I am writing a small application, creating statistics for Twitter users (no tweets, friends, etc.). I am using this api
http://api.twitter.com/1/users/show.json?user_id=12345
I can only make 150 calls per hour, which is very small given the size of Twitter. How can companies that rely on the Twitter API overcome this limit?
150 API calls for each application. Large companies, probably the broker is engaged in Twitter.
You need to get a whitelist to get a higher speed limit. They are open to all kinds of developers if you give a good reason for what you are developing:
http://twitter.com/help/request_whitelisting
You will easily get a whitelist, just apply. They will accept a more or less reasonable application, but simply do not want to leave it "open". If they do not accept you, and you still want to receive the data, just clear them.