In experimental fields, such as physics, chemistry, and engineering, every professor has their own lab/workshop, normally with several externally funded projects. A PhD student may work on currently funded projects.

However, it is the responsibility of the university or department to provide the cost of this PhD project. How and by whom is the budget of a PhD project set?

I mentioned experimental fields, because the costs of these PhD projects are normally much higher than tuition fees (consider that the student has no research fellowship).

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    What do you mean it is the department's responsibility to provide the cost of this PhD project? In general, that duty falls on the principal investigator, not the university. – aeismail Sep 19 '14 at 18:21
  • @aeismail You mean if a PI does not have external funding cannot supervise PhD students? University does not have research budget for academic projects? – user13854 Sep 19 '14 at 18:26
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    Universities typically have very limited research budgets for projects—far less than would be needed to cover the costs for all of the doctoral candidates. Typically in the US, a new professor will get funding for one student or postdoc for a few years at the outset, but is expected to raise her own funds thereafter. Even in Germany, where funding is more plentiful, faculty will only have enough "permanent slots" for two or three assistants (while groups typically are many times larger than that). – aeismail Sep 19 '14 at 18:29
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    And yes, if faculty members don't have the funding to take on new students, they normally are not allowed to. – aeismail Sep 19 '14 at 18:31
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    @aeismail: Yes, it is different in math. At least in the US and in pure math, the department is the main source of financial support for Ph.D. students. Of course, typically the project itself has no costs other than the student's and advisor's time (maybe some paper and chalk). – Nate Eldredge Oct 5 '14 at 15:36

In the US and UK, at least, PhD students in he sciences and engineering generally receive funding that covers both tuition and a modest stipend to for living expenses. The exact details of the funding (e.g., taxable or non-taxable, benefits, and whether funding is given for tuition or tuition is waived) vary widely. The funding can come from a number of sources.

The easiest to understand are external grants directly to a student. The grant has a budget and the student is expected to keep the research costs within the budget. Additional costs, potentially including space charges and other overhead type fees, need to either be covered by the student or negotiated directly with the supervisor/department/university.

Grants (both internal and external, and start up funds) to the advisor generally cover a project bigger than a single student. It is the advisor's responsibility to make sure each sub project is appropriately budgeted for and negotiate with the department/university for additional money. While some students will be given an "official" budget by the supervisor, most are required to have the supervisor sign off on all expenses. Budget issues often come up during the design stages of a project.

Departments and universities also fund PhD students. This type of funding is sometimes in the form of Research Assistantships, but more often is for Teaching Assistantships where the student needs to teach in order to get the funding. Research costs can be, but are not always, covered by this type of internal funding. It is left to the student to either cover the research costs themselves or negotiate with supervisor/department/university to make sure the costs are covered.

My experimental research is relatively cheap, but I think in the vast majority of fields, the big cost is staff. Apart from possibly the most expensive types of experimental research, a supervisor with reasonable funding, will likely be able to find the money to cover experimental costs for a PhD student. It might require some limits to be placed on the project (e.g., including some modeling or theoretical work to reduce the costs).

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Typically, a PhD is not a job and thus a candidate does not have to have wage. Thus, it is not anyone's responsibility to provide any costs.

Professors, in different grades (but capable to be supervisors to PhDs), accept PhD candidates and conduct with them (as supervisors) novel research in various scientific disciplines. From this research, the candidate proves that he/she is able to hold the title of PhD and this whole process leads to the PhD tite (if the candidate succeeds).

Funding is side effect/project/what_ever. There are various opportunities for the state, country, companies to actually buy/fund novel research results and by this process there is a useful feedback from the scientific domain to the professional one which, in many cases, drives the production of new products and services.

So, if a Professor has a vacant position for a candidate and if the field of the research is close related or exactly at the field of a fund opportunity and if the Professor cares to apply for funding and if the application is approved then money can come for this research.

If the money finally come, then there is a usual division of labor with an appropriate "wage". These may (and is most likely that they do) vary between countries, universities, continents.

Thus, if someone needs to conduct experiments which need some money to spent then either the institution provide them, or he/she provide them, or the Professor has already a funding going on and cares to actually "hire" a PhD candidate to conduct the novel research based on the experiments.

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    "Typically, a PhD is not a job and thus a candidate does not have to have wage. Thus, it is not anyone's responsibility to provide any costs." A lot of western European countries disagree with that. – Moriarty Oct 5 '14 at 11:17
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    It would be helpful to state the field and country from which your experience comes. As @Moriarty says, your answer is not applicable to all fields and all countries. – Nate Eldredge Oct 5 '14 at 15:38
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    @Kostas It depends on the country and the degree. Why are you being rude to Nate? As you say, the European model does not guarantee funding/a job. In the US, however, most of the science/computer fields guarantee funding for all PhD students as long as they are in good standing. Our students get their tuition covered, and receive a stipend each month. In the humanities, on the other hand, there may not be such guarantees. Nate's point is reasonable and accurate: it varies by country and field. Arguing about it without knowing those is pointless. – Blair MacIntyre Mar 8 '15 at 3:15
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    @Kostas This most definitely does not apply to the Netherlands. And it's also highly misleading for France, Germany, Switzerland and probably all your other other examples. It's true that in many cases you can technically be hired for some related project/teaching. But as you conceded already, in many places/disciplines, you just cannot do a PhD if there are no funds and no position for you. In this context, it makes no sense to write that “It is not anyone's responsibility to provide any costs”… – Relaxed Mar 8 '15 at 4:04
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    Incidentally, I don't think that it's what the question is about at all. It's not PhD candidates wages, it's about the costs of running (expensive) experiments, which you only briefly allude to in one sentence at the end without providing any concrete info. – Relaxed Mar 8 '15 at 4:07

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