This is kind of a broad question and hard to answer.
For a low-end single page app(not Instagram) you are looking at a base starting price at $15,000 to $20,000.
This is for a team completely giving you a turn-key application.
There are a lot of factors that play into "having an app".
Performance, scalability, maintenance, support, etc.
An app like Instagram is content-driven and is pretty much automated. However, who is going to maintain issues and who is going to give support. Are you going to have a team in place?
Let's break it down in math. Looking at the bottom rate of $50 per hour in the US for web developers and engineers and designers. So say you have one app developer, web developer, and graphic designer.
That is roughly $8,000 per month for each person.This is not including the project manager, etc.
Each project that big takes a minimum of 6 months with a 3 person team who is highly skilled.
That is $24,000 per month which is $144,000 for the 6 month period.
To have a site built such as Instagram that is professional and scalable will cost a minimum of $200,000 just to get the MVP. This stuff is really expensive. I am a developer myself and can outsource projects on freelancer.com because I know how to manage a project and understand all aspects from concept to implementation. Although having something built remotely is slower.
Now, you can hire some amateur PHP developer who can give you all the features, but the performance will break when you have more than 500 simultaneous users on simple hosting. There is so much that goes into this and that is why professionals charge the big bucks.
When you have an app built, there is more than the app built. So you are paying for the app, web development(API, front-end, back-end), and database dev.
Then again, there is the other side of the table. The creator of "Yo" developed his app in 8 hours...
Having the original Yo app developed by a company would probably cost $10,000 from a local small app company in Denver, CO.