The Arrow-Debreu model for exchange economies with a finite number of commodities and consumers.Kakutani fixed-point theorem.
A Walras equilibrium in a neoclassical exchange economy.Welfare theorems.
Riesz spaces. Linear functionals and linear operators.Riesz spaces of commodities and prices.Model for exchange economy with infinitedimensional space of commodities and countably many consumers.
Riesz spaces in mathematical economics
2019/2020
Programme:
Mathematics, Second Cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
M5
ECTS:
6
Language:
slovenian, english
Course director:
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Content (Syllabus outline)
Readings
C. D. Aliprantis, D. J. Brown, O. Burkinshaw: Existence and optimality of competitive equilibria, Springer-Verlag, Berlin, 1990.
C. D. Aliprantis: Problems in equilibrium theory, Springer-Verlag, Berlin, 1996.
C. D. Aliprantis, O. Burkinshaw: Locally solid Riesz spaces with applications to economics, Mathematical Surveys and Monographs 105, American Mathematical Society, Providence, RI, 2003.
Objectives and competences
Students learn about the application of the theory of Riesz spaces in mathematical economics. They get acquainted with
some models of exchange economies.
Intended learning outcomes
Knowledge and understanding:
Knowledge and understanding of the basic concepts of the theory Riesz spaces. The ability of its use in mathematical economics.
Application:
Using the theory of Riesz spaces on models of exchange economies.
Reflection:
Understanding of the theory and the ability to apply it to concrete examples.
Transferable skills:
Identifying and solving problems.Formulation of nonmathematical problems in mathematical language.Ability to use domestic and foreign literature.
Learning and teaching methods
Lectures, exercises, homeworks, consultations, seminars
Assessment
Homeworks
Exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
Lecturer's references
Roman Drnovšek:
DRNOVŠEK, Roman. Triangularizing semigroups of positive operators on an atomic normed Riesz space. Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, 2000, let. 43, št. 1, str. 43-55. [COBISS-SI-ID 9480281]
DRNOVŠEK, Roman. On positive unipotent operators on Banach lattices. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2007, vol. 135, no. 12, str. 3833-3836. [COBISS-SI-ID 14382937]
DRNOVŠEK, Roman. An infinite-dimensional generalization of Zenger's lemma. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 2012, vol. 388, iss. 2, str. 1233-1238. [COBISS-SI-ID 16214617]
Boris Lavrič:
LAVRIČ, Boris. The isometries of certain maximum norms. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2005, vol. 405, str. 249-263. [COBISS-SI-ID 13679961]
LAVRIČ, Boris. The isometries and the G-invariance of certain seminorms. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 2003, vol. 374, str. 31-40. [COBISS-SI-ID 12751193]
LAVRIČ, Boris. Monotonicity properties of certain classes of norms. Linear Algebra and its Applications, ISSN 0024-3795. [Print ed.], 1997, let. 259, str. 237-250. [COBISS-SI-ID 7388761]
