Lecture 17: Equilibria in systems with distortions.

In the final lecture of the course, we study some problems of solving systems with distortions. As we have seen, equilibrium and Pareto efficient allocation of a system coincide under specific conditions only, so in cases where any of these circumstances are not met the efficient allocation and the equilibrium of the same system are

Lecture 15: Applications of equilibrium theory. Part A.

In Lecture 15 we start studying the implications and applications of our previous results in general equilibrium theory. First of all, we define the key concept of recursive competitive equilibrium of rational expectations equilibrium. This is the core theoretical basis of dynamic macro, invented by Muth in his ‘Rational expectations and the theory of price

Seminar session 7: Bellmanize, all over again! An investment problem.

In this seminar session we turn back to the use of the Bellman equation again. The problem is about an astronaut who is supposed to survive on the Mars by growing potatoes. The dynamic aspect of the problem is familiar. Investment in future crops can be increased only at the cost of giving up some

Seminar session 6: Bellmanize, again! An information problem.

In this short TA session, we return to the art of formulizing the Bellman equation. Recall that mastering this art, referred to as the imperative ‘Bellmanize!’, is one of the basic creeds of the Chicago School of Economics—this is the reason why we are also trying to learn as much as we can about this

Lecture 12, Addendum 2: The discrete-space inventory problem in MATLAB.

In this short MATLAB session, we revisit the inventory problem of Lecture 12. Our goal is to formulize the problem to be solvable in MATLAB to have a clear visual representation of the dynamics of the optimally managed inventories. Throughout the exercise we actively use what we learnt in the previous session about defining Markov

Seminar session 5: Bellmanize. A time-allocation problem.

The basic creed of Chicago economics is ‘Bellmanize!’. The Bellman equation, named after Richard Bellman, is a key part of the dynamic programming approach we use to analyze intertemporal optimization problems. Chicago economics lays a huge emphasis on building the ability of translating intertemporal problems into the formal language of the Bellman equation. In this

Lecture 9, Addendum 2: Applications of stochastic dynamic programming. A model of search unemployment.

In this final extra part of Lecture 9, we deal with a model of search unemployment. Search models are special. On the one hand, there is a lot of economic phenomena that can best be described as a search problem–just think about selling an old chair when you, the seller, look for the best offer.

Lecture 9, Addendum 1: Applications of stochastic dynamic programming. Investment under uncertainty.

Investment under uncertainty is a widely celebrated paper by Lucas and Prescott from 1971. In this exercise we meet again the paper we have already met in Chapter 10, and now we learn more about the characteristics of the Markov process defining the demand shock faced by the surplus-maximizing industry. First and foremost, we are

Lecture 9: Applications of stochastic dynamic programming. The one-sector model of optimal growth.

In this lecture we go over some applications of the theory of stochastic dynamic programming in the framework of the well-known basic neoclassical growth model. After studying the sequential form of the problem, we turn to the Bellman equation. By checking if the necessary conditions hold we show that there is a unique value function

Seminar session 4: Solving a Riccati equation for the optimal linear regulator.

When we have a quadratic one-period return function, solving the problem in the optimal linear regulator framework is an effective option. At the core of the framework, there is a Riccati matrix difference equation, as described in Chapter 5 of Ljungqvist – Sargent’s (2018) Recursive macroeconomic theory. Finding the policy function (which is always linear,