Reddit reviews Microeconomic Theory
We found 29 Reddit comments about Microeconomic Theory. Here are the top ones, ranked by their Reddit score.
Reddit reviews Microeconomic TheoryWe found 29 Reddit comments about Microeconomic Theory. Here are the top ones, ranked by their Reddit score.
What are you interested in learning about? I would be weary about the books peppajac217 suggested, I don't know anything about them, but such books usually don't go into any detail and are often very biased (some of the amazon reviews make them sound pretty awful). (Come on guys and girls, this is the math reddit, don't be like the rest of the idiots who claim economics is all bullshit and only ever used for bad reasons, that is incredibly naive and stupid).
Game theory (not sure if that needs explaining or not?) is used a lot for economic theory (particularly for microeconomics), so having at least a basic understanding of that can be useful, and it's a really fun topic. If you want a simple treatment, get Osbornes introductory text, otherwise get either Myersons or Fudenberg and Tiroles.
Microeconomics is mostly concerned with situations/decisions at the "micro" level, whether that be for individuals, producers, small groups etc. My favourite part of microeconomics is consumer theory which concerns itself with how people can optimally use their time and resources to maximise the enjoyment they get out of life. The core consumer theory basically assumes people/consumers are able to form a total order over the set of goods as otherwise you get messy properties (like cyclic ordering), a lot of people give economics flack for such assumptions, they're idiots, due to the impredictable nature of human decision making, economics is quite complicated, but it doesn't mean people shouldn't try to study it, such assumptions allow us to make interesting insights into the problem being studied (something physicists and other scientists do all the time) and one can always relax any of the assumptions they wish when analysing stuff if they want to. There is also producer theory which concerns itself with how producers can optimally produce to maximise benefit to society, profits or any other such objective, then general equilibrium theory basically takes these two subjects and throws them together to study it all at once, although the basics often take out producers and deal with a set of consumers with a starting allocation of resources. If you are more interested in learning about microeconomics, the most common graduate level text is the one from Mas-Collel, Green and Whinston, although you might want to look somewhere else to get a basic understanding of microeconomics before jumping right into that text. (People bitch about the amount of maths in that text, but if you have some background with differential equations, linear algebra and real analysis (ripping that straight from an amazon review, but it's about on par) then I don't see why you shouldn't be able to follow it).
Another part of microeconomics that is really interesting is industrial organisation (although one could possibly just class it with producer theory) which is concerned with studying the different types of market structure, like competitive markets, monopolies, duopolies etc. I'm not really sure about resources for this, I believe Tiroles text is considered good.
And now we get to macroeconomics, which is a beast. I work as an RA for a macroeconomist, have a degree in economics (I did undergrad majors in cs, economics and maths, I'm currently doing an honours year in pure maths) and yet the more I learn about macroeconomics, the less I feel like I understand what the fuck is going on. I feel like a lot of people equate economics with predicting the future state of an/the economy (like studying weather is only concerned with predicting the temperature long in the future? or biology is only concerned with predicting the exact population of a species long into the future?) which can be really annoying, but generally macroeconomics concerns itself with what happens aggregately and how that affects us as a whole. I'm not even going to attempt to suggest where the best place to look for learning macroeconomics, as I have no idea. Just note that it's rather complicated (anyone that claims otherwise is an idiot) and there is often a lot of disagreement on the topics that arise. Generally most economists consider most of the Austrian school to be a bunch of whackos (which is most certainly true for the large bulk of self called "Austrian economists" with absolutely no economics training, or a couple of undergraduate classes in college), I personally don't feel I have a good enough understanding to really hold my own opinions (not like it stops everyone else from it though right? It really annoys me how many people are willing to have an opinion on economics but not with physics or a lot of other subjects).
Edit: I should probably mention econometrics, which is basically the application of statistics to testing claims in economics. Sure that's a bit "shady", but as I've mentioned before, economics is complicated, having a "best approximation" of things is better than making wild guesses. One problem is that a lot of "economists" are idiots and shouldn't be calling themselves as such, and hence a lot of the work they do is absolute garbage as they aren't suitably qualified to analyse stuff at a level of rigour that I would consider acceptable with our current knowledge of maths and other subjects, this is also a problem in the natural sciences, but nowhere near as much as with economics and other social sciences.
Edit2: Actually, a fun topic is international economics (which arguably fits into macroeconomics), learn what comparative advantage is and why trade is generally considered good for society as a whole.
Where are you in economics right now? Undergraduate? Graduate?
Advanced mathematics appears everywhere in economics, though your mileage may vary depending on your definition of "advanced". As a mathematician, I suspect that quantitative finance contains the most advanced mathematics, since in modern mathematics research the majority of interaction with economics is through quantitative finance. But unless you plan on doing the most advanced math, there's more than enough advanced math in non-finance economics to keep you interested.
Generally speaking, professional economists build up some skill in real and functional analysis, as well as a variety of other skills like optimization, stochastics, and PDEs, depending on their specific research interests. These are all graduate-level math topics, so I'd consider them reasonably advanced. Take a look into econ PhD prelim coursework. When I took the sequence, we used the texts Microeconomic Theory by Mas-Colell-Whinston-Green, Recursive Macroeconomic Theory by Ljungqvist and Sargent, and Econometrics by Hayashi. I think they're good springboards for you to evaluate the math in higher economics.
In quantitative finance, I'd maybe start by checking out Portfolio Risk Analysis by Connor, Goldberg, and Korajczyk, then if you're still interested, I'd pick up measure-theoretic probability. I recommend Probability with Martingales by Williams. Once you're comfortable with measure theory, look through Stochastic Calculus and Financial Applications by Steele. You'll very quickly enter the area of research mathematics while studying quantitative finance, e.g. jump-diffusion models and Levy processes appear in the pricing of exotic derivatives, and they're heavily studied by even pure mathematicians.
There's no substitute for just picking up a graduate economics textbook and staring at the math yourself.
In general, comfort with multivariable calculus and linear algebra are necessary at the econ PhD level. Familiarity with theoretical mathematics is also a plus.
It's generally considered important to take a lot of math as an undergrad, and if you don't have at least a minor, it will be difficult to compete with those who do, or even have a second major. I asked my undergraduate advisor a similar question in my sophomore year, and I was told that math courses were the most important thing you can do in preparation for Grad School. He was right - you can have holes in your Economics knowledge, that's what they're teaching you, after all. If you have to go back and learn the math to follow the theory, though, the first year will absolutely bury you. If you want to see what you're up against, your school's library might have a copy of Mas-Colell or Romer, which are the standard first year theory books in Micro and Macro.
Leaving admissions completely aside, you should have a good foundation in Multivariate Calculus, Differential Equations, Linear Algebra, and Analysis just to make sure you don't have to learn that alongside your actual coursework. By the time you take those classes and the prerequisites, you may find that you already have basically everything for a math minor. Add a couple stats/probability classes on top to fill out the credits, and you're probably done.
Before you get too discouraged, note that you don't have to do really well in those courses to be considered. You (presumably) aren't looking to do the sort of high-end theory that's more like pure math, so if you can make it through with Bs and the occasional C you still have a shot at respectable programs. You don't have to be the next Walter Rudin to remember a concept that you saw in an undergrad math class when it shows up on the board and not be totally lost.
EDIT: On a related note, if you want to go to Graduate School, don't be one of those undergrads that shies away from Econometrics. Take as much of it as you can.
The standard graduate micro book is Mas-Colell, Whinston, & Green, https://amzn.com/0195073401 – If you have a solid matrix algebra and vector calculus background it’ll be fine for you.
Personally, I feel like the very complicated technical/mathematical arguments used in economics are often an obscurantist / diversionary tool, not as well justified by concrete evidence as their proponents pretend. It’s important to think carefully and critically about the limits of economic models’ applicability, and about whether their assumptions match reality in any particular case.
It’s not particularly math-heavy, but I recommend Bowles’s micro book as a complement/alternative to standard introductory textbooks at an undergraduate level, https://amzn.com/0691126380
Sometimes they do, however, there are infinite ways to be irrational, so adding too many variables has the problem of over fitting. If you have X observations and X variables, you can always perfectly explain the data, NO MATTER WHAT the actual causal chain is. (I can help give intuition here if you don't buy this).
Also, economics in its purest form is rather technical. I think macro is rather technical too, I believe solving a DGSE with just a few frictions is very hard by hand. So in some sense, these assumptions help make the model more easily solvable (useful, if you are doing the base case, like perfect competition).
Sometimes relaxing these assumptions is useful. However, I would arguing some of them are obviously wrong and not useful is engaging in hindsight bias.
It doesn't look great. A classic book that's used by Phd programs for the micro sequence is [MWG] (https://www.amazon.com/Microeconomic-Theory-Andreu-Mas-Colell/dp/0195073401) (pdf copies exist online). If you can follow it then you have a chance at graduating from a phd program.
I'd recommend taking more upper level and graduate level math classes and getting A's. In addition if you can RA for a professor try to get a co-authorship on some publications. After that, you may have a shot at UCSC, UC Riverside, anywhere 70+ in ranking. Getting into an Econ phd program means that you beat out a handful of candidates, you really have to sell yourself that your better than that handful.
the standard first year graduate level micro textbook
meme answer: mwg
Well, I just read a bunch of stuff. So regarding the marginal cost supply curve debate going on, I googled decreasing marginal cost and came up with this, where the second answer says:
> Again, there's nothing significant, necessary, or truthful about a U-shaped MC curve. It's just a common element in the exposition at the introductory level. More advanced texts (e.g., Mas-Colell) examine other "shapes".
So this is the textbook in question I'm pretty sure. According to this it's "the textbook almost every first year grad micro class uses, regardless of rank." Which seems to be true looking at syllabi on google. Also something by someone named Kreps maybe.
If you google "mas-colell pdf", you can get a pdf of the book. So I did, because I obviously have nothing better to do. Chapter 5, "Production," is about supply stuff. I didn't look at any other chapters. I can't copy and paste from the pdf, and summarizing it is kind of hard and boring, especially because some of it relies on theorems from previous chapters. But here's a couple of points:
If you're looking for an objection to the shape of the supply curve, free disposal seems more important than increasing marginal cost. On page 138 it lists a set of theorems that follow from free disposal and the existence of a production set. These theorems imply the direct relationship between supply and price, but they don't mention increasing marginal cost. This is on page 138 by the way, and it seems like you need some stuff from chapter 3 to get it all.
Second, further down on page 144-146 it shows a bunch of graphs of marginal cost under various situations. Marginal cost is sometimes horizontal, sometimes upward sloping, sometimes U shaped. There isn't one of it just sloping down, it always slopes back up after, and this is consistent with other graphs I've seen. Which honestly makes sense, why wouldn't a firm keep producing until its marginal costs are increasing? When your marginal costs are falling, then what you receive from each sale needs to be falling even faster to deter you from producing more to sell, right?
So I don't know, but I feel like if you want to say economists are ignoring falling marginal costs, or however you want to put it, you need to grapple with economics on the level of rigor of this textbook. This book is a major step up from something like this.
(I feel like a rationalist principle for these kinds of debates is that the conversation should go something like this: "I think X." "Well I think Y." "Hold on, are you a random guy on the Internet?" "I'm a random zuy, but yes." "Oh, right - sorry. Anyway, I don't know a whole lot about this." "Me neither." "Hey, /r/badeconomics is right over there. Let's pop into their open thread and ask them." "$@#! you, Nazi." "Back at you, cuck." It would save me having to do any work ever.)
A reading group for this economics textbook would be really fun, by the way. It was interesting trying to read it, probably even more so if you start at chapter one. It has a lot of math but nothing nerdy STEM types shouldn't be able to handle. It could be a great way to understand economics on a level higher than blogs and Wikipedia can give you, which is honestly kind of interesting. Think of the "well, actually" opportunities for your next Internet debate! We could do a chapter a week or something and focus on comprehension and interpretation. Anyone want to try it?
It depends on what you expect to get out of it. Just because he advocated the labor theory doesn't mean that he was stupid. After all, Aristotle was a geocentrist and Galileo believed that the moon did not cause tides. Mill is an early pioneer of economics and utilitarianism, which on one hand means that he greatly influenced those schools of thought, and on the other hand means that other thinkers have refined and surpassed his ideas. If you want to know more about economic utilitarianism, check out some graduate economics textbooks like this one.
For graduate (at quals-level) courses my undergrad institution used Mas-Colell, Whinston, and Green's Microeconomic Theory and Ljungqvist and Sargent's Recursive Macroeconomic Theory.
Lots of microeconomics. See Mas-Colell, Whinston, and Green.
As others have already said, you'll get even more of this than you want in any graduate micro textbook. I recommend either of the ones from David Kreps from where you are because I think his writing is relatively accessible and chatty. MWG is generally thought of as the definitive one, though
I assume you went through this?
In that case, you could just jump to the next Varian book which, if I remember correctly, is more advanced.
I reckon it beats going full MWG. Though, if you want to do that, be my guest.
The text likely refers to the first welfare theorem in general equilibrium theory, which states that a competitive equilibrium is a Pareto efficient allocation. On one hand, this is often considered a formalization of the invisible hand argument. On the other hand, the model in which the theorem holds abstracts away from a lot of real-world issues that may lead to suboptimal market outcomes. The best way to think about it, IMO, is as a theoretical benchmark that allows us to better understand properties of markets, not as an actual policy-relevant result.
A classic reference is Debreu's Theory of Value. More modern treatments can be found in graduale-level microeconomics texts, such as the one by Mas-Collel, Whinston & Green. There are also several lecture notes online, for example these by J. Levin are quite short and accessible.
I think any intermediate or advanced Microeconomics textbook will provide you with the understanding you're looking for. The flaws in the models are self-evident when analyzing the construction from assumption. The best way to go through this is to start with the very basics work through the 5(ish?) assumptions of consumer theory (axioms of choice I think?) and then start thinking of how the model exists when relaxing said assumptions. During this I would maintain the fundamentals of producer theory (profit maximization) to not overly complicate things initially. Then if you really want to you can start moving on from there (market structure, information etc.). This will give you a better understanding of microeconomics than 99% of undergraduate economic students/grads.
If you can do math this book is ideal and comprehensive:
http://www.amazon.ca/Microeconomic-Theory-Andreu-Mas-Colell/dp/0195073401
PDF:http://graduateeconomist.files.wordpress.com/2012/06/published-1995-microeconomic-theory-by-mas-colell-whinston-green.pdf
If you want to not be bored to death:
Price Theory and Applications - Steven Landsburg
http://www.cengagebrain.com.au/content/landsburg46459_0538746459_01.01_toc.pdf
That's rough. None of the graduate classes I took had textbooks, so I won't be able to tell you if it bores you with math or not. But there's mascollel winston greene (http://www.amazon.com/Microeconomic-Theory-Andreu-Mas-Colell/dp/0195073401) which is the classic one all the schools use and graduate varian (http://www.amazon.com/Microeconomic-Analysis-Third-Edition-Varian/dp/0393957357/ref=ntt_at_ep_dpt_4)
Disclaimer: I am referring to US PhD programs. Things are a bit different in Europe/Canada, but not in terms of material, only structure.
So what you learn in an Econ PhD is drastically different from undergrad. Unless you go to a heterodox PhD program, an Econ PhD is a “STEM” PhD whereas the same can’t be said for most undergrad Econ degrees. I wouldn't say it's impossible to learn the material on your own; however, 1) only wannabe researchers will gain from learning the material at the level of rigor of a Ph.D. program (some of the exercises are just intellectual exercises rather than providing you with tools you can use at a "normal job") and 2) the material is rather high level and it can be difficult to grasp if not being explained by someone who really understands it. The first year sequence at almost all schools is Micro 1, Macro 1, and Econometrics 1 in the fall, the the corresponding “course_title 2” course in the spring.
The first year sequence essentially lays the standard models/techniques in each of the overarching fields (micro, macro, Econometrics) along with the assumptions that those models rely on. The goal is for you to not just be able to memorize the assumptions and solve the standard models, but to truly understand why we need each assumption, what we gain by using it, and what limitations it imposes on the model. That way when we’re doing our own research and we have to relax an assumption or derive a completely new model, we understand what we’re doing.
After the first year, you choose a subfield of specialization (micro theory, macro theory, applied micro, Industrial Organization, behavioral economics, Econometrics, etc) and take courses which continue doing what you learned in your first year, but specifically for your subfield. Then after the second year, you write your dissertation.
If you’re curious what you learn in a first year micro class, here’s a link to download Ariel Rubinstein’s book Lecture Notes in Microeconomic Theory: The Economic Agent. It’s free on his website as long as you provide an email address. While Microeconomic Theory by MWG is a more standard book for first year Micro, I think Rubinstein’s book is better written, especially when compared to the consumer/producer theory sections of MWG. Also, it’s free :)
Λοιπόν ανάμεσα σε διοίκηση και οικονομικά πρώτο πτυχίο κατά τη γνώμη μου, ασυζητητί οικονομικά.
Το να μάθεις σωστά και αυστηρά, πως και γιατί πηγάζουν σαν μαθηματική αναγκαιότητα όλα αυτά που μετά βρίσκουν πρακτική έκφραση μέσα από fields όπως η διοίκηση, τα χρημαστηριακά, τα logistics, το shipping, οι επιτροπές ανταγωνισμού και οι ρυθμιστικές αρχές, το marketing, το data mining και data processing and on and on,
το να μάθεις λοιπόν σωστά και αυστηρά, επανέρχομαι, γιατί λειτουργούν όπως λειτουργούν όλα τα παραπάνω, θα είναι τεράστιο συγκριτικό πλεονέκτημα για εσένα στο μέλλον έναντι των αποφοίτων αυτών των σχολών.
Το MBA είναι καλό όταν νιώθεις από data processing και κάνεις σωστό business modeling και όχι όταν είναι από το ALBA με αποφοίτους απο το BCA που η μόνη παλινδρόμηση που έχουν δει είναι η ενδοπαλάμια πεοπαλινδρόμηση ( no offence ) που έλεγε και ο Μουζουράκης.. Διαφορετικά, δια στόματος Russell Ackoff, "Τους μαθαίνουμε τρία πράγματα: πρώτον, πώς να μιλούν με αυτοπεποίθηση για πράγματα που δεν καταλαβαίνουν. Δεύτερον, τους προσφέρουμε «αρχές» οι οποίες τους βοηθούν να μην κάμπτονται όταν η πραγματικότητα συγκρούεται με τις απόψεις τους. Τρίτον, τους δίνουμε ένα πτυχίο το οποίο τους ανοίγει την πόρτα σε μια εταιρεία στην οποία μπορεί να μάθουν κάτι περί μάνατζμεντ"
Στη συγκεκριμένη φάση και για το μεσοπρόθεσμο μέλλον, κατά τη γνώμη μου δώσε πόνο αυστηρά σε Οικονομική Επιστήμη αντί για μανατζέριαλ προπτυχιακό, μετά ενίσχυσε με ένα μαστερ είτε σε οικονομική θεωρία ( pure econ ) είτε σε applied econ και δευτερευόντως ακόμα κάτι σε data mining/processing.
Όλα μαζί είναι κάτι τύπου 6 χρόνια αν δεν μαλακίζεσαι ή δεν δουλεύεις, θα μάθεις όπως πρέπει να γνωρίζεις οικονομική θεωρία, θα μάθεις κάποιες βασικές εφαρμογές με το πρώτο μαστερ και με το δεύτερο θα μάθεις πως να κάνεις research essentially σαν μέρος της δουλειάς σου ή θα πάρεις ότι χρειάζεσαι για ακαδημαϊκή πορεία.
Από τα πανεπιστήμια δεν έχω άποψη πλην ΟΠΑ οπότε δεν μπορώ να βοηθήσω
important edit: Και για όσους φοβούνται τα μαθηματικά... καμία σχέση με το approach που έχεις δει μέχρι τώρα στα μαθητικά σου χρόνια, ειδικά αν την ψάξεις την φάση και σε επίπεδο ανάλυσης αντί μόνο σε επίπεδο calculus. Πάρε όσα πιο πολλά math courses σου δίνεται η ευκαιρία να πάρεις, θα αποδειχθούν τεράστιας σημασίας στις μετέπειτα σπουδές σου, όποιες και αν είναι αυτές και όσο εφαρμοσμένες να είναι. Άσε που έχει και μια άλλη ομορφιά όταν αρχίσεις να μιλάς για το πως δομείς τα αξιώματα των preferences, πως φτιάχνεις την utility function, πως μελετάς existence. Δεν μπορώ καν να σου εξηγήσω πόσο καλύτερα μαθαίνεις μίκρο από εδώ παρά από εδώ, και όλα pretty much είναι μίκρο <3
I'm curious what utility theory you've read?
Certainly based off what I'd say is the premier graduate text on microeconomic theory, it's quite standard to take preferences as being transitive. That transitivity does then carry over into utility function mapping from there.
I don't mean to be patronizing, but I can't see your argument and to make sure we're not talking past each other, let's rehash the definitions.
Let a person gets utility value from good x equal to U(x).
Transitivity requires that if for a person, U(a) > U(b) and U(b) > U(c), then U(a) > U(c).
So if the guy prefers scotch to gin and gin to wine, then he prefers scotch to wine. Is this always true in every possible collection of choice problems? Eh, maybe not. We can find behaviorists pointing to weird marketing and price packaging phenomena that break this. But does it not seem reasonable for you to believe it's true to most economic situations at large for most people? At the very least it seem to work well for our models and really is required to get utility functions that are even remotely usable. Without it, it'd be pretty much entirely impossible to do any economic modeling. And at the very least, we can probably assume it's true in quantities of money. All other things being equal (that's important here), surely 99.9% of the population would prefer more to less consistently. Therefore, in utility over strictly monetary values, we have transitivity.
While you're right in that we need transitivity to really talk about utility functions (particularly for them to be continuous and monotone), after that it's use really goes away. Transitive preferences certainly don't imply DMU. A counter example would be a utility function where say U($10) = 100, U($20) = 400, U($100) = 10000, i.e U(x) = x^2. That's transitive and has strictly increasing marginal utility. It's just that economists don't generally believe that's how people work. You don't seem to agree with that though - why? Would you really value $100 the same if you were broke on the street vs a billionaire? On one hand it keeps you alive, on the other hand you might be spending more than that for your drinks.
Regardless of your personal assumptions, I'm going to go ahead and say I'm not sure you understand utility theory that well. Or we disagree on what you think utility theory is, in which case you're going to need to explain it for me (or really any traditionally trained economist) to know what you're talking about.
> I do have trouble having economic discussions with people who think utility functions are transitive... "Who do you think gets more utility from a $100 bill, a millionaire or a homeless person?!" In their minds, DMU means the homeless person must get greater utility from that money, but that's a nonsensical application of utility theory.
... where are you getting this claim. I'm willing to talk about to what degree people have transitive preferences, but to say it's nonsensical is absurd. It's the standard economic model and use of utility theory. Do you have a source or an argument that goes deeper?
> The study isn't telling you that you should care about it.
Well then why do they want us to read it? I think you're looking at this wrong. They are trying to speak to an audience by telling them something that interests them. If not, it's just background blither on the internet, a supply of which is as nearly infinite phenomena as they get. We're the consumers, they're the producers. It's getting posted because people want economists and people interested in economics to discuss it. Why else?
And I'm not trying to make it a policy prescription, I'm just wanting to see data that would better inform me about the world. I really don't understand your criticisms with my comment. I'd get it if you find the absolute numbers more interesting, but I don't get how you can't see people thinking other measures might be more interesting. If that doesn't make sense then I don't know if I can help you.
How could you forget the granddaddy of Micro texts: Mas-Colell. This book is the standard in many first year grad courses, and it covers everything pretty well -- the game theory is a little obtuse, though. It won't help much with economic intuition, but for people like the OP who want to learn the mathematical models, it's encyclopedic and definitive.
Otherwise, you have some very good links.
Edit: Apologies, I just noticed that the OP only wanted online links. I'll still recommend Mas-Colell in the case that the OP wants a good Micro text.
This is a little bit clearer now. Your original question was:
> Does this path dependency violate any assumptions in the model?
which is still completely opaque to me. This entire notion you've come up with of some dynamic game in which you can take some paths but not others, and after you've taken some paths you can't go back and take other paths, while possibly interesting, is entirely unrelated to the environment in which the term Pareto efficiency is defined, and so cannot violate any assumptions.
Look, I don't know if you're an alternate account for /u/teryret or not.
If not, I apologize for being so snippity. Another commenter was making up a bunch of crap and it irritated me. You've got some sort of idea in your head about path dependence and what a computer scientist might call a greedy heuristic for traveling along paths. And that's fine, but it's unrelated to Pareto efficiency.
If you are an alternate account for /u/teryret, then read a textbook. You have a number of foundational misunderstandings on this topic and you're misleading a lot of people. The classic reference is Mas-Collel, Winston, Green.
>but is mathematically as sophisticated as it needs to be
You can find micro textbooks at basically every level of mathematical complexity. MWG is a comprehensive overview of microeconomic theory. I don't think you need any particularly arcane math to get through it, but i wouldn't call it a page-turner either.
Hi callum_cglp-
Economics, at its heart, is based on calculus. Linear algebra is important mostly for econometrics, although matrix calculus does come up a fair bit. Generally, MA programs are not as rigorous as PhD programs.
I'd suggest having a look at the first 6 chapters of Mas-Colell et al. "Microeconomic Theory" and seeing if you're comfortable with the level of rigor. It's the standard text for microeconomics at almost every PhD program:
http://www.amazon.com/Microeconomic-Theory-Andreu-Mas-Colell/dp/0195073401
Yes. Building the "bottom up theory of the economy" is the work of generations of theorists in economics.
You mention you have a math background. If you can do math at the level of a first course undergraduate course in real analysis then you can go directly to Microeconomic Theory by Mas-Collell, Whinston, and Green. This has been the standard grad text in North America for over 10 years and for very good reason. It is a masterpiece. Beyond the content, the references and suggestions for further reading are fantastic. While this book is not the last word on micro theory, it certainly the first.
There are also a number of important lessons for macro theorists in the text. Chapter 4 has important lessons for those who want to do any kind of aggregation, and chapters 15-20 build a general equilibrium model from first principles and point out all the holes that macro theorists paper over.
https://www.amazon.com/Microeconomic-Theory-Andreu-Mas-Colell/dp/0195073401
Only if you're no pussy
The classic grad micro text is this one. Chiang and Carter both have written good mathematical economics book which are someplace around upper undergrad lower grad. Mostly I think just drilling as many problems as you can find is the best strategy. Look at math calc books to find Lagrange multiplier stuff. Also don't forget that the math is only a part of it. Understanding the economics the models are trying to convey is the most important part.
Good question! I haven't seen much in the way of general literature review books. As I see it, you have a couple options:
http://www.amazon.com/Microeconomic-Theory-Andreu-Mas-Colell/dp/0195073401
Really, there is no one "Economics" but a series of overlapping subfields. At the vanguard, research is done within these fields, and so you should focus on the ones that interest you.