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I was formerly an economics major and now also majoring in mathematics. I want a textbook that is rigorously based on mathematics; not just using mathematcis whenever the author wants, but in a more unified way to explain a concept. I've learned enough mathematics in undergraduate level so mathematics will hardly be a problem. I've searched for information, but I really wanted textbooks that satisfy this specific condition; explaining concepts with sound mathematics in a unified way.

Any help will be grateful.

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You should also try Advanced Microeconomic Theory (3rd Edition) by (Jehle, Reny, 2011). Note that, imho, Mas-colell-Whinston-Green (1995!) is the best choice for those with initial background in Math switching to Economics. When it comes to Economics majors the former seems to be more appropriate (and more modern). For modern Macro with strong math see Introduction to Modern Economic Growth (Acemoglu, 2009). To integrate the micro/macro problems with econometrics and math see "Economic Modeling and Inference" (Christensen & Kiefer, 2009). Hope, that helps.

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For microeconomics with a proper mathematical formalisation, you will want a graduate textbook. The standard book is Microeconomic Theory by Mas Colell, Whinston, and Green.

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  • $\begingroup$ Thanks. Any recommendation for macroeconomics at graduate level with proper mathematical foundation? $\endgroup$ – Taxxi Mar 27 '15 at 22:00
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    $\begingroup$ Macro seems to be a lot less unified than micro so I guess you will need several books. Books that come to mind are "Monetary Theory and Policy" by Walsh, "Advanced Macroeconomics" by romer, "Recursive Macroeconomic Theory" by Ljungqvist and Sargent, and "Recursive Methods in Economic Dynamics " by Stokey et al. But get a second oppinion from a real macroeconomist . $\endgroup$ – Ubiquitous Mar 27 '15 at 23:20
  • $\begingroup$ Thanks, that was really helpful. I'll just wait for some additional replies and accept your answer if no better recommendation comes up. $\endgroup$ – Taxxi Mar 27 '15 at 23:52
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    $\begingroup$ Neither Romer nor Ljungqvist and Sargent come close to being rigorous in mathematics. Good macro textbooks though. $\endgroup$ – Michael Mar 28 '15 at 8:38
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I would like strongly recommend David Kreps' latest textbook, Microeconomic Foundations I: Choice and Competitive Markets .

It contains true virtuosity and is very inspiring.

Take utility representation theorem as an example. Kreps forsake the assumption in MWG of taking $\mathbb R^n$ as the underlying space so that readers won't be left with the false impression that this theorem is of limited interest.

I also $\heartsuit$ the presentation of GE as a generalized NE which helps developing connections between different areas.

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For economics, both micro and macro, written in mathematics as mathematicians would know it, try the Handbook of Mathematical Economics series, 4 volumes in total.

See for example, this very nice article by Mas-Colell and Zame in volume 4 on general equilibrium. (Microeconomics, for example, by Mas-Colell-Whinston-Green falls far below this standard of rigor.)

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  • $\begingroup$ Thanks for the suggestion. I think I have to read the Mas-Colell-Whinston-Green first and then read the handbook; it seems to be rather specific in certain fields. $\endgroup$ – Taxxi Mar 28 '15 at 11:43
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    $\begingroup$ Yeah, I don't claim the Handbook series should serve as introductions. MWG doesn't use more than calculus but it's an excellent intro to micro. $\endgroup$ – Michael Mar 28 '15 at 12:15
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    $\begingroup$ I'm familiar with both MWG and the Mas-Colell/Zame-article. Where do the standards of rigor (and not just the mathematical sophistication) differ? $\endgroup$ – Michael Greinecker May 30 '15 at 20:21
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Given what you said about mathematics, I would recommend Theory of Value by Gerard Debreu. This book is probably more than what you need, but it defines almost everything clearly. Debreu writes in the famous Bourbaki style so mathematics is rigorous enough.

For macro it is hard to get everything in the same book. There are books very rigorous, but they generally covers techniques that are essential to do research.

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I think it depends on what exactly you want to focus on within Macroeconomics and Microeconomics.

For Microeconomics, THE book is Microeconomic Theory by Mas-Colell, Whinston and Green For Macroeconomics, Advanced Macroeconomics by David Romer is the book

In my opinion, both books cover the most important issues in each branch of Economics, and the development authors give is mathematically grounded. But again I would say it depends on what you want to focus on.

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Macroeconomics by William Mitchell, L Randall Wray, and Martin Watts. Macroeconomics through an Modern Monetary Theory (MMT) lens.

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