Econ 510a General Economic Theory: Macroeconomics

Transcription

1 Econ 510a General Economic Theory: Macroeconomics Fall 2016 Instructor: Zhen Huo Office: HH 28 Room 303 Office Hours: Monday 3:30-5:00 Teaching Fellow: Marcos Frazao Lecture: TTh , Room B8 1 Overview This is the first half of the first semester in the graduate macroeconomics sequence. The aim is to lay the foundation of modern macroeconomics. We will learn how to properly define an equilibrium, including the Arrow-Debreu equilibrium and sequential market equilibrium. We will show that solving a social planner s problem is equivalent to solving the allocation in the market equilibrium under certain conditions. Then we move to dynamic programming, which is a standard tool in modern economic analysis. This tool is useful in solving the social planner s problem, and many others. We will first cover its mathematical properties in the deterministic case. Some of the applications of dynamic programming can be solved by hand, but most of them can only be solved numerically. We will learn briefly how to do it. One important application is to use the dynamic programming tool to study the growth model, and how to link the growth model with data. We then turn to the definition of recursive equilibrium. Recursive equilibrium (RE) is a very useful concept in formalizing many economic problems in a parsimonious way. We will learn the big K, little k trick. When a sequential market equilibrium is not equivalent to a social planner s problem, the dynamic programming tool may not be able to be applied. However, the recursive competitive equilibrium always allows us to use the dynamic programming tool to solve for the equilibrium prices 1

2 and allocations. In previous applications, we abstract from the behavior of the government. We will introduce the government by studying the tax distorted competitive equilibrium (TDCE). We will focus on the optimal taxation problem faced by the government. Particularly, we will derive the celebrated Chamley-Judd result via the primal approach. Finally, if we have time, we will also look at the consumption-saving problem faced by an individual consumer who receives a flow of stochastic income. We will extend the results derived at the beginning of this class to a stochastic environment. 2 Organizational details There will be weekly problem sets and a closed book midterm exam on October 25th during class time. The second half of the course, taught by Tony Smith, will be evaluated in the final exam. The midterm and final exam will be given equal weights in the final grade, accounting for 80% of the final grade. The problem sets account for the remaining 20%. 3 s We will rely on mostly Methods in Economic Dynamics, by Stokey, Lucas and Prescott (SLP) Recursive Macroeconomic Theory, by Ljungquivst and Sargent (LS) 2

3 4 Tentative Schedule No Date Day Topic Lecture TA Problem Session Set 1 9/1 Th CE Competitive equilibrium and planner s problem, endowment 2 9/6 T CE Competitive equilibrium and planner s problem, production PS 1 3 9/8 Th DP Principle of optimality 1 4 9/13 T DP Contraction mapping and examples PS 2 5 9/15 Th DP Implementation on computer 2 6 9/20 T DP Growth model with data PS 3 7 9/22 Th RE RE in growth model 3 8 9/27 T RE More examples of RE PS 4 9 9/29 Th TDCE Primal approach /4 T TDCE Chamley-Judd 11 10/6 T TDCE Solve Ramsey problem 5 PS /11 T Consumption Risk Sharing 13 10/13 Th Consumption Income fluctuation /18 T Consumption Income fluctuation PS /20 Th Review /25 T Midterm exam 5 Syllabus 5.1 Competitive Equilibrium Arrow-Debreu and sequential market equilibrium Welfare theorem SLP, Chapters Dynamic Programming Principle of optimality Contraction mapping Growth model 3

4 SLP, Chapters 3, Recursive Equilibrium Recursive competitive equilibrium SLP, Chapter 16 LS, Chapter Tax Distorted Competitive Equilibrium Tax Distorted Competitive Equilibrium Ramsey problem, Chamley-Judd, Werning-Straub LS, Chapter 16 Chari, V.V. and P. Kehoe. (1999), Optimal Fiscal and Monetary Policy, Handbook of Macroeconomics, Vol 1, Straub, Ludwig, and I. Werning. (2014), Positive Long Run Capital Taxation: Chamley-Judd Revisited, NBER Working Paper No Consumption-Saving Problem Risk sharing in complete markets Income fluctuation problem 4

5 LS, Chapter 17 Lecture notes 5