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

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

**Schedule:**Monday (LUISS) 9:00-10:30, Wednesday (EIEF) 2:45-4:15, Thursday (LUISS) 9:00-10:30

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

## Outline

The course is an introduction to modern macroeconomics analysis based on first principles: planning optima, utility maximization, asset pricing and competitive equilibrium theory. The first part of the course focuses on dynamic efficiency and optimal growth with capital accumulation (the Ramsey Problem). The second part 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, precautionary saving and asset pricing. The third 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.

## Textbooks and reading materials.

The course content is based on my class notes:

Class Notes (to be checked up to section 6.3)

Most of the material covered in the course can be found in the textbook by D. Romer (D. Romer, *Advanced Macroeconomics*, McGraw Hill, 2006).

Assignment 4 – due february 28

**Macroeconomic Analysis – Module I**

Tentative day-by-day program |
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01 | 1/29 | Review of the Solow Model. Introducing dynamic efficiency and Cass criteria and Malinvaud transversality. |

02 | 1/31 | Introducing Ramsey Plans. Euler equations, transversality, proving sufficiency. |

03 | 2/01 | Lagrange Method. Stability analysis and linearization. Homework 1 assigned. |

04 | 2/05 | Introduction to Bellman equations. Some standard examples. |

05 | 2/07 | REVIEW SESSION – Solution of Homework 1 – Homework 2 assigned. |

06 | 2/08 | Ramsey Plans and social welfare: heterogeneous long lived individuals and overlapping generations. Modeling uncertainty. |

07 | 2/12 | Characterizing Ramsey Plans under uncertainty. Costs of business cycles. Examples. |

08 | 2/14 | REVIEW SESSION – Solution of Homework 2 – Homework 3 assigned. |

09 | 2/15 | Consumption and savings with sequential markets. Budget sets, debt limits and the Euler equation. |

10 | 2/19 | Ponzi games, transversality, integrability of life-time budget constraints, consumption smoothing and the permanent income hypothesis. |

11 | 2/21 | REVIEW SESSION – Solution of Homework 3 – Homework 4 assigned. |

12 | 2/22 | The case of uncertainty: complete markets and incomplete markets. The certainty equivalent model. Precautionary savings. |

13 | 2/26 | Asset pricing with long lived assets. |

14 | 2/28 | REVIEW SESSION – Solution of Homework 4 – Homework 5 assigned. |

15 | 3/01 | Competitive equilibrium with complete markets. Consumption smoothing and full risk sharing with no aggregate uncertainty. |

16 | 3/05 | First and second welfare theorems. |

17 | 3/07 | REVIEW SESSION – Solution of Homework 4 |

18 | 3/08 | The Bewley model. The pure exchange equilibrium in overlapping generations. |