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It should fine. The quant score is what counts for the most, and as long as your scores in the other two sections are decent (better than 50th percentile) it should not matter much.

I sent you a PM.

I am not as familiar with mechanism design and who is doing what at the moment. For microstructure no lower ranked school has a large group. Even at the top schools most only have 3-4 microstructure people. But a few lower ranked schools come to mind. Rutgers Business School has a couple microstructure people with a couple more doing work in information or financial econometrics that overlaps with microstructure and the university has a few other people split up between the OR, econ, stat and math departments that do some work in microstructure. Baruch - Zicklin has a few people in the finance department and I think one or two more in the Stats and IS department. UIUC - Gies has Mao Ye who has started making a name for himself in microstructure, plus a couple junior faculty. I think Copenhagen Business School in Denmark has a few people. Emory U - Goizueta has Clifton Green, and possibly a couple other people who do it as a secondary area. There is Ingrid Werner at Ohio State University but I don't think any one else there. USC Marshall has Larry Harris, but I don't know of anyone else, though David Hirshleifer just moved there and he has done work in almost every part of finance. ASU - Carey has Hendrik Bessembinder and couple others. WUSTL - Olin has a few people who do it as a secondary area, but off the top of my head I don't think anyone does it as a primary area. University of Houston used to have a few people but I am not sure if they still do. If you want to add a few more top departments, there are a number of people at U Toronto - Rotman and a couple at UCLA - Anderson. Columbia actually has two top people in the Finance department, Larry Glosten and Charles Jones. CMU - Tepper also has a few people. Wharton probably has the most well rounded finance department out there and has people doing everything. Duke has some people doing econometric theory work that has applications in microstructure, but I think they are actually in the econ department (Tim Bollerslev, a couple others). The Bendheim Center at Princeton has a couple of people, but they don't have their own PhD program. Instead you get accepted into either Econ or ORFE and then get into Bendheim Center. Honestly, your grades are all over the place, and that may keep you out of the top programs, even if you do explain it in your SOP.

From what I see (I am a finance PhD student with a secondary interest in empirical microstructure) not much is being done anywhere right now on the theory side of market design in financial market microstructure. A lot is being done right now on the empirical side of that, and a lot of theory work is being done on information and transaction cost topics in microstructure. But the specific stuff you mention does not seem to be very active at the moment (unless there is stuff being done on the OR side that I am not familiar with). Therefore it might be better for to just look at programs that are strong in mechanism design, or programs that are strong in microstructure in general though this will be more in finance departments than OR departments.

You should be applying to more B-school PhD programs and fewer Econ PhD programs. As tutonic said, for econ Phd programs LOR's outside of economics (and maybe finance) are not worth much. And almost every top person in financial market microstructure is in a B-school finance department, and a lot of mechanism design stuff is also being done by B-school faculty outside econ departments. B-school departments are also a little more flexible about who writes your LOR's so long as they are from people who work in relevant fields and are well published, though obviously the closer the business field you are applying to is to the LOR writers' field, the better it is. Since your LOR's are from OR people, besides for B-school finance and econ departments you should also look at B-school departments such as OR, MS, Managerial Econ and Decision Sciences. Obviously you should look at the faculty at each program at each school to see what fits you best at each school. Your LOR writers are connected to Columbia IEOR which is strongly connected to Columbia Business School, especially the DRO department, and you should look at that. You will need to improve your GRE score. And I think you should add on some lower ranked programs whether for Econ or Business, unless you would rather do a masters degree and apply again in a couple of years should you not get into a top 15 this year. Most B-school programs only take 1-4 students each year (maybe 4-8 for a few top tier finance programs) so the number of slots is extremely limited.

Switching to Berkely, Penn, Columbia or NWU would likely improve your profile (assuming you maintain grades, get good LOR's etc) and Cornell probably would too, but Georgetown almost definitely will not. And don't think too much about things like econ club or econ honors society. I don't know of many PhD students who bothered with any of that and it does nothing for your application. Research assistantships matter a lot, but few students anywhere get a chance to do serious RA work before Junior year either way. UVA has a top 30 Econ department in its own right. You should have a solid shot at getting into a top 10 econ PhD program coming from UVA so long as your grades and LOR's are good and your chances will be even better if you take the PhD Micro and/or Metrics sequence and do well. Ask the professors in the department where recent undergrads going for PhDs have gotten into, but it would not suprise me if they get a couple students each year into top 10 PhD programs, and a couple more into Federal Reserve positions who then get into a top 10 PhD 2-3 years down the line. If you just started your Freshman year which is what it sounds like the costs of transferring are probably low, so if you want to transfer do it soon. But if you have extracurriculars at UVA that you enjoy and those might not be available elsewhere, it might be better for you to stay. While it is a good idea to get started on coursework, getting RAships, connections for LOR's etc as early as possible, the people I know who centered their entire undergrad years around getting into grad schools (of any type) tended to regret it in the long run. And again you are at a school that should be capable of getting students into top 10's.

A lot of departments are reluctant to take on students for a second PhD. I have heard of a few, but it is not common. You might find some econ postdoc positions that would be interested in you. Look around and see what you can find. I have come across a few people with STEM PhD's who did a second PhD in a business field at a B-school, but all were people whose first PhD was in a field with little to no overlap with business like Chemistry or Physics or Biology, never someone from CS/Math/Stat. However, it might be a good idea to look at postdocs in B-schools in departments that have overlap with your interests. B-school departments are generally a little more interdisciplinary than econ departments, and I have come across a few B-school postdocs with PhD's in other fields doing research in stuff that overlapped with relevant B-school fields. For example in your case you might find overlapping interests in Management/Strategy, Operations Management, Managerial Economics, Decision Sciences, MIS, etc. The AACSB started a program a few years back called "Post-Doctoral Bridge to Business" to allow people with PhD's in non business fields who want to do research in business related fields to move into business school jobs, but the only participating school (AFAIK) is U Florida and I suspect it is more oriented toward people who want to do empirical work. There are also at least two universities I know of that allow PhD students in almost any related non-business field to do a joint/dual PhD with a related business school field - CMU and Rutgers - and I have heard of a few more allowing this on a case by case basis. If you are at such a school, that might also be an option for you (again, this relates to the somewhat more interdisciplinary nature of business schools). Also, if you are interested in micro theory and getting a good academic job afterward, you will probably have to aim higher than 30-100. I can think of very few theorists in econ who did not graduate from top 30 programs. In fact I know of quite a few people who graduated from top 10 programs as theorists but have spent their entire careers doing empirical work. I still think you should take your school's micro theory course which may help getting an econ or business post doc, even if you don't go for a second PhD. And don't worry about a lack of formal math classes, since you are doing a CS Theory PhD and therefore obviously have a solid math background.

What is your academic background besides for the MBA? Any research experience? Who would be your letter writers? To be blunt if you are aiming to get into a serious research oriented finance PhD, the MBA will not help much beyond perhaps giving you some access to letter writers. The finance coursework for most MBA programs has almost no relation to the type of coursework in a finance PhD which is much closer to the type of coursework in an economics PhD. I don't know of too many people with MBA's who have gotten into US top 75 finance PhD programs in recent years and those who did either had the type of profile that would have enabled them to get into a PhD straight from undergrad anyway, or had undergrad degrees in math or engineering, or had also done masters degrees in something like quant finance or statistics or a PhD track economics masters. Minimum math for a decent research oriented finance PhD program to even give your application a look is multivariable calculus and linear algebra and you probably will also need to add a calc based probability class and a stats/econometrics class. And that is just to even have a chance. If you are willing to look a little farther down the rankings, you will probably find programs willing to look at someone with weaker formal math background though multivariable calculus and linear algebra will probably still be necessary. But these programs are typically less research oriented and tend to place their graduates at lower ranked business schools that concentrate on teaching. If you want to stay in Australia, I can't comment anything specific about the universities there.

It is still relatively early and you don't seem definitively set on the program that accepted you, so just wait a couple more weeks. Any DGS will understand why you want to wait a little longer to make a fully informed decision. A lot of people dislike when someone gets into a significantly better program which they will definitely choose over the lower ranked program but still does not inform the lower ranked program that they are turning down the offer. That is not your situation here.

Booth used to have a rep for accepting a larger incoming cohort while having a low completion rate with a lot of students failing quals, but from what I have heard that is not much of an issue anymore. Overall Booth still has rep for being less caring than other top programs. I would consider the faculty at both to be roughly comparable. Wharton's finance faculty is slightly larger than Booth's but Booth has a few Nobel winners. If you look at the UTD rankings based on the top 3 finance journals, over the last 5 years Booth has slightly more top 3 publications, but Wharton has a slightly higher publication score (publications adjusted for the number of co-authors). Otherwise the two programs are roughly comparable and it comes down to personal preferences on location, funding, who you want to work with etc. There is no clear cut answer on which is better.

Finance PhD student, married, started the PhD with two kids under age 5 and had another one summer between first and second year. A couple other students in my program are married and had little kids either when they entered the program or during the program. In some ways it is tougher, with childcare being the biggest factor. If you are in the US, a number of states have childcare subsidy programs for parents who are working or are full time students, though you need family income below a certain level in order to qualify. In my case we were able to qualify for a small subsidy my first two years, and it was enough to keep us from having to go into debt (in my third year my wife received a promotion with a significant raise at her job). Some universities have discounted childcare available for graduate students. Email or call them to find out. No matter what, you will have less time available to study than single students without children. On the other hand, having family to emotionally support you is a big help - PhD students have some of highest levels of anxiety and depression and having a supportive significant other and having children to play with and distract you at times definitely helps. Whether to buy or rent depends on where you live. But many universities have some form of graduate student family housing for full time students who are married and/or have children, and this is usually cheaper than renting in the area especially after utilities are taken into account.

UCLA and UCSD are both top 20 programs. Which of the two is better depends on your subfields/interests since they have different strengths. I think UCSD has placed slightly better the last few years. The other 4 are all top 50 programs but definitely a step below UCLA/UCSD. Again, which is "best" depends on your subfields/interests. Too many people concentrate on a precise ranking like US News or their own subjective ranking, but you should be looking at things in context of tiers, top 10, top 20, top 50 etc. Within a given tier different schools tend to be roughly comparable in terms of educational quality and placement, but once you get outside the "top 10" schools are usually not able to maintain a large enough department to be strong in every subfield. In general, assuming you are funded at both choices, always pick a school in a higher tier unless it does not fit your interests at all (and if it does not fit your interests at all you probably should not have applied there). But if two programs are in the same tier and one program has a slightly higher rank than another according to some ranking like US News, but the slightly lower ranked one is a better fit for your interests and funding is similar, then go to the one that better fits your interests. I am not familiar with COL, crime etc for California so I can't help you with that.

We may finally be able to settle the GRE useful/not useful debate, though we will have to wait 6-7 years to see the job market results of this cohort.

I suspect a lot of the econ stuff on GC right now is EJMR trolls. In fact, I know that a number of graduate programs still do not know how many funded slots are available this year, and might not know until late February. We have a lot of data (both here and on GC) from past cycles on when various programs tend to send out their offers and while every so often a school changes their pattern, it is extremely unlikely that 5 top 15's are all simultaneously sending out offers extremely early.

I've been around here for a very long time and I can only think of a handful of applicants with profiles as strong as yours (assuming all your math and grad econ classes are A/A-) and all got multiple funded top 10 admits.