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Partial differential equation models in macroeconomics.

Yves Achdou¹, Francisco J Buera², Jean-Michel Lasry³

¹Université Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, Paris, France.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|October 8, 2014

Summary

Mathematicians can explore challenging partial differential equations (PDEs) from economics. This research highlights complex PDEs in macroeconomics, offering new avenues for mathematical study and open questions.

Keywords:

firm size distribution heterogeneous agents income and wealth distribution mean field games

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Area of Science:

Economics and Mathematics
Mathematical Economics
Applied Mathematics

Background:

Macroeconomic models address critical economic questions.
These models generate complex partial differential equations (PDEs).
The mathematical structure of these PDEs presents significant challenges.

Approach:

Introduce and exemplify PDEs arising in macroeconomics.
Review existing mathematical knowledge on their properties.
Identify and present open research questions.

Key Points:

Partial differential equations (PDEs) from macroeconomics offer rich mathematical problems.
The complexity of these economic PDEs is a key feature.
Understanding these PDEs can advance both economics and mathematics.

Conclusions:

Encourage mathematicians to investigate these challenging PDEs.
Highlight the interdisciplinary potential for advancing economic theory and mathematical understanding.
Outline future research directions in this specialized field.