Facoltà di Economia

You will find a treatment of the Certainty Equivalent Principle and an introduction to consumption-based asset pricing theory in Chapter 8 (Consumption) of Romer’s Advanced Macroeconomics, as well as in Chapter 7 (The model under uncertainty) of Rechilin’s Notes on Macroeconomic Theory.

Dear all, I have spotted a typo in the budget constraint of the last exercise of practice 4. You find the correct version on the website.

Sorry for the inconvenience,

Federico

The exam has been rescheduled on Friday, April 5, at 9:30am.

• Constant returns to scale and Euler's Theorem
• The law of motion of capital in Solow growth model
• Existence and uniqueness of a steady state in Solow growth model
• Transitional dynamics and long-run convergence in Solow growth model
• Types of technological progress
• Technological progress and Uzawa’s Theorem
• Necessary conditions for the dynamic efficiency of a steady state
• Sufficient conditions for the dynamic efficiency of a steady state
• Dynamic programing and the Bellman equation
• Euler equation and the transversality condition
• Derivation of the Euler equation in the Ramsey growth model
• Long-run convergence in the Ramsey growth model
• Saddle-path stability in the Ramsey growth model
• Competitive equilibrium and Ramsey optimal growth
• Euler equation for Ramsey optimal growth in a stochastic environment
• Euler equation in the deterministic optimal saving framework
• Euler equation in the stochastic optimal saving framework
• Exact determination of optimal saving in a deterministic environment with CES utility
• The law of motion of capital in an overlapping generations economy
• Substitution and wealth effects in an overlapping generations economy
• Dynamic inefficiency in an overlapping generations economy
• Social security and dynamic inefficiency in an overlapping generations economy
• First Welfare Theorem in an overlapping generations economy
• Consumption under uncertainty and the Certainty Equivalent Principle
• Interest rate and saving
• Precautionary saving
• Consumption-based asset pricing

Dear all,

The last practice class for the course will be held on March 28, from 2 pm to 4 pm.

Best,

Federico

Dear All,

I have uploaded the last problem set for the course. I am available for discussing the exercises with you if you need.

Best, Federico

Growth with overlapping generations is exhaustively discussed in Chapter 9 (Growth with Overlapping Generations) of Acemoglu’s Introduction to Modern Economic Growth, excluding Sections from 9.6 to 9.8.

You will find an introduction to optimal consumption and saving in a deterministic environment in Part 2 (Consumption and savings) of Reichlin’s Notes on Macroeconomic Theory.

In addition, interest rate and saving in the two-period case is presented in Chapter 8 (Consumption) of Romer’s Advanced Macroeconomics.

I will be in the office on Monday from 2pm to 3pm, or by appointment.

Dear Students,  I have uploaded the third problem set on the website.

Should you need support, feel free to contact me.

Best,

Federico

Dear Students,  I have uploaded the first problem set for the course. You can find the material used in today's class, with some worked out examples on dynamical system as well.

Should you need any support, feel free to contact me.

Best,

Federico

The exams of Macroeconomics I and II can be taken in different dates and in any order.

The two exams must be taken in the same academic year.

Students have to pass both exams and the final grade will be the average of the grades in the two exams.

• Daron Acemoglu, Introduction to Modern Economic Growth, Princeton University Press, 2009
• David Romer, Advanced Macroeconomics, McGraw-Hill, 2011
• Additional lecture notes will be distributed during classes

The class on Monday, March 18, will exceptionally start at 11:30am.

You will find a presentation of Ramsey optimal growth under uncertainty in Section 17.1 of Chapter 17 (Stochastic Growth Models) of Acemoglu’s Introduction to Modern Economic Growth, as well as in Chapter 3 (Optimal Growth with Uncertainty) of Reichlin’s Notes in Macroeconomic Theory.

A simple illustration of the offer curve for pure-exchange economies of overlapping generations is available in Section 20.H  (Ovelapping Generations) of Mas-Colell’s et al.’s Microeconomic Theory.

Growth with overlapping generations is presented in Chapter 9 (Growth with Overlapping Generations) of Acemoglu’s Introduction to Modern Economic Growth, excluding Sections from 9.6 to 9.8.

You will find a proof of sufficiency of the Euler Equation and the Transversality Condition in Theorem 6.10 of Acemoglu’s An Introduction to Modern Economic Growth.

A continuous-time and a discrete-time versions of Ramsey optimal growth are presented in Chapter 8 (The Neoclassical Growth Model) of the same textbook.

An alternative presentation can be found in Chapter 2 (Optimal Growth) of Reichlin’s Notes on Macroeconomic Theory.

During the course students will be working on home assignments. These assignments will be graded and, overall, will count for 40% of the final grade. The final exam will consist of a written test cointaining, tentatively, two exercises and two theoretical questions. The final exam will count for the residual 60% of the final grade.

I advise you complete the study of Chapter 2 (The Solow growth model) in Acemoglu’s Introduction to Modern Economic Growth.

You will find the relevant material on dynamic programming in Chapter 6 (Infinite-horizon optimization and dynamic programming) of Acemoglu’s Introduction to Modern Economic Growth, limiting your study to Sections from 6.1 to 6.3.

Upon request, this is the relevant material in Acemolgu's Introduction to Modern Economic Growth:

• Chapter 2 - The Solow Growth Model;
• Chapter 5 - Foundations of Neoclassical Growth;
• Chapter 6 - Infinite-Horizon Optimization and Dynamic Programming;
• Chapter 8 - The Neoclassical Growth Model;
• Chapter 9 - Growth with Overlapping Generations.

You will find an extended illustration and discussion of the Solow growth model in Chapter 2 (The Solow growth model) of Acemoglu's Introduction to Modern Economic Growth (up to section 2.6 included).