• Classes are M, W 1:30-3:00 in McNeil 167-168.

• Sometimes it will be on Fridays somewhere between 12:00 and 4:30 pm. Please take a look at this page every Monday morning to check for the weekly schedule.

• Off Hours: Wed 10:30 to 11:30. (better by appointment).

• The account to deposit the homeworks is /econ/econ751 in sun.ssc.upenn.edu.

What is in this page?

• What are we doing? (3/22/00)

  Brief description of previous classes and next one.

• Homeworks. (3/22/00)

  List of homeworks and due dates.

• Course description. (1/15/00)

  Brief description of previous classes and next one.

• Calendar. (1/15/00)

  Info about change of dates/locations/instructors/office hours.

• Textbooks or other class material (1/15/00)

• Grading rules. Never change. (1/15/00)

• Guest Stars (1/15/00)

  List of invitees to lecture in class.

What are we doing?

Day 1.

We read this document. After that we looked at the general problem of optimal taxation. We almost finished proving the fundamental theorem of optimal taxation that shows the equivalence between a Comp Eq and an allocation that satisfies feasibility and implementability.

Day 2.

We finished the discussion of the Ramsey problem in the static context with n goods and labor and start characterizing the solution: We argued for higher taxation for income inelastic goods (under separability) and for equal taxation under homotheticity.

Day 3.

We talked about the no taxation of intermediate goods. We started defining the notation for the stochastic growth model.

Day 4.

We continued setting up the Ramsey equilibrium in the stochastic growth model. In particular we look at the government budget constraint and at the proposition that yields the Ramsey problem.

Day 5.

We finished the proof of the main proposition, and talked about the indeterminacy of the capital income tax rates, and of possible additional criteria to fix them. We also restated the problem by using a function W, that makes the problem have two separate parts that can be solved sequentially. One of those parts is time independent, while the other is not.

Day 6.

We showed the properties of taxation if the economy converges to a stationary situation. We also discussed taxation with two types of agents.

Day 7.

We showed that if utility is separable in cons and labor and if the cons part is CRRA, then taxes on capital are zero after the first period..

Day 8.

We showed how in a model without capital, optimal taxation inherits the structure of the shock. We also documented the nature of the time consistency problem in the simple model of Chari in the QR.

Day 9.

We defined Markov perfect equilibria of the growth model.

Day 10.

We reviewed Markov perfect equilibria. We looked at some of its quantitative properties and we will expand it to look at economies with debt.

Day 11.

Marina started telling us how to thnk of all possible equilibria of these economies as outcomes of repeated games and also of how to work with them in a recursive manner. She follows Phelan and Stachetti. We devoted some time to two issues that are not obvious. First that a Walrasian equilibrium given a strategy by the government is NOT the same that given a policy. The difference is that that former specifies the outcomes of the public sector for policies that future governments will not take, but would have taken had current governments done something different. The other issue pertains the definition of the new state variable for the use of recursive formulations and its timing conventions. This will be resolved on Wednesday.

Day 12.

Marina continued with her job. She dealt with the problems raised. She mapped the set of equilibria in sequence language into the set of equilibria in recurcusive language, by using two things. First, the original equilibria is used to define one shot games. Then Marina defined an operator that takes possible continuation values and maps to current continuation values with the aid of the auxiliary one period games that she had defined. It turns out that the largest fixed point of that operator is the set of values of all equilibria of the original game.

Day 13.

Marina gave us her final thoughts on the Phelan Stachetti paper. Then we discussed loosely some of the problems associated to policy analysis. Finally, we started discussing political economy. The issue at hand being political aggregators.

Day 14.

We looked more at political economy growth models. We posed a recursive notioin of the problem and started comparing the equilibrium concepts with full and limited rationality. What we do is in part from my JEDC paper with Krusell and Quadrini.

Day 15.

We finished with the problem of how to distinguish the fully rational with the boundededly rational model of political equilibrium.

Day 16.

We started looking at the problem of how do taxes get determined in a a multicountry economy with the possibility of capital flight.

Day 17.

We finished looking at the problem of how do taxes get determined in a a multicountry economy with the possibility of capital flight. In particular, contrary to what we had guessed in class we established what the dynamic problem of firms are. This is important because firms do not maximize expected profits, just present value.

Next Day, 18.

Andrea will talk to us regarding the issue of how is it that minorities get perks from the government.

Homeworks and due dates.

Students will place the solution in electronic form in /work/econ/econ751 in subdirectories that each student should create under her own name. The solutions should be in pdf format. You will not have access for another week or so.

Homework 1. (1/24/00), Due February 10. Show that the solution to the Ramsey problem of the first model that we looked at can be implemented with the tax rate of good one being zero as long as we can tax labor.

Course Description (this may change).