how the IT project price is constructed ?

First, let's consider development team hourly rates. Frontend/Backend Developer per hour price vary between 15-50USD, I personally know very good developers that work for 15USD/hour and average developers that just do their work and invoice 30USD/hour, unfortunately if You think that paying high will bring You good services is not always true. If You want to reduce the costs, finding a good developer that work 15USD/hour is not easy, if You don't have tech skills, You may need a good tech recruiter first to scrutinize the candidate together with You.

If You ever tried to hire a freelancer, You will know how difficult it is to find right person. Difficulty is in lack of organization and commitment. Many freelancers do freelancing as extra job, so they never dedicate a full time for You, because there is no big commitment and engagement, possibility to bring good end results is low. I always ask myself when starting working with new person, what is his/her motivation ?

I would recommend only freelancers that are highly motivated and have good organization of their work, this allow them to scale their services and be more productive.

Why do I pay 50USD/hour ? Good English and communication, understanding of Your business requirements, consultations and experience, solving problems.

Agency will not only charge for development, we need to consider quality assurance(testing), project management, business analysis, solution architect, devops. Are those positions more important than developers ? At the initial phase of the project yes, without good software specification and project preparations any budget can be exploited and project not delivered.

Even if freelancer is very good, there are limits, he must do all project activities, because of that on some of them he will spend less time, if time is a pressure he may spend not enough time on preparations resulting in, that not all business requirements being considered.

Last thing to mention is a team and collaboration, good agency will have teams that work very well together, this is an investment and give results after some time.

My personal advise is to spend a lot of time on software specification, You need to make sure that You have explained all business requirements, it is an agency responsibility to get this out from You, but more You help at this part better product You get latter, closer to Your expectations. Functional requirements and Your business problems are critical and must be understood by agency. What works best in my opinion, are old use case and swim-lane diagrams, one picture more than thousand words, very true. I like to draw diagrams to make sure that there is mutual agreement of what's need to be done.

IT project development is not a magic or black box for sure, spending time on software specification, having weekly calls with the team, maybe being part of development, all of that works for Your benefit.

At Techs we work with clients very closely, clients have access to code base, project management, communication is on daily basis. I must say that daily communication with clients and full transparency guarantee success, at least in our case. My attitude toward clearing out all puzzles maybe tiresome for any client as I ask a lot of question, there cannot be a single space left without explanation :)