Mathematical Economics I

2019-2020
Dit vak wordt in het Engels aangeboden. Omschrijvingen kunnen daardoor mogelijk alleen in het Engels worden weergegeven.

Doel vak

- Acquaint participants with classic mathematical models of economic
decision making developed in the second half of the twentieth century,
the fundamental critique of fact-driven behavioral economics (classic
anomalies) and a sketch of economic models of the future.
- The focus is on three topics: individual decision making, collective
decision making (voting in groups or societies) and interdependent
decision making (or game theory).
- Participants understand the purpose and the mathematical properties of
each model. Participants are able to execute several strategies to
calculate simple models by hand, embed such strategies in algorithms
(pseudo-code for software) and being able to use freeware Gambit.
- Participants are confronted with the important difference between
descriptive theory, aimed at explaining and predicting reality, and
normative theory, what intervention should ideally be done.
- Economic modeling of reality, embedding economic models in software
and bringing economic models to the data will also be addressed.
To summarize, participants will learn, understand and reflect on
important economic models, their implementation in algorithms, and
experiments.

Inhoud vak

Society asks for evidence-driven economic theories that are ready for
use in economic decision making situations. This requires on the one
hand descriptive theory that explains and predicts economic reality, and
on the other hand normative theory that guides the decision maker what
economic intervention should ideally be done. The rise of Behavioral
Economics and the financial crisis of 2007 made clear that classical
economic models were not up to this task. Since then, (mathematical)
economics is in transition, which is reflected in this course. It also
requires more academic reflection from participants than they are used
in other EOR courses.
This course deals with modeling individuals, companies, governments,
NGOs that take economic decisions in an economic context, e.g. Apple
deciding its pricing strategy taking into account its competitors. The
interaction of decision makers and their economic surrounding is at the
heart of this course. We distinguish three major topics: individual
decision making, collective decision making (f.e. how do groups or
societies reach decisions) and strategic decision making (f.e. how to
bid in an auction anticipating others’ bids).

Individual decision making (period 1)
In order to evaluate whether a decision is a good decision, economists
developed the notion of preference relations that rank available
alternatives and maximization of objective functions, called utility
functions. From a normative perspective, you deal with calculating the
utility maximizing alternative, which is facilitated by studying
constructive mathematical proofs that can be transformed into pseudo
code for software (programming is outside the scope of this course).
From a descriptive perspective, you learn whether the mathematical
structure imposed is evidence-based.
Classical economic theories include market demand of price-taking
consumers, the market supply of output and market demand for inputs by
price-taking firms, and discrete choice (popular in A/B testing in Data
Analytics). Decision making under risk discusses expected utility
theory, the Allais’ paradox and Prospect theory.

Collective decision making (period 1)
Individual decision makers often participate in groups or teams, and
live in a society. Is it mathematically possible to derive group
preferences from individual preferences? No, what then? This part of the
course is merely normative in analyzing classic ranking methods and
voting procedures that are observed in reality. These methods and
procedures will be compared with each other. One criterion employed is
Pareto efficiency.

Strategic decision making (period 2)
In many, if not all, economic situations what eventually happens depends
upon decisions made by more than one individual of individuals. Whether
your team assignment is evaluated with a high grade depends upon your
own effort and that of your other team members. Or, whether you win the
item in an auction depends upon your own bid strategy and that of
others. In many economic situations some individual are better informed
than others, which is called private information. For example, in Poker
you know the cards you are holding while the others do not.
Predicting what others will do, how they predict what you will do, etc.
is crucial in the mathematical analysis of strategic decision making. In
this course, classical game theoretic concepts of Nash equilibrium and
backward induction, as well as recent evidence-based concepts such as
k-level reasoning and (agent) quantal response equilibrium, will be
discussed. Because calculations for medium-sized games by hand is rather
hard, you will learn to solve such games numerically in Gambit.
(Freeware Gambit is an open-source software tool programmed in Python.)
Interpretation of computed solutions and its economic interpretations
will be addressed. Gambit will be part of an assignment that counts as
part of the final grade.
Game theory is widely applied in industrial organization (the modeling
of market competition). Some influential models such as Cournot
competition in quantities (e.g. OPEC cartel), Bertrand competition in
prices, Hoteling’s model of spatial competition are part of this course.

Onderwijsvorm

Classes. One lecture and one practical per week. Active participation is
key.
Participants may be partitioned to groups for the practical.
Participants of the practical PREPARE BEFORE coming to class and are
expected TO PRESENT their answers before the Canvas in class and
discuss where problems in solving questions arose.

Toetsvorm

One team assignment based upon Gambit in period 2 – team assessment
Partial exams in October (covering period 1) and December (covering
period 2) – individual assessment
An exam in March (covering period 1 and 2) – individual assessment
Individual Assignment (presenting before class) – individual assessment

Literatuur

A syllabus that contains exercises and that is supplemented by some
videos from Massive Open Online Courses (MOOCs). All compulsory
literature and links will be provided through Canvas.

Doelgroep

This course is an obligatory second-year course in the bachelor
Econometrics and Operations Research. Exchange students and other
students from other bachelors, such as
Economics, are welcome but should be motivated to follow a course with a
lot of mathematics. Preferably, you have a sufficient mathematical
background and can reason logically. For more information, or in doubt,
contact the course coordinator.

Aanbevolen voorkennis

Knowledge of elementary mathematics and elementary probability theory.
This includes differentiation, the Lagrange method, expectation, Bayes
Rule.
For EOR students this translates in knowledge from Analysis I and II,
Linear Algebra and Probability Theory, and to a much lesser extent
Finance, Statistics and Programming.

Algemene informatie

Vakcode E_EOR2_ME1
Studiepunten 6 EC
Periode P1+2
Vakniveau 200
Onderwijstaal Engels
Faculteit School of Business and Economics
Vakcoördinator dr. H.E.D. Houba
Examinator dr. H.E.D. Houba
Docenten dr. H.E.D. Houba
prof. dr. J.R. van den Brink

Praktische informatie

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Werkvormen Hoorcollege, Werkgroep
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