Competition and New Keynesian Economics . . . . . .              50
                                     2.5.1   Macroeconomic E®ects of Imperfect Competition . . . . .            50
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                                        iv                                                                    CONTENTS
                                                 2.5.2   Imperfect competition and costs of changing prices . . . .       51
                                                 2.5.3   Dynamic Models . . . . . . . . . . . . . . . . . . . . . . .     56
                                            2.6  Evidence and New Directions . . . . . . . . . . . . . . . . . . . .      57
                                            2.7  Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   58
                                        3 Macroeconomic Policy                                                           65
                                            3.1  Rules v. Discretion . . . . . . . . . . . . . . . . . . . . . . . . . .  66
                                                 3.1.1   The Traditional Case For Rules . . . . . . . . . . . . . . .     66
                                            3.2  The Modern Case For Rules: Time Consistency . . . . . . . . . .          68
                                                 3.2.1   Fischer’s Model of the Benevolent, Dissembling Government 69
                                                 3.2.2   Monetary Policy and Time Inconsistency . . . . . . . . .         73
                                                 3.2.3   Reputation . . . . . . . . . . . . . . . . . . . . . . . . . .   75
                                            3.3  The Lucas Critique . . . . . . . . . . . . . . . . . . . . . . . . . .   77
                                            3.4  Monetarist Arithmetic: Links Between Monetary and Fiscal Policy 79
                                            3.5  Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   80
                                        4 Investment                                                                     87
                                            4.1  The Classical Approach . . . . . . . . . . . . . . . . . . . . . . .     87
                                            4.2  Adjustment Costs and Investment: q Theory . . . . . . . . . . .          88
                                                 4.2.1   The Housing Market: After Mankiw and Weil and Poterba 91
                                            4.3  Credit Rationing . . . . . . . . . . . . . . . . . . . . . . . . . . .   93
                                            4.4  Investment and Financial Markets . . . . . . . . . . . . . . . . .       95
                                                 4.4.1   The E®ects of Changing Cash°ow . . . . . . . . . . . . .         98
                                                 4.4.2   The Modigliani-Miller Theorem . . . . . . . . . . . . . . .      99
                                            4.5  Banking Issues: Bank Runs, Deposit Insurance and Moral Hazard 100
                                            4.6  Investment Under Uncertainty and Irreversible Investment . . . . 103
                                                 4.6.1   Investment Under Uncertainty . . . . . . . . . . . . . . . 107
                                            4.7  Problems: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
                                        5 Unemployment and Coordination Failure                                         117
                                            5.1  E±ciency wages, or why the real wage is too high . . . . . . . . . 117
                                                 5.1.1   Solow model . . . . . . . . . . . . . . . . . . . . . . . . . 118
                                                 5.1.2   The Shapiro-Stiglitz shirking model     . . . . . . . . . . . . 118
                                                 5.1.3   Other models of wage rigidity . . . . . . . . . . . . . . . . 120
                                            5.2  Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
                                                 5.2.1   Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
                                                 5.2.2   Steady State Equilibrium . . . . . . . . . . . . . . . . . . 122
                                            5.3  Coordination Failure and Aggregate Demand Externalities . . . . 123
                                                 5.3.1   Model set-up . . . . . . . . . . . . . . . . . . . . . . . . . 123
                                                 5.3.2   Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 125
                                                 5.3.3   De¯nitions    . . . . . . . . . . . . . . . . . . . . . . . . . . 126
                                                 5.3.4   Propositions    . . . . . . . . . . . . . . . . . . . . . . . . . 126
                                            5.4  Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
                                        Continuous-Time Dynamic Optimization                                            131