Ramesh is correct with regards to how the Upwork user interface works.
But to further address Ellen's question...
Technically, when a client creates a job post, there is no "maximum amount I am willing to pay" field.
I'm not sure such a field is necessary.
The truth of the matter is that MOST clients:
"want something done"
Most clients are not:
"looking to pay a certain amount."
Clients want value.
So if a client hires me to do a project thinking that it will cost $1000...
It is common for the client to spend $5000 or more.
Because the client found great value in the work. And wanted to take things further. Paying $5000 when one thought she was going to pay $1000 can be a great value.
Let me see if I can explain. When I applied for these past two jobs, I requested $13/hr (to give me $10.40/hr) even though Upworks recommended me requesting $24-30 (due to expertise). But when the Client responded back, this is when they inform me of what they are willing to pay. One of them was only $9/hour even though their posting listed it as and Intermediate ($$) job. Same with this other job that I went ahead and took due to needing $$. He responds back $7/hr (giving me less than min wage). I finally got him up to $10/hr, But I think this amount should be in the original posting, because I would not have applied for it if I had known. These both should have been posted as Entry ($) level jobs.
There was also more involved in both of the jobs than what they listed as well.
Now does that make sense?
Up work is a playground where adults play. Both you and buyers are free to negitiate whatever. In my case whenever I see a $50 fixed price job that wants a moon I put in my hourly rate and tell them that it is my hourly rate. Most times I lose, but some times I win.
I don't have conclusive data, but it seems to me that I ruin cheapskate buyer's posting (becasue my bid gets advertized at a much lower rate then the posting. Most freelancer's have learned that majority of buyers are cheapos. They wouldn't want to waste their connects by under bidding me).