## Macroeconomics G105 Fall Quarter 2016, Last Four Weeks

##### José-Víctor Ríos-Rull: vr0j@upenn.edu, <!-- var LastUpdated = document.lastModified; document.writeln ("Page last updated " + LastUpdated ); // --> This page requires JavaScript, which is not enabled on your browser.

• Course Code: ECON G105, Term 1, Last four weeks

• Compulsory course for M.Res. students

• Prerequisites: Knowledge of macro and micro at MSc level

• Course Owner: José-Víctor Ríos-Rull:

• Office Hours: Before and after class and by appointment.

• Homepage www.sas.upenn.edu/~vr0j/uclg105f16/index.html

• email: vr0j@upenn.edu,

• Teaching assistant: Mr. Carlo Galli (carlo.galli.14@ucl.ac.uk)

• ## Class notes from a similar course

What we are doing each day.
1. #### November 24

I describe the course and discuss some context of what are the main facts over which macro has to be organized around:
1. output per capita has grown at a roughly constant rate
2. the capital-output ratio (where capital is measured using the perpetual inventory method based on past consumption foregone) has remained roughly constant
3. the capital-labor ratio has grown at a roughly constant rate equal to the growth rate of output
4. the wage rate has grown at a roughly constant rate equal to the growth rate of output
5. the real interest rate has been stationary and, during long periods, roughly constant
6. labor income as a share of output has remained roughly constant
7. hours worked per capita have been roughly constant.

I discuss what restrictions do these facts pose on the models that we use.

I discuss some of the limitations of this point of view.

I also discuss what is the meaning of an equilibrium (a mapping from environment to allocations) and then talked about why the social planner problem may be a problem whose solution is interesting (it is because it is the unique equilibrium of the economy once we use the welfare and other theorems). We talk of how an Arrow Debreu Equilibrium for the growth model, supports the social planners solution using the second welfare theorem. I refer to how to build a sequence of markets equilibrium out of an Arrow-Debreu equilibrium (and viceversa) and argue that we can then solve for Social Planner problem sometimes, but that we do so using recursive methods (dynamic programming). Why not then always recursive methods? This is to define equilibria recursively.

We define Recursive Competitive Equilibrium. We look both at rational expectations equilibria and at recursive equilibria with arbitrary expectations.
2. I go over the role of the first welfare theorem (to yield uniqueness). I continue by describing equilibrium of economies where the welfare theorems are of no use. A government financing a public good with lump sum, labor and capital income taxes, and then with debt.
3. #### Nov 25

I finished the discussion of debt in RCE.
4. I talked about RCE with agents differing in wealth and or skills. We also viewed the economy with two countries. We looked at the Lucas tree and discussed the role of supply and demand shocks in generating business cycles. We then extended the Lucas tree to have some search frictions in the goods markets. We posed the comepetitive search equilibrium for this economy.
5. #### Dec 1

We will define one period ahead Arrow securities. We will use them to price stuff.
6. Measure Theory and Hopenhayn's Industry Equilibria.
7. #### First half of December 2 and Second half of December 9

Models with Incomplete Markets and Heterogeneous Agents: The Aiyagari Economy.