### Office Hours: Tue 15:00-16:00

**Email:** preichlin@luiss.it.

**Office hours:**Tuesday, 15:00-17:00

**T.A.:**Pasquale Filiani (pfiliani@luiss.it)

The course is an introduction to modern macroeconomics analysis based on utility maximization, asset pricing and competitive equilibrium theory. A first part focuses on optimal consumption, savings and asset accumulation from the individual point of view. We introduce the notions of inter-temporal budget constraints, Euler equations, consumption smoothing over time and states, risk aversion and precautionary saving. Then, we present some basic insights on asset pricing under risk. The second part of the course is devoted to the equilibrium restrictions on consumption and asset accumulation in competitive economies under two alternative frameworks: a finite number of infinitely lived individuals and overlapping generations. We will establish conditions under which an equilibrium configuration implies consumption smoothing and risk sharing and examples in which these properties may fail. Then, we discuss some topics in public finance, Ricardian equivalence and existence of bubbles and positive outside assets. Finally, we examine what conditions insure or prevent the Pareto efficiency of competitive equilibria.

## DETAILED PROGRAM

**1. Consumption Choices in the Deterministic Model**

1.1. Budget constraints and debt limits

1.2. The Euler equation

1.5. The Lagrange method

1.6. The transversality condition

1.7. The Arrow-Debreu budget constraint (how it arises and why)

1.8. Consumption smoothing and the permanent income hypothesis

1.9. An example of optimal plans with binding debt limits

**2. Consumption and Savings under Uncertainty**

2.1. Modeling uncertainty (the date-event tree, events probabilities)

2.2. Budget constraints and Euler equations with complete markets

2.3. Budget constraints and Euler equations with incomplete markets

2.4. The consumption function under certainty equivalence

2.5. Precautionary savings

2.6. Asset pricing with long-lived assets, no arbitrage and risk premiums

2.7. Market fundamentals and bubble components

**3. Equilibrium**

3.1. Defining equilibria and basic properties of the equilibrium price sequences

3.2. The CRRA example

3.3. Consumption smoothing and risk sharing with no aggregate uncertainty

3.4. The cost of Business Cycles

3.5. Equilibrium with tight debt limits in a Bewley economy

3.6. Overlapping generations with and w/out parental altruism

3.7. Social security in the overlapping generations model

3.8. First Welfare Theorem

3.9. Pareto inefficiency in the overlapping generations model

**4. Outside Assets**

4.1. Long-Term assets and bubbles in equilibrium

4.2. Existence of asset bubbles in the overlapping generations model

4.3. Public debt and Ricardian equivalence

4.4. Government Debt in the Bewley economy with tight debt limits

Teaching material is based on my Lecture Notes (updated April 24, 2017)

## Homeworks

### GRADES FOR THE MIDTERM EXAM (03/17)

### GRADES OF THE FINAL EXAM, MAY 22 (YOU ARE ADVISED TO SEE THE EXAM NEXT WEEK EITHER ON MONDAY OR WEDNESDAY)

## TENTATIVE DAY-BY-DAY PROGRAM (’16-’17)

14/2 | Introduction, Preferences, Budget Sets, Debt Limits | 01 |

15/2 | Euler Equations, Transversality – Problem Set 1 assigned | 02 |

21/2 | Inter-Temporal Budget Constraints in Infinite Horizons | 03 |

22/2 | Consumption Smoothing and the Permanent Income Hypothesis | 04 |

28/2 | Review Session – Problem Set 2 assigned | 05 |

01/3 | Decisions under Uncertainty, complete markets | 06 |

07/3 | Review Session – Problem Set 3 assigned | 07 |

08/3 | Incomplete Markets and the Certainty Equivalence Model | 08 |

14/3 | Review Session – Problem Set 4 assigned | 09 |

15/3 | Prudence and Precautionary Savings | 10 |

21/3 | Review Session – Problem Set 5 assigned | 11 |

22/3 | Asset Pricing and Long-Lived Assets | 12 |

28/3 | Break | /// |

29/3 | Midterm Exam | /// |

04/4 | Review Session | 13 |

05/4 | Review Session – Problem Set 6 assigned | 14 |

11/4 | Equilibrium with Long Lived Individuals | 15 |

12/4 | Consumption Smoothing and Risk Sharing – Problem Set 7 assigned | 16 |

18/4 | Easter Break | /// |

19/4 | Welfare Theorems – Problem Set 8 assigned | 17 |

25/4 | Holiday | /// |

26/4 | Overlapping Generations, Parental Altruism | 18 |

02/5 | Review Session – Problem Set 8 assigned | 19 |

03/5 | Outside Assets, Long-Lived Assets and Bubbles | 20 |

09/5 | Review Session – Problem Set 9 assigned | 21 |

10/5 | Government debt and Ricardian equivalence | 22 |