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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 :)

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.

https://www.amazon.com/Naked-Economics-Undressing-Dismal-Science/dp/0393356493/ref=dp_ob_title_bk

Chicago uses it alongside the Mankiw text in the intro micro/macro classes. Great readable intro to the economics concepts get defined more rigorously in the textbooks. You can just pick it up and read it casually, like you would Freakonomics, but its goal is to teach intro concepts rather than give "neat" examples of economics at play.

I 100% agree that suggesting textbooks to people who ask questions like this is just completely out of touch. Half of the kids in an intro econ class don't even read most of the textbook...they learn from the lectures/supplementary readings and only review the textbook enough to finish the homework assignments.

Maybe /u/grok_it is one of the few people who wants to actually crack a textbook in their free time, but most people would be better served by something like Naked Economics.

There are lots of good "popular press" books. Why Nations Fail is boring and deeply flawed, but is ultimately a must-read. Deaton's Great Escape is fine. For a micro approach you can't do any better than the magnificent Banerjee and Duflo.

You might enjoy leafing through some growth textbooks as well. I'd recommend Jones and Vollrath. Vollrath also has an (infrequently updated) blog that I like.

My pleasure! Again, this is just my experience and I only have a masters in econ, not a PhD, so someone researching in the field could probably be more insightful.

If you're getting ready for a master's, your immediate best friend is something like this guy. This is the textbook we used in my program.

Before my masters, I focused almost exclusively on real analysis and as a result, found myself over prepared in the math that I wasn't tested on and underprepared in the math I was tested on. This book (and books like it) will make you much more prepared for the stuff you'll be tested on than the advanced math used in modern microeconomic research. Pay special attention to the chapters on optimization.

If you're well versed in Lagrange multipliers, KKT conditions, and optimization using matricies, you're probably all set.

Edit: I should add, this book is neither very advanced nor very rigorous, but I would have had an easier time in my masters program if I prepared with a book like that instead of the more rigorous stuff I was focusing on.

Freakonomics (and sequel) are entertaining, but they don't actually explain economics--they try to use economics to explain other things. In doing so, they explain a few economic concepts, but that was never their goal.

If you want some enjoyable reading that actually aims to teach econ, I highly recommend naked economics. It is well written, easy to understand, and a number of elite undergrad econ classes use it as a companion to a "real" textbook (like Mankiw) because it does a really good job building intuition. Covers micro and macro, and I might not have majored in econ had I not read it in my intro class.

You can get older editions super cheap on amazon...I can't say what the differences are, but they probably all cover the basics. What you'd miss out on by using an older edition is probably refined explanation of the financial crisis (which might be worth the extra few bucks).

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.

You've stumbled onto a whole subfield of economics: Development Economics.

Here is a list of all NBER papers tagged with development.

This is a good resource regarding the EITC (check the citations).

If you are looking for "lay person friendly" books, I'd recommend:

• Gregory Clark- A Farewell to Alms (more of an economic history but essential context in my view)
  
  
• Acemoglu & Robinson- Why Nations Fail (This is a book that attempts to answer the age old "why are the poor poor" question and possible ways out)
  
  
• Angus Deaton- The Great Escape (Deaton recently won the economics Nobel)
  
  
• William Easterly- The White Man's Burden (A pretty scathing view of the West's efforts to help poor countries).
  
  This is a really wide field in economics.

In general, Peterson is not reliable. He tends to cherry pick, selectively omit, or outright distort, the 'facts' he cites. For the case of the Pareto Principle, which is often stated as "20% of the population will own 80% of the wealth", this is only true for certain parameters of the Pareto distribution. In reality, human societies are diverse; some societies have a high concentration of wealth and income, while other societies have much lower concentrations. As you correctly surmised, much has to do with the institutions that exist in the society. As Acemoglu and Robinson argue, when the elite control the government, they set up institutions that enriches the elite while dispossessing the majority of the people. A strong government that strives to restrain the exploitative tendencies of the elites will enable the majority of the people to reap the economic benefits of their work and will lead to faster economic growth and a more equal society.

If I can offer up a possible partial explanation from a non-economist with a strong interest in demography, I think a lot of the "hollowness" people feel today comes from mistaken beliefs about how well-off the typical person of 1950something was compared to the typical person of today.

A surprisingly easy way to start getting a handle on this is to look at old mail-order catalogs in one tab and using the BLS Inflation Calculator in another tab to convert historical prices to 2019 dollars. I tend to focus on electronics, specifically television sets and audio equipment. So, like, the cheapest television set available through Sears in 1957, a 21" black and white TV, sold for the equivalent of $1,539.35 in 2019 dollars. I bought a 60" 4k TV for less than half that price two years ago, so.

Also, people tend to think that strong-union manufacturing jobs were typical back then, ignoring the vast swaths of the population who lived in anti-union states, who toiled in the fields, who tried to scratch out a subsistence living in the pre-Great Society-reforms era, and who were locked out of "good" jobs because of their race. (I've tried asking around about exactly what percentage of the population held relatively-well-paying manufacturing jobs, but I've never gotten an answer.)

EDIT with data! I'm having a manic episode, so I couldn't stop digging. I found a handy breakdown of 1957 incomes, in 1957 dollars. The 1957 median income in 1957 dollars was $4,175; adjusted to 2017 dollars for comparison purposes, the 1957 median personal income was $35,492. Flashing forward, the 2016 median personal income in 2017 dollars was $31,099. So there was a pretty big decline in the median personal income between 1957 and 2016. But the median earner in 1957 could buy 21 cheap TVs, while the median earner in 2016 could buy 236 cheap TVs--an order of magnitude more. So I guess ultimately it comes down to the unsatisfying conclusion that there isn't even really a good way to compare the lifestyle of today to the lifestyle of yesteryear because there are just so many moving parts. (I'm not even addressing the increasing number of earners per household because I'm lazy like that.)

A PhD program with professors who study MD teaching a MD course while funding your life in order to give you free time to study MD is probably the best resource available.

Maybe this book? https://www.amazon.com/Game-Theory-Introduction-Steven-Tadelis/dp/0691129088?ref_=Oct_BSellerC_13922_6&pf_rd_p=69cae946-7b1e-5471-ad6b-68cb8cd88dee&pf_rd_s=merchandised-search-6&pf_rd_t=101&pf_rd_i=13922&pf_rd_m=ATVPDKIKX0DER&pf_rd_r=MSFW9P1T62G0KQXBDGPK&pf_rd_r=MSFW9P1T62G0KQXBDGPK&pf_rd_p=69cae946-7b1e-5471-ad6b-68cb8cd88dee

If you're interested in all of that, you should start by reading up on mechanism design, which you can find in any good microeconomics or game theory textbook. I like Fudenberg and Tirole.

• Fudeberg and Tirole - Game Theory
  
  I mainly see Krishna's book used for auctions. Menezes and Monteiro is also good. There are also books by Paul Klemperer and Paul Milgrom which are less textbook like.
  
  
• Auction Theory - Vijay Krishna
  
  
• Menezes and Monteiro - An Introduction to Auction Theory
  
  For matching, the guide to the "classical" theory is Roth & Sotomayor, but it's getting pretty old. There's a new "Handbook of Market Design" but I haven't read it and can't vouch for it.
  
  
• Roth and Sotomayor - Two-Sided Matching
  
  For bargaining, you can't go wrong with Osbourne and Rubinstein.
  
  
• Osbourne and Rubinstein - Bargaining and Markets
  
  Sadly, I don't know of a good voting textbook. Much of the recent work in voting has moved out of economics into computer science, political science, etc., so I would look there for current work on voting.

I'd recommend a growth textbook, like Weil's Economic Growth or Jones and Vollrath's Introduction to Economic Growth.

If you want something different than recessions, you could look at growth theory and / or development economics. Acemoglu and Robinson have a good pop book on the institutional view.

I would not recommend that book, though I've never really heard of it, to be honest.

In my high school economics class we used the following (https://www.amazon.com/Principles-Economics-7th-Mankiws/dp/128516587X/ref=sr_1_1?ie=UTF8&qid=1485981589&sr=8-1&keywords=mankiw+economics). The good thing is, you'll possibly use that book in your intro economics class in college, too, so you get a head start.

There are plenty of books named "Money, Banking and Financial Markets" and pretty much they teach the same. I used Pearson version by Mishkin and it was well explained and demonstrated with lots of real-life examples
https://www.amazon.com/Economics-Money-Banking-Financial-Markets/dp/0134733827/ref=sr_1_4?crid=2ARPQ35QRKU2&keywords=money%2C+banking+and+financial+markets&qid=1565963646&s=books&sprefix=money%2C+banking+and%2Cstripbooks%2C127&sr=1-4

I'm a PhD student at the moment, this is a great book.

It's big, but I've never before read anything that explained as well as that book does, where the different schools came from, why, who was involved, etc.

Mishkin's textbook is probably the best place to start. It will give you an overview and a foundation.

If you want a solid foundation I would start with something like This starting at chapter 29.

I recommend this book https://www.amazon.co.uk/Principles-Microeconomics-Robert-H-Frank/dp/007110657X
Is the one that I use in my microeconomics class. First semester

I would recommend Acemoglu and Robinson's book Why Nations Fail on this topic. Expands on the other answers already given.

For that I recommend Mishkin's Money Banking and Financial markets 100x over a general intro econ textbook. Its understandable by a layman, imo. You can get a fairly recent edition here used hardcover for under $20

Here is the table of contents from an older edition to give you an idea of the type of stuff covered in the book

If I were you I would read the last part of the book (the last few chapters which covers general macroeconomics) before reading the rest, but its up to you

MWG is the bible of microeconomics, but it's almost entirely unreadable. If you want a step up from Mankiw I'd start with Blanchard's Macroeconomics and Varian's Intermediate Microeconomics. These are the books I use when I teach intermediate macro/micro. The math is straight-forward (nothing beyond calculus), but you're going to be swimming in MWG or Stockey and Lucas unless you have the fundamentals down first.

Math econ isn't a sub-field of, it's a set of mathematical tools used in econ. You can't specialize in math econ in grad school.

Chiang and Wainright and Simon and Blume are what you want to at least cover the basics. Although most if not all of it will be review which is the intention.

Dixit, Skeath and Reiley is the standard undergrad text. And Fundeberg and Tirole is the standard graduate level book. Gibbons is somewhere in between the two.

When I was in grad school, the book we all read to get a intuitive understanding of the various schools of thought was Snowdon and Vane's Modern Macroeconomics: Its Origins, Development, and Current State. That was a while ago, though, so it may not be the most current resource.

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.

Modern Macroeconomics by Snowdon and Vane

Sorry I know there's a PDF somewhere online but I couldn't find it.

My health econ professor for undergrad made us use folland's health econ book. I'm not sure how good it is though compared to other textbooks.