Getting residence permit for my boyfriend in Sweden

There are a lot of other things to be considered too apart from money factor. But anyways there is a high degree of probability,  he'll be denied visa based on the economics you have presented.

Moreover the lead time to such visa cases is typically 18 months. Not sure you being Danish makes it more complicated or not.

How much should we be earning so that they would allow him to stay? I feel like that’s a lot of money and that it is enough...

I don’t think that the Denmark thing is going to complicate it more since I am a EU residence I can stay in every EU country for how long I want to stay.

I know EU citizens can live anywhere in EU what I mean there could be additional checks in the process. But I don't know that part for sure, I'm no expert in that area.

Alright. But how much do you think we should earn monthly if that amount is not enough?

From what I understand,  the migration dont consider the income or finance of the person applying for the permit, they only consider the income of the person he is coming to live with in Sweden.
I think it is highly possible he will be denied unless you have a permanent job that pays the required amount

@Gentleking: Financials of the EU partner are a consideration in case of partner visa. She doesn't seem to be in sound financial standing, at least not seems to be meeting the minimum wage criteria either way. Plus she have liabilities as student and cannot work full time.

Ohh wow...so I need a full-time job? So he basically can't come here until I am finished with my studies?...

Not really, he can still come.
There would be several other things to consider too.  But just from financial standing you presented, doesn't look like a  good case for two people.
Maybe it could be good if he finds a job first.

But you just told me that they wouldn't look at his income? He has his own business though so he has a job. But should he apply for a work permit then?

You are getting me wrong.

Since you are his potential partner, you should be in sound financial standing to support him. Financials do matter, insufficient financial situation can hint about potential issues such exploitation etc. (Speaking in general terms). I know in person two people who did not have a consistent jobs were unable to get visa for their potential partners untill they got a long term contract. Before deciding on the case the migration agency will try to evaluate the case from different perspectives including if there is a serious relationship or not?

Anyways he can still come but maybe not on a partner visa, maybe as an employee of a company with job offer. Does he have skills to make it? Does he have enough financials to start his self employment? These are the questions that could be considered. Or he could come in as a student too. Just throwing in some ideas.