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.
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.
You can construct most of micro from
a. People have complete, transitive preferences over bundles of goods and services.
b. People choose the most preferred bundle in the choice set.
a. Firms have technologies to convert inputs to outputs.
b. Firms choose the input-output bundle that minimizes cost or maximizes profit.
a. In the simplest case, this is the anonymous, price-taking market.
b. But it could be more complicated, as in a game theory model.
c. Usually this goes under the heading of an "equilibrium concept."
For rigorously deriving the standard models from first principals, Mas-Colell, Whinston and Green is the authority for micro, and Stokey, Lucas and Prescott is the authority for macro. (I personally prefer the early chapters of Jehle and Reny to Mas-Colell, though.)
Be warned: even for someone that knows graduate level math, these are challenging, especially Stokey. On the spectrum from "accessible" to "rigorous," these are all the way on the "rigorous" end.
https://www.amazon.com/Microeconomic-Theory-Andreu-Mas-Colell/dp/0195073401
Only if you're no pussy
I agree with that recommendation. Mankiw is great.
While we are on the subject of economics, I would like to bring attention to the fact that micro and macro economics are two entirely different beasts.
With microeconomics, you can study your problem, apply the math, and get results which actually work. Any kind of useful microeconomics is going to be math-heavy. Microeconomics can be considered a science. My favourite parts of it are consumer theory and producer theory. Consumer theory which concerns itself with how people can efficiently use their resources to maximise the satisfaction they get out of life. Industrial organisation is also a really interesting field. The basics of game theory and a few economic principles are all you need to get started.
I do wish more economists would study modal logic. My field of study makes me distrustful of economists, especially when they start talking about beliefs and expectations, and a little bit of modal logic here and there would do a lot to calm my nerves.
Here are a few of the books I've used as a student.
Speaking of Greg Mankiw, here are his recommendations on what kind of maths to study: http://gregmankiw.blogspot.in/2006/05/which-math-courses.html
Then we come to marcoeconomics, which is a different ball game altogether. It isn't really meant to be treated as a science. Anyone who does so is bound to make a fool of themselves. Treat it more like history. Macroeconomics focus is as much on telling you what policies you should enact as history's is on telling you what to do to have a glowing future. An economist can tell you as much about the future of the economy as a historian can tell you about the future of the world. Economics is simply not about that.
Here are two macroeconomic textbooks I enjoyed:
There are handful standard theories of labor market value that are relevant to this conversation
1) Negotiating power, outside options, and surplus. The classic example is 100 farms that each need only one worker. If there are 99 workers, the workers have all the power, and can negotiate all the surplus value from the farm so they will be well paid because they can hold the farmers 'hostage' in the negotiations. This is the debate between wage takers vs wage setters.
2) Marginal revenue product of labor - workers earn in real terms the marginal value of their production. Effectively, the amount of revenue earned from the marginal worker.
3) Contract theory and incentives - Management is paid to optimize effort and appropriate risk taking. Because of the unique way managers operate, incentives are developed to encourage desired behavior. They still are assumed to not be worth more than the marginal revenue product of their labor, but as that is less clear than for other workers, there are incentive structures to align their pay along with profits, finding generally show management should and is paid in accordance with what is believed to be their marginal contribution to profits.
We add on top of these theories of search, learning, risk and expectations, stickiness, and such but the two above are the key drivers of wage. CEO pay is more complicated because they're generally not seen as interchangeable marginal producers of value like most labor - they are different
As the fortune 500's profits are on average only 7% of sales, I thought I was playing the part safe just keeping the discussion to profits but for what it's worth, CEO salaries are 0.04% of revenue on average in the fortune 500. Surely it's reasonable that CEOs marginal product of labor is at least .04% of total revenue and incentive alignment can expect them to be compensated up to 1% of profits? Do you really disagree with that?
As for other labor, that becomes harder. There really isn't much theory tying their pay in to profit. Is the first, negotiating wage market a reasonable way to look at it? I don't really think so, especially in dynamic economies firms and labor is so constantly adjusting that bargaining power has to be at best temporary. If that was the case, immigration and other increases in the labor supply would probably be met with greater evidence of bringing down wages. We'd also not see as much movement between jobs as we do as it depends on a much more static wage formulation. I think firms learn over time what marginal value workers bring, there is probably bargaining power problems in the lowest wage occupations, but the average worker spends time searching for a good fit - somewhere where their marginal value is best.
I got most of the numbers from this article and quick googling skills. The economic concepts come from grad school but can be found in detail in this grad school bibl and in this undegrad text.